CN105488601A - Multi-target optimization method for solving complete Pareto frontier - Google Patents
Multi-target optimization method for solving complete Pareto frontier Download PDFInfo
- Publication number
- CN105488601A CN105488601A CN201610030464.6A CN201610030464A CN105488601A CN 105488601 A CN105488601 A CN 105488601A CN 201610030464 A CN201610030464 A CN 201610030464A CN 105488601 A CN105488601 A CN 105488601A
- Authority
- CN
- China
- Prior art keywords
- ripples
- node
- pareto
- forward position
- goal
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
Landscapes
- Business, Economics & Management (AREA)
- Human Resources & Organizations (AREA)
- Engineering & Computer Science (AREA)
- Strategic Management (AREA)
- Economics (AREA)
- Marketing (AREA)
- Game Theory and Decision Science (AREA)
- Entrepreneurship & Innovation (AREA)
- Development Economics (AREA)
- Operations Research (AREA)
- Quality & Reliability (AREA)
- Tourism & Hospitality (AREA)
- Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention provides a multi-target optimization method for solving a complete Pareto frontier. The multi-target optimization method belongs to the fields of computer algorithms and management optimization. The invention aims to solve the complete (not partial or approximate) Pareto frontier for a multi-target path optimization problem (or equivalent problems). The multi-target optimization method comprises the steps of simulating a ripple diffusion relay race which starts from an initial ripple of which the wave source is a given starting point; making the ripple diffuse in a link in a road network in a preset speed; when a ripple diffuses to a node at the other end of the link, if the path which is represented by the ripple is Pareto non-inferior compared with the paths represented by all ripples which have already generated on the node, exciting a new ripple of which the wave source is the node and making the new ripple diffuse; when one ripple has already arrived at all nodes which are connected with the wave source node, making the ripple be perished; and when all ripples in the relay race are perished, obtaining the complete Pareto frontier from the given starting point to the node through backtracking all ripples on one node.
Description
Technical field:
The invention provides a kind of Multipurpose Optimal Method solving complete Pareto forward position, belong to computerized algorithm and management optimization field.
Background technology:
Multi-objective optimization question (multi-objectiveoptimizationproblem, be called for short MOP) relate to the every aspect of life, relevant method for solving plays vital effect to the programmed decision-making problem solving each side such as politics, finance, military affairs, environment, the manufacturing, social security.Pareto optimum solution and Pareto forward position are the key concepts in MOP, and they originate from economics the research that distribution of earnings is optimized.Briefly, for a given solution, if there is no any one solution is all poor unlike it in each index, and at least good than it in an index, then this given solution is exactly a Pareto optimum solution.The projection of all Pareto optimum solutions in purpose-function space just constitutes complete Pareto forward position.The key solving MOP is just to find Pareto forward position.But existing most MOP method for solving all can only find part or approximate Pareto forward position.
The method of the existing MOP of solving can be divided into three major types substantially: reconstruct single-goal function method (aggregateobjectivefunction, be called for short AOF), constrained objective function method (constrainedobjectivefunction, be called for short COF), with Pareto standard grading method (Pareto-compliantranking is called for short PCR).AOF can be incorporated into all primal objective functions in MOP in a single reconstruct objective function, then carries out single object optimization for this reconstruct single-goal function, can obtain a Pareto optimum solution.But, there is subjectivity during definition reconstruct single-goal function, and the definition of a lot of reconstruct single-goal function just determines AOF theoretically can not find the Pareto optimum solution corresponding to concave surface on Pareto forward position.COF changes into a single objective with constraints problem MOP, is namely only optimized for a target of MOP, and other targets all as extra constraint condition.PCR is substantially the various evolution algorithms based on population, by the current noninferior solution in screening and Advanced group species, is exported by current Noninferior Solution Set after Evolution of Population terminates as approximate Pareto forward position.Although PCR does not have the problem (as subjectivity etc.) of AOF, the output of AOF is Pareto optimum solution certainly, and the output of PCR likely not comprises any Pareto optimum solution.
For some AOF based on nonlinear reconstruction single-goal function, to arbitrary given Pareto optimum solution, in theory always can prove existence one group of reconstruction parameter, make the output of AOF be the Pareto optimum solution that this is specified.But, but lack actual effective and feasible Theories and methods and ensure to find out the reconstruction parameter set corresponding can containing all Pareto optimum solutions.COF in theory, by optimization aim is changed into constraint condition, may solve complete Pareto forward position.But the same with the situation of AOF, COF lacks actual effective and feasible Theories and methods to determine required Transformation Parameters set, is thus difficult to guarantee that generated constraint condition can find complete Pareto forward position.Few in number about solving in the research report in complete Pareto forward position at present, be substantially all by the well-designed AOF reconstruction parameter set for specific type problem or the set of COF Transformation Parameters, thus all Pareto optimum solutions are all found out.Although PCR is method the most popular in MOP research, because its evolution algorithm relied on has random character, so PCR can not ensure to find complete Pareto forward position in theory at all.
Recently in document [1] and document [2], proposing one utilizes ripples broadcast algorithm to solve front k single goal optimum solution, and then solves the method in the complete Pareto forward position of MOP based on k single goal optimum solution before under each objective function again.It is emphasized that: the ripples broadcast algorithm itself in (1) document [1] and document [2] can not solve MOP, but only for single-object problem, that is, the ripples broadcast algorithm in document [1] and document [2] is single goal ripples broadcast algorithms; (2) in order to solve the complete Pareto forward position of MOP, need under each objective function, repeatedly run the single goal ripples broadcast algorithm in document [1] and document [2]; (3) in multiple goal routing problem, whenever solving given starting point to the complete Pareto forward position of another one network node, all need the method in isolated operation primary document [1] or document [2], in other words, suppose there is N in road network
nindividual node, one of them node is given starting point, if we need to solve given starting point to (N in addition
n-1) the complete Pareto forward position of each node in individual node, so we need to run (N altogether
n-1) method (in method is run each time, needing again to run several times single goal ripples broadcast algorithm) in secondary document [1] or document [2].So the method solving complete Pareto forward position in document [1] and document [2] is unusual poor efficiency.
The present invention will propose a kind of real multiple goal ripples broadcast algorithm, and it solves effect and is: only need to run once method of the present invention, just can solve from given starting point to all (N in addition
n-1) the complete Pareto forward position of each node in individual node.
[1]X.B.Hu，M.Wang，andE.DiPaolo，“CalculatingCompleteandExactParetoFrontforMulti-ObjectiveOptimization：ANewDeterministicApproachforDiscreteProblems”，IEEETransactionsonSystems，ManandCybernetics，PartB，Vol.43，No.3，pp：1088-1101，2013.
[2] Hu little Bing, " solving the multiple-objection optimization new method research in complete Pareto forward position ", research project (item number: 61472041), in January, 2015 on state natural sciences fund face.
Summary of the invention:
The object of the invention is to provide a kind of Multipurpose Optimal Method solving complete Pareto forward position.For multiple goal routing problem, suppose there is N in road network
nindividual node, method of the present invention has and solves effect as follows: only need to run once method of the present invention, just can solve from given starting point to all (N in addition
n-1) the complete Pareto forward position of each node in individual node.
Suppose to have a network system (can be real physical network system, as: network of highways also can be abstract Virtual Networking System, as decision tree), comprise N
nindividual node.Link between node can be represented by an adjacency matrix A, and elements A (i, j)=1 wherein represents to there is a link between node i and node j; A (i, j)=0 item represents not link between node i and node j.Suppose to there is a link between node i and node j, then this chain is connected to N
objindividual target weight value, can be designated as C respectively
k(i, j), k=1 ..., N
obj.Suppose that P represents a paths, path P comprises N
l>=2 nodes, P (i) represents i-th node of path P, 1≤i≤N
l, 1≤P (i)≤N
n.
For multiple goal one to routing problem (that is, from a given starting point to a given terminal), suppose that node S is given starting point, and node D is given terminal, so we need to solve following minimization problem:
Wherein
P(1)＝S，P(N
L)＝D，(2)
P(i)≠P(j)，ifi≠j，i＝1，...，N
L，andj＝1，...，N
L，(3)
A(P(i)，P(i+1))＝1，(4)
Ω
prepresent the set of all possible paths, f
ka kth single-goal function, k=1 ..., N
obj, f
kcan be any type of function meeting following condition:
If f
k(P
1)≤f
k(P
2), so f
k(P
1+ P)≤f
k(P
2+ P), (5)
If f
k(P
1) < f
k(P
2), so f
k(P
1+ P) < f
k(P
2+ P).(6)
For multiple goal one to multi-path optimization problem (that is, each other node from a given starting point to road network), on the mathematical description of problem, (N can be used as
n-1) individual independently multiple goal one to routing problem, the terminal in each one to one problem is the other (N beyond starting point
n-1) some in individual node.Obviously, one to one problem is a part or the special case arriving many problems.So, the method that arrives many problems can be solved, also must can solve one to one problem.
The present invention solves above-mentioned multiple goal one to multi-path optimization problem, realizes by following scheme.Method of the present invention simulates a ripples diffusion relay race in road network; Relay race starts from the initial ripples being wave source with given starting point; Ripples press the VELOCITY DIFFUSION preset along the link in road network; When ripples are diffused into the node of the other end of a link, if the path representated by these ripples is that Pareto is non-bad compared with the path representated by all ripples that this node has produced, then new ripples will be excited out for wave source with this node and spread; When ripples have reached all nodes be connected with its wave source node, these ripples are just withered away; When all ripples in relay race have all been withered away, then by all ripples on backtracking node, just can obtain the complete Pareto forward position from given starting point to this node.
For solving from given starting point to all (N in addition
n-1) the complete Pareto forward position of each node in individual node, the one-off optimization computation process of method of the present invention comprises following key step:
(step one) is if at N
objat least there is a summation single-goal function in individual single-goal function, that is, at least there is a f
kthere is following functional form
Then select a single-goal function of suing for peace in order to demarcate the path in ripples relay race, suppose kth
bMindividual single-goal function is selected; If at N
objnot sue for peace in individual single-goal function single-goal function, then artificially increase the summation single-goal function f that has functional form (7)
nObj+1, in order to demarcate the path in relay race, thus k is set
bM=N
obj+ 1, for the purpose of simple, can f be defined
nObj+1(P)=N
l-1, that is, (the N of every article of link
obj+ 1) individual target weight value all equals 1, that is, to any 1≤i≤N
nwith 1≤j≤N
nif A (i, j)=1, then define C
nObj+1(i, j)=1; Then a ripples rate of propagation v is preset.
The variable of the various state in order to record the ripples in ripples relay race of (step 2) initialization.
(step 3), with starting point S for wave source generates initial ripples (that is, first is enlivened ripples), arranging current ripples quantity is N
r=1, the wave source arranging first ripples is E (1)=S (that is, starting point is wave source), and the radius arranging first ripples is R (1)=0, and the state arranging first ripples is S
r(1)=1 (namely, active), arrange first ripples excite ripples be T (1)=0 (namely, first ripples be can't help any ripples and are excited, but spontaneous generation), each single-goal function value (i.e. 0 vector, because path is S → S corresponding to first ripples) in fitness vector path corresponding to it of first ripples is set; Setting the current emulation moment is t=0, to start ripples relay race.
(step 4): judge whether this terminates in ripples relay race? if without any enlivening ripples in ripples relay race, that is, to any one 1≤r≤N
r, have S
r(r)=0, namely ripples r is inactive, then arrive step (eight); Otherwise, to step (five).
(step 5): upgrade simulation time t=t+1; Radius is upgraded, that is, to any one 1≤r≤N by the ripples rate of propagation preset and chronomere's length to each ripples that enliven
rif, S
rr ()=1, then upgrade R (r)=R (r)+v.
(step 6): to any one node n, if having ripples to arrive in this chronomere's length current (may be 1 ripples or multiple ripples, must link between the wave source node of ripples and node n), that is, to node n, there is at least one 1≤r≤N
r, meet S
r(r)=1, A (E (r), n)=1, R (r)>=C
kBM(E (r), n), so, according to all single-goal functions, the ripples these newly arrived carry out Pareto odds comparatively each other, Pareto odds is carried out comparatively again with the existing ripples of node n, these are newly found out to the non-bad ripples of the Pareto in ripples (for this node), comparatively routine with the Pareto odds of two ripples i and j, calculate respectively or extract along the path corresponding to ripples i and each single-goal function value going to node n along the path corresponding to ripples j from node S, then each single-goal function value of ripples i and ripples j is compared by the definition of Pareto quality, thus determine the good and bad relation of Pareto between ripples i and ripples j, only have when one is newly all that Pareto is non-bad to ripples compared with other new existing ripples to ripples and node n all, this is newly non-bad concerning being only Pareto node n to ripples, then by each Pareto non-bad new to ripples excite in node n generation one new enliven ripples (that is, all ripples produced that newly excite enliven ripples), and the state of new ripples to be arranged accordingly, main as follows to arranging of the new ripples inspired by ripples i of in node n: current ripples quantity adds 1 (that is, N
r=N
r+ 1), be then new ripples N
rs is set
r(N
r)=1, E (N
r)=n, T (N
r)=i, R (N
r)=R (i)-C
kBM(E (i) n), and arranges new ripples N according to each single-goal function value going to node n along the path corresponding to ripples i from node S
rfitness vector (for Pareto odds from now on comparatively).
(step 7): enliven ripples to any one, if these ripples have reached other nodes all (not considering the node that corresponding to these ripples, path has comprised) having with its wave source node and link, that is, to any one r, 1≤r≤N
r, S
rr ()=1, if meet A to each, (E (r), the node n of n)=1 have R (r)>=C
kBM(E (r) n), so, arranges ripples r and becomes inactive, that is, arrange S
r(r)=0, ripples r has withered away in other words; Then get back to (step 4).
(step 8): to any one node (non-starting point), complete Pareto forward position from starting point to this node is determined by all ripples that this node produces, that is, the corresponding Pareto optimum solution of each ripples that produces of this node.If people is for adding a summation single-goal function f in (step one)
nObj+1, then from the (N determining this node
obj+ 1) tie up in Pareto forward position to filter out and do not consider this summation single-goal function f
nObj+1n
objdimension Pareto forward position is exactly the complete Pareto forward position from starting point to this node in primal problem.
Although above-mentioned (step one) to (step 8) is for solving multiple goal one to multi-path optimization problem (namely, each other node from a given starting point to road network), but based on (step one) to (step 8), without the need to any amendment, just can solve multiple goal one to routing problem (that is, from a given starting point to a given terminal).But, in order to avoid unnecessary calculating is to improve the efficiency of one to one problem that solves, slight modifications can be carried out to above-mentioned (step 4), (step 6) and (step 8), as follows:
(step 4 changes): judge whether this terminates in ripples relay race? if without any enlivening ripples in ripples relay race, or all ripples that enliven are not that Pareto is non-bad, that is, to any one 1≤r≤N compared with ripples existing on terminal D
r, have S
r(r)=0 (that is, ripples r is inactive), or, to arbitrary 1≤r≤N
r, S
rr ()=1, if the path corresponding to ripples r is not that Pareto is non-bad compared with the path corresponding to ripples existing on terminal D, then arrives step (eight); Otherwise, to step (five).
(step 6 changes): start all with (step 6), until: then bad newly in node n, excite the new ripples of generation one (may be enliven ripples to ripples by each Pareto is non-, also may be inactive ripples), other of new ripples arranges with (step 6), the active state of only new ripples needs following setting: if node n is not terminal (that is, n ≠ D), then arrange new ripples for enlivening ripples, that is, S
r(N
r)=1; Otherwise (that is, n=D), arranging new ripples is inactive ripples, that is, S
r(N
r)=0.In other words, the ripples that the node of non-terminal produces all are initialized as and enliven ripples, and the ripples that terminal D produces are all inactive ripples.
(step 8 changes): all ripples produced according to terminal D, determines the complete Pareto forward position from starting point S to terminal D, that is, the corresponding Pareto optimum solution of each ripples that produces of terminal D.If people is for adding a summation single-goal function f in (step one)
nObj+1, then from the (N determined
obj+ 1) tie up in Pareto forward position to filter out and do not consider this summation single-goal function f
nObj+1n
objdimension Pareto forward position is exactly the complete Pareto forward position from starting point S to terminal D in primal problem.
Need benly be, when describing method of the present invention, in order to more vivid and easy understand, we are likened into ripples diffusion relay race, but this metaphor not necessarily, core is the content of the calculation procedure corresponding to metaphor, these contents can be likened into other any appropriate things or process, or need not liken, but purely represent with abstract mathematical variable and term, such as, the radius of ripples r: R (r), we completely can " ripples " and " radius " these two vocabulary wordings, but say into abstractively: r element R (r) of vectorial R.
In like manner, each variable symbol itself used when describing method of the present invention not necessarily, core is the meaning of variable and the operation computation process to variable, such as, ripples radius is upgraded: R (r)=R (r)+v in (step 5), can rewrite with aleatory variable symbol, as: W (m)=W (m)+z, its effect is the same.
Method of the present invention can adopt various appropriate hardware computing device (such as: single-chip microcomputer, mobile phone, PC, mainframe computer, computer network in realization, etc.) and software programming technique (such as: the link of road network represents without adjacency matrix A, but adopt link vector table data structure; Centralized algorithm design thinking can be adopted, also can adopt the algorithm design thinking of dispersion parallel type; Various computer programming language and software systems can be adopted).
A kind of Multipurpose Optimal Method solving complete Pareto forward position of the present invention has following beneficial effect: for any problem that can be converted into multiple goal path optimization, and method of the present invention can solve complete (instead of part or approximate) Pareto forward position; For multiple goal one to multi-path optimization problem (that is, each other node from a given starting point to road network), suppose that road network has N
nindividual node, method of the present invention does not need to it can be used as (N
n-1) individual independently multiple goal one to routing problem (that is, from a given starting point to a given terminal) solves respectively, but by disposable calculating, just can solve from given starting point to all (N in addition
n-1) the complete Pareto forward position of each node in individual node.
Accompanying drawing illustrates:
Accompanying drawing provides a kind of schematic diagram solving the Multipurpose Optimal Method in complete Pareto forward position of the present invention:
Fig. 1: a kind of key step schematic diagram (for one to one problem) solving the Multipurpose Optimal Method in complete Pareto forward position.
Fig. 2: a kind of key step schematic diagram (for many problems) solving the Multipurpose Optimal Method in complete Pareto forward position.
Fig. 3: a kind of solution procedure schematic diagram solving the Multipurpose Optimal Method in complete Pareto forward position.
Fig. 4: a kind of solve the Multipurpose Optimal Method in complete Pareto forward position solve effect schematic diagram.
Embodiment:
Below in conjunction with accompanying drawing, the optimal way that a kind of Multipurpose Optimal Method solving complete Pareto forward position of the present invention adopts is described further.
Fig. 1 gives method of the present invention the key step included when solving multiple goal one to routing problem (that is, from a given starting point to a given terminal):
(step one) is if at N
objat least there is a summation single-goal function in individual single-goal function, that is, at least there is a f
kthere is functional form (7), then select a single-goal function of suing for peace in order to demarcate the path in ripples relay race, suppose kth
bMindividual single-goal function is selected; If at N
objnot sue for peace in individual single-goal function single-goal function, then artificially increase the summation single-goal function f that has functional form (7)
nObj+1, in order to demarcate the path in relay race, thus k is set
bM=N
obj+ 1, for the purpose of simple, can f be defined
nObj+1(P)=N
l-1, that is, (the N of every article of link
obj+ 1) individual target weight value all equals 1, that is, to any 1≤i≤N
nwith 1≤j≤N
nif A (i, j)=1, then define C
nObj+1(i, j)=1; Then a ripples rate of propagation v is preset.
The variable of the various state in order to record the ripples in ripples relay race of (step 2) initialization.
(step 3), with starting point S for wave source generates initial ripples (that is, first is enlivened ripples), arranging current ripples quantity is N
r=1, the wave source arranging first ripples is E (1)=S (that is, starting point is wave source), and the radius arranging first ripples is R (1)=0, and the state arranging first ripples is S
r(1)=1 (namely, active), arrange first ripples excite ripples be T (1)=0 (namely, first ripples be can't help any ripples and are excited, but spontaneous generation), each single-goal function value (i.e. 0 vector, because path is S → S corresponding to first ripples) in fitness vector path corresponding to it of first ripples is set; Setting the current emulation moment is t=0, to start ripples relay race.
(step 4): judge whether this terminates in ripples relay race? if without any enlivening ripples in ripples relay race, or all ripples that enliven are not that Pareto is non-bad, that is, to any one 1≤r≤N compared with ripples existing on terminal D
r, have S
r(r)=0 (that is, ripples r is inactive), or, to arbitrary 1≤r≤N
r, S
rr ()=1, if the path corresponding to ripples r is not that Pareto is non-bad compared with the path corresponding to ripples existing on terminal D, then arrives step (eight); Otherwise, to step (five).
(step 5): upgrade simulation time t=t+1; Radius is upgraded, that is, to any one 1≤r≤N by the ripples rate of propagation preset and chronomere's length to each ripples that enliven
rif, S
rr ()=1, then upgrade R (r)=R (r)+v.
(step 6): to any one node n, if having ripples to arrive in this chronomere's length current (may be 1 ripples or multiple ripples, must link between the wave source node of ripples and node n), that is, to node n, there is at least one 1≤r≤N
r, meet S
r(r)=1, A (E (r), n)=1, R (r)>=C
kBM(E (r), n), so, according to all single-goal functions, the ripples these newly arrived carry out Pareto odds comparatively each other, Pareto odds is carried out comparatively again with the existing ripples of node n, these are newly found out to the non-bad ripples of the Pareto in ripples (for this node), comparatively routine with the Pareto odds of two ripples i and j, calculate respectively or extract along the path corresponding to ripples i and each single-goal function value going to node n along the path corresponding to ripples j from node S, then each single-goal function value of ripples i and ripples j is compared by the definition of Pareto quality, thus determine the good and bad relation of Pareto between ripples i and ripples j, only have when one is newly all that Pareto is non-bad to ripples compared with other new existing ripples to ripples and node n all, this is newly non-bad concerning being only Pareto node n to ripples, then by the non-bad new ripples exciting generation one new in node n to ripples of each Pareto, and the state of new ripples is arranged accordingly, main as follows to arranging of the new ripples inspired by ripples i of in node n: current ripples quantity adds 1 (that is, N
r=N
r+ 1), be new ripples N
re (N is set
r)=n, T (N
r)=i, R (N
r)=R (i)-C
kBM(E (i) n), and arranges new ripples N according to each single-goal function value going to node n along the path corresponding to ripples i from node S
rfitness vector (for Pareto odds from now on comparatively), new ripples N
ractive state need following setting: if node n is not terminal (that is, n ≠ D), then new ripples N is set
rfor enlivening ripples, that is, S
r(N
r)=1, otherwise (that is, n=D), arranges new ripples N
rfor inactive ripples, that is, S
r(N
r)=0.In other words, the ripples that the node of non-terminal produces all are initialized as and enliven ripples, and the ripples that terminal D produces are all inactive ripples.
(step 7): enliven ripples to any one, if these ripples have reached other nodes all (not considering the node that corresponding to these ripples, path has comprised) having with its wave source node and link, that is, to any one r, 1≤r≤N
r, S
rr ()=1, if meet A to each, (E (r), the node n of n)=1 have R (r)>=C
kBM(E (r) n), so, arranges ripples r and becomes inactive, that is, arrange S
r(r)=0, ripples r has withered away in other words; Then get back to (step 4).
(step 8): all ripples produced according to terminal D, determines the complete Pareto forward position from starting point S to terminal D, that is, the corresponding Pareto optimum solution of each ripples that produces of terminal D.If people is for adding a summation single-goal function f in (step one)
nobj+1, then from the (N determined
obj+ 1) tie up in Pareto forward position to filter out and do not consider this summation single-goal function f
nObj+1n
objdimension Pareto forward position is exactly the complete Pareto forward position from starting point S to terminal D in primal problem.
Fig. 2 gives method of the present invention solving multiple goal one to key step included time multi-path optimization problem (that is, each other node from a given starting point to road network).Comparison diagram 1 and Fig. 2 can find out, solving multiple goal one to multi-path optimization problem and the basic step solving multiple goal one to routing problem is mostly that the same, trickle difference is only (step 4), (step 6) and (step 8).
In (step 4), for solving multiple goal one to routing problem, the termination condition of ripples relay race is: without any enlivening ripples in ripples relay race, or all ripples that enliven are not that Pareto is non-bad compared with ripples existing on terminal; And for solving multiple goal one to multi-path optimization problem, the termination condition of ripples relay race is: without any enlivening ripples (because the single terminal of not specifying in many problems in ripples relay race, namely, other nodes all beyond starting point are all terminals, so termination condition does not have relation with any single terminal).
In (step 6), for solving multiple goal one to routing problem, the new ripples that terminal produces are all inactive ripples (thus avoiding unnecessary calculated amount, to improve counting yield); And for solving multiple goal one to multi-path optimization problem, on any node excite the new ripples produced to be all enliven ripples (so just can guarantee to solve the complete Pareto forward position of each other node in from starting point to network).
In (step 8), for solving multiple goal one to routing problem, only need to recall all ripples that terminal produces, to determine the complete Pareto forward position from origin-to-destination; And for solving multiple goal one to multi-path optimization problem, then need to recall all ripples that the node of each non-starting point produces, thus determine the complete Pareto forward position of each other node in from starting point to network.
Fig. 3 gives an application method of the present invention and minimizes to a Bi-objective solution procedure example that one to one routing problem solves the complete Pareto forward position from node S to node D.Two target weight values (g1, g2) of each bar link are labeled in the road network of moment t=1.In the example in figure 3, certain single-goal function value of a paths is defined as the summation of this single goal weighted value of all-links on this path.Multiple goal ripples broadcast algorithm in method of the present invention is in given road network, carry out a ripples diffusion relay race.The initial ripples R1 that it is wave source that relay race starts from starting point S.Initial ripples R1 from the close-by examples to those far off spreads along 3 links of starting point S by the speed preset.
Initial ripples R1 is taken up in order of priority at moment t=2 and reaches node 2, node 1 and node 3.Because node 2, node 1 and node 3 did not now also produce any ripples, so initial ripples R1 is concerning these 3 nodes, all that Pareto is non-bad, thus initial ripples R1 excites the ripples R2 that makes new advances respectively on node 2, node 1 excites the ripples R3 that makes new advances, node 3 excites the ripples R4 that makes new advances.New ripples start diffusion along the peer link in road network separately.And initial ripples R1 is because reached and all nodes that its wave source node S-phase connects, so after moment t=2, initial ripples R1 just withers away (that is, becoming inactive).
At moment t=3, ripples R2 reaches terminal D.Now terminal D did not also produce any ripples, so ripples R2 is that Pareto is non-bad concerning terminal D.So by backtracking ripples R2, obtaining S → 2, path → D is a Pareto optimum solution, simultaneously ripples R2 terminal D inspire inactive ripples (for one to one multiple goal routing problem ripples broadcast algorithm in, terminal can only produce inactive ripples).Ripples R2 also reaches node 1 at moment t=3, but because ripples R2 (compared with state when being excited with R3) compared with ripples R3 existing on node 1 is not that Pareto is non-bad, so ripples R2 could not excite the ripples that make new advances on node 1.At moment t=3, ripples R3 reaches node 2, because ripples R3 is that Pareto is non-bad compared with ripples R2 existing on node 2, so ripples R3 inspires a new ripples R5 at node 2.
At moment t=4, ripples R4 reaches terminal D.Because the ripples of ripples R4 and the D that reaches home other same period (namely, ripples R3 and ripples R5) and terminal D on existing ripples to compare be that Pareto is non-bad, so by backtracking ripples R4, obtaining S → 3, path → D is a Pareto optimum solution, and ripples R4 inspires inactive ripples at terminal D simultaneously.At moment t=4, ripples R3 also reaches terminal D.But not that Pareto is non-bad because ripples R3 (is excited the inactive ripples of generation) compared with ripples existing on terminal D by R2, so the path corresponding to ripples R3 is not Pareto optimum solution.Although ripples R5 also reaches terminal D at moment t=4, compared with the inactive ripples excited at terminal D with ripples R4, ripples R5 is not that Pareto is non-bad, so the path corresponding to ripples R5 neither Pareto optimum solution.At moment t=4, ripples R4 also reaches node 2, because ripples R4 is that Pareto is non-bad, so ripples R4 excites the ripples R6 that makes new advances on node 2 compared with ripples existing on node 2.At moment t=4, ripples R2 reaches node 3, but because ripples R2 is not that Pareto is non-bad compared with ripples existing on node 3, so ripples R2 could not excite the ripples that make new advances on node 3.Now, because ripples R2 has reached all nodes (without the need to considering the node comprised in path corresponding to ripples R2, as starting point S) be connected with its wave source node 2, so after moment t=4, ripples R2 has just withered away.In like manner, ripples R3, R4 and R5 has withered away after moment t=4.
At moment t=5, ripples R6 reaches terminal D.Because ripples R6 is that Pareto is non-bad compared with ripples existing on terminal D, so by backtracking ripples R6, obtaining S → 3 → 2, path → D is a Pareto optimum solution, and ripples R6 inspires inactive ripples at terminal D simultaneously.Ripples R6 also reaches node 1 at moment t=5, because ripples R6 is that Pareto is non-bad, so ripples R6 excites the ripples R7 that makes new advances on node 1 compared with ripples existing on node 1.Now, because ripples R6 has reached all nodes be connected with its wave source node 2, so after moment t=5, ripples R6 has just withered away.
At moment t=6, ripples R7 reaches terminal D.Because ripples R7 is not that Pareto is non-bad compared with ripples existing on terminal D, so the path corresponding to ripples R7 is not Pareto optimum solution.Now, because ripples R7 has reached all nodes be connected with its wave source node 1, so after moment t=6, ripples R7 has just withered away.
So far, without any enlivening ripples in ripples relay race, terminate so optimize to calculate.Just by 3 inactive ripples that terminal D produces, (ripples R2, R4 and R6 respectively inspire one in complete Pareto forward position in Fig. 3 problem, respective path S → 2 → D, S → 3 → D, and S → 3 → 2 → D respectively) determine, that is, this complete Pareto forward position is made up of 3 points.
Fig. 4 gives the result of the contrast experiment of one group of method of the present invention and existing AOF side (that is, reconstructing single-goal function method) and PCR method (that is, Pareto standard grade method).The experiment of Fig. 4 solves a Bi-objective routing problem, two objective function, i.e. g1 and g2, all needs to be minimized.In Fig. 4, each pockmarks triangle represents a Pareto optimum solution found by AOF method, each white circle represents a current noninferior solution finally exported by PCR method, and each black squares represents a Pareto optimum solution found by method of the present invention, all black squares together constitute the complete Pareto forward position of Fig. 4 experiment.
As seen from Figure 4, in contrast experiment, AOF method have found 4 Pareto optimum solutions on the convex surface of Pareto forward position, but but could not find out the Pareto optimum solution on the concave surface of Pareto forward position.And that Pareto optimum solution on concave surface obviously represents optimal half-way house between two objective functions, be likely that decision maker wishes the effect reached most.The experimental result of Fig. 4 shows, although the result that AOF method obtains is all Pareto optimum solution, AOF method fully can not meet the demand (because AOF method only have found the Pareto forward position of part) of decision maker.
Be it can also be seen that by Fig. 4, in contrast experiment, 5 current noninferior solutions (also there are 5 Pareto optimum solutions in complete Pareto forward position) that PCR method finally outputs, and the shape of front that these 5 current noninferior solutions form is also very similar to the shape in complete Pareto forward position.But, in these 5 current noninferior solutions, have 3 to be not Pareto optimum solution.So obviously, PCR method also cannot provide optimal decision support for decision maker.
The complete Pareto forward position solved based on method of the present invention can provide decision support comprehensively and accurately for decision maker.
Claims (9)
1. one kind solves the Multipurpose Optimal Method in complete Pareto forward position, in order to solve as multiple goal routing problem solves the technical matters in complete (instead of part or to be similar to) Pareto forward position, it is characterized in that: the solution procedure of described method can be likened into simulation ripples diffusion relay race in road network visually and (liken not necessarily, just in order to more vivid and easy understand; In other words, core is the content of the computation process corresponding to metaphor, and these contents can be likened into other any appropriate things or process, or need not liken, but purely with abstract mathematical variable and term statement); Ripples relay race starts from the initial ripples being wave source with given starting point; Ripples press the VELOCITY DIFFUSION preset along the link in road network; When ripples are diffused into the node of the other end of a link, if the path representated by these ripples is that Pareto is non-bad compared with the path representated by all ripples that this node has produced, then new ripples will be excited out for wave source with this node and spread; When ripples have reached all nodes be connected with its wave source node, these ripples are just withered away; When all ripples in relay race have all been withered away, then by all ripples on backtracking node, just can obtain the complete Pareto forward position from given starting point to this node.
2. the Multipurpose Optimal Method solving complete Pareto forward position according to claim 1, it is characterized in that: for multiple goal one to routing problem (namely, from a given starting point to a given terminal), described method can solve the complete Pareto forward position from given starting point to given terminal.
Suppose to have a network system (can be real physical network system, as: network of highways also can be abstract Virtual Networking System, as decision tree), comprise N
nindividual node; Link between node can be represented by an adjacency matrix A, and elements A (i, j)=1 wherein represents to there is a link between node i and node j, and A (i, j)=O then represents not link between node i and node j; Suppose to there is a link between node i and node j, then this chain is connected to N
objindividual target weight value, can be designated as C respectively
k(i, j), k=1 ..., N
obj; Suppose that P represents a paths, path P comprises N
l>=2 nodes, P (i) represents i-th node of path P, 1≤i≤N
l, 1≤P (i)≤N
n; For multiple goal one to routing problem (that is, from a given starting point to a given terminal), suppose that node S is given starting point, and node D is given terminal, so needs to solve following minimization problem:
Wherein
P(1)＝S，P(N
L)＝D，
P(i)≠P(j)，ifi≠j，i＝1，...，N
L，andj＝1，...，N
L，
A(P(i)，P(i+1))＝1，
Ω
prepresent the set of all possible paths, f
ka kth single-goal function, k=1 ..., N
obj, f
kcan be any type of function meeting following condition:
If f
k(P
1)≤f
k(P
2), so f
k(P
1+ P)≤f
k(P
2+ P),
If f
k(P
1) < f
k(P
2), so f
k(P
1+ P) < f
k(P
2+ P).
For above-mentioned multiple goal one to routing problem, described method mainly comprises following step:
(step one) is if at N
objat least there is a summation single-goal function in individual single-goal function, that is, at least there is a f
kthere is following functional form
Then select a single-goal function of suing for peace in order to demarcate the path in ripples relay race, suppose kth
bMindividual single-goal function is selected; If at N
objnot sue for peace in individual single-goal function single-goal function, then artificially increase the summation single-goal function f that has above-mentioned functional form
nObj+1, in order to demarcate the path in relay race, thus k is set
bM=N
obj+ 1, for the purpose of simple, can f be defined
nObj+1(P)=N
l-1, that is, (the N of every article of link
obj+ 1) individual target weight value all equals 1, that is, to any 1≤i≤N
nwith 1≤j≤N
nif A (i, j)=1, then define C
nObj+1(i, j)=1; Then a ripples rate of propagation v is preset.
The variable of the various state in order to record the ripples in ripples relay race of (step 2) initialization.
(step 3), with starting point S for wave source generates initial ripples (that is, first is enlivened ripples), arranging current ripples quantity is N
r=1, the wave source arranging first ripples is E (1)=S (that is, starting point is wave source), and the radius arranging first ripples is R (1)=0, and the state arranging first ripples is S
r(1)=1 (namely, active), arrange first ripples excite ripples be T (1)=0 (namely, first ripples be can't help any ripples and are excited, but spontaneous generation), each single-goal function value (i.e. 0 vector, because path is S → S corresponding to first ripples) in fitness vector path corresponding to it of first ripples is set; Setting the current emulation moment is t=0, to start ripples relay race.
(step 4): judge whether this terminates in ripples relay race? if without any enlivening ripples in ripples relay race, or all ripples that enliven are not that Pareto is non-bad, that is, to any one 1≤r≤N compared with ripples existing on terminal D
r, have S
r(r)=0 (that is, ripples r is inactive), or, to arbitrary 1≤r≤N
r, S
rr ()=1, if the path corresponding to ripples r is not that Pareto is non-bad compared with the path corresponding to ripples existing on terminal D, then arrives step (eight); Otherwise, to step (five).
(step 5): upgrade simulation time t=t+1; Radius is upgraded, that is, to any one 1≤r≤N by the ripples rate of propagation preset and chronomere's length to each ripples that enliven
rif, S
rr ()=1, then upgrade R (r)=R (r)+v.
(step 6): to any one node n, if having ripples to arrive in this chronomere's length current (may be 1 ripples or multiple ripples, must link between the wave source node of ripples and node n), that is, to node n, there is at least one 1≤r≤N
r, meet S
r(r)=1, A (E (r), n)=1, R (r)>=C
kBM(E (r), n), so, according to all single-goal functions, the ripples these newly arrived carry out Pareto odds comparatively each other, Pareto odds is carried out comparatively again with the existing ripples of node n, these are newly found out to the non-bad ripples of the Pareto in ripples (for this node), comparatively routine with the Pareto odds of two ripples i and j, calculate respectively or extract along the path corresponding to ripples i and each single-goal function value going to node n along the path corresponding to ripples j from node S, then each single-goal function value of ripples i and ripples j is compared by the definition of Pareto quality, thus determine the good and bad relation of Pareto between ripples i and ripples j, only have when one is newly all that Pareto is non-bad to ripples compared with other new existing ripples to ripples and node n all, this is newly non-bad concerning being only Pareto node n to ripples, then by the non-bad new ripples exciting generation one new in node n to ripples of each Pareto, and the state of new ripples is arranged accordingly, main as follows to arranging of the new ripples inspired by ripples i of in node n: current ripples quantity adds 1 (that is, N
r=N
r+ 1), be new ripples N
re (N is set
r)=n, T (N
r)=i, R (N
r)=R (i)-C
kBM(E (i) n), and arranges new ripples N according to each single-goal function value going to node n along the path corresponding to ripples i from node S
rfitness vector (for Pareto odds from now on comparatively), new ripples N
ractive state need following setting: if node n is not terminal (that is, n ≠ D), then new ripples N is set
rfor enlivening ripples, that is, S
r(N
r)=1, otherwise (that is, n=D), arranges new ripples N
rfor inactive ripples, that is, S
r(N
r)=0.In other words, the ripples that the node of non-terminal produces all are initialized as and enliven ripples, and the ripples that terminal D produces are all inactive ripples.
(step 7): enliven ripples to any one, if these ripples have reached other nodes all (not considering the node that corresponding to these ripples, path has comprised) having with its wave source node and link, that is, to any one r, 1≤r≤N
r, S
rr ()=1, if meet A to each, (E (r), the node n of n)=1 have R (r)>=C
kBM(E (r) n), so, arranges ripples r and becomes inactive, that is, arrange S
r(r)=0, ripples r has withered away in other words; Then get back to (step 4).
(step 8): all ripples produced according to terminal D, determines the complete Pareto forward position from starting point S to terminal D, that is, the corresponding Pareto optimum solution of each ripples that produces of terminal D.If people is for adding a summation single-goal function f in (step one)
nObj+1, then from the (N determined
obj+ 1) tie up in Pareto forward position to filter out and do not consider this summation single-goal function f
nObj+1n
objdimension Pareto forward position is exactly the complete Pareto forward position from starting point S to terminal D in primal problem.
3. the Multipurpose Optimal Method solving complete Pareto forward position according to claim 1, it is characterized in that: for multiple goal one to multi-path optimization problem (namely, each other node from a given starting point to road network), described method only needs to run once, just can solve the complete Pareto forward position of other each nodes all from given starting point to road network.
Suppose that network system comprises N
nindividual node, then multiple goal one is to multi-path optimization problem on mathematical description, can be used as (N
n-1) individual independently multiple goal one to routing problem, the terminal in each one to one problem is the other (N beyond starting point
n-1) some in individual node.When solving multiple goal one to multi-path optimization problem, described method does not need to solve separately each one to one problem, but by following key step, carries out disposable calculating:
(step one) is if at N
objat least there is a summation single-goal function in individual single-goal function, that is, at least there is a f
kthere is following functional form
Then select a single-goal function of suing for peace in order to demarcate the path in ripples relay race, suppose kth
bMindividual single-goal function is selected; If at N
objnot sue for peace in individual single-goal function single-goal function, then artificially increase the summation single-goal function f that has above-mentioned functional form
nObj+1, in order to demarcate the path in relay race, thus k is set
bM=N
obj+ 1, for the purpose of simple, can f be defined
nObj+1(P)=N
l-1, that is, (the N of every article of link
obj+ 1) individual target weight value all equals 1, that is, to any 1≤i≤N
nwith 1≤j≤N
nif A (i, j)=1, then define C
nObj+1(i, j)=1; Then a ripples rate of propagation v is preset.
The variable of the various state in order to record the ripples in ripples relay race of (step 2) initialization.
(step 3), with starting point S for wave source generates initial ripples (that is, first is enlivened ripples), arranging current ripples quantity is N
r=1, the wave source arranging first ripples is E (1)=S (that is, starting point is wave source), and the radius arranging first ripples is R (1)=0, and the state arranging first ripples is S
r(1)=1 (namely, active), arrange first ripples excite ripples be T (1)=0 (namely, first ripples be can't help any ripples and are excited, but spontaneous generation), each single-goal function value (i.e. 0 vector, because path is S → S corresponding to first ripples) in fitness vector path corresponding to it of first ripples is set; Setting the current emulation moment is t=0, to start ripples relay race.
(step 4): judge whether this terminates in ripples relay race? if without any enlivening ripples in ripples relay race, that is, to any one 1≤r≤N
r, have S
rr ()=0 (that is, ripples r is inactive), then arrive step (eight); Otherwise, to step (five).
(step 5): upgrade simulation time t=t+1; Radius is upgraded, that is, to any one 1≤r≤N by the ripples rate of propagation preset and chronomere's length to each ripples that enliven
rif, S
rr ()=1, then upgrade R (r)=R (r)+v.
(step 6): to any one node n, if having ripples to arrive in this chronomere's length current (may be 1 ripples or multiple ripples, must link between the wave source node of ripples and node n), that is, to node n, there is at least one 1≤r≤N
r, meet S
r(r)=1, A (E (r), n)=1, R (r)>=C
kBM(E (r), n), so, according to all single-goal functions, the ripples these newly arrived carry out Pareto odds comparatively each other, Pareto odds is carried out comparatively again with the existing ripples of node n, these are newly found out to the non-bad ripples of the Pareto in ripples (for this node), comparatively routine with the Pareto odds of two ripples i and j, calculate respectively or extract along the path corresponding to ripples i and each single-goal function value going to node n along the path corresponding to ripples j from node S, then each single-goal function value of ripples i and ripples j is compared by the definition of Pareto quality, thus determine the good and bad relation of Pareto between ripples i and ripples j, only have when one is newly all that Pareto is non-bad to ripples compared with other new existing ripples to ripples and node n all, this is newly non-bad concerning being only Pareto node n to ripples, then by each Pareto non-bad new to ripples excite in node n generation one new enliven ripples (that is, all ripples produced that newly excite enliven ripples), and the state of new ripples to be arranged accordingly, main as follows to arranging of the new ripples inspired by ripples i of in node n: current ripples quantity adds 1 (that is, N
r=N
r+ 1), be then new ripples N
rs is set
r(N
r)=1, E (N
r)=n, T (N
r)=i, R (N
r)=R (i)-C
kMB(E (i) n), and arranges new ripples N according to each single-goal function value going to node n along the path corresponding to ripples i from node S
rfitness vector (for Pareto odds from now on comparatively).
(step 7): enliven ripples to any one, if these ripples have reached other nodes all (not considering the node that corresponding to these ripples, path has comprised) having with its wave source node and link, that is, to any one r, 1≤r≤N
r, S
rr ()=1, if meet A to each, (E (r), the node n of n)=1 have R (r)>=C
kBM(E (r) n), so, arranges ripples r and becomes inactive, that is, arrange S
r(r)=0, ripples r has withered away in other words; Then get back to (step 4).
(step 8): to any one node (non-starting point), complete Pareto forward position from starting point to this node is determined by all ripples that this node produces, that is, the corresponding Pareto optimum solution of each ripples that produces of this node.If people is for adding a summation single-goal function f in (step one)
nObj+1, then from the (N determining this node
obj+ 1) tie up in Pareto forward position to filter out and do not consider this summation single-goal function f
nObj+1n
objdimension Pareto forward position is exactly the complete Pareto forward position from starting point to this node in primal problem.
4. according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 2, it is characterized in that: described method can adopt various appropriate formulation form (such as, link in network can represent without adjacency matrix A, but adopts the data structure of link vector table; Each variable symbol used itself not necessarily, core is the meaning of variable and the operation computation process to variable, such as, ripples radius is upgraded in (step 5), namely, R (r)=R (r)+v, can rewrite with aleatory variable symbol, as, W (m)=W (m)+z, even do not use " ripples " and " radius " these vocabulary wordings, but say into abstractively: r element R (r) of vectorial R increases v, and its effect is the same).
5. according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 3, it is characterized in that: described method can adopt various appropriate formulation form.
6. according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 2, it is characterized in that: described method can be applied to the various problem (such as: multiple goal Combinatorial Optimization and multiobjectives decision problem of management) that can be converted into multiple goal path optimization.
7., according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 3, it is characterized in that: described method can be applied to the various problem that can be converted into multiple goal path optimization.
8. according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 2, it is characterized in that: described method can adopt various appropriate hardware computing device and software programming technique to realize.
9. according to claim 1 and the Multipurpose Optimal Method solving complete Pareto forward position according to claim 3, it is characterized in that: described method can adopt various appropriate hardware computing device and software programming technique to realize.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610030464.6A CN105488601A (en) | 2016-01-19 | 2016-01-19 | Multi-target optimization method for solving complete Pareto frontier |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610030464.6A CN105488601A (en) | 2016-01-19 | 2016-01-19 | Multi-target optimization method for solving complete Pareto frontier |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN105488601A true CN105488601A (en) | 2016-04-13 |
Family
ID=55675570
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610030464.6A Pending CN105488601A (en) | 2016-01-19 | 2016-01-19 | Multi-target optimization method for solving complete Pareto frontier |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105488601A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105956357A (en) * | 2016-04-15 | 2016-09-21 | 北京师范大学 | Method for evaluating anti-interference capability of network system |
| CN108549222A (en) * | 2018-04-08 | 2018-09-18 | 黄淮学院 | A kind of device and method solving mathematical programming problem |
| CN110119839A (en) * | 2019-04-24 | 2019-08-13 | 华南理工大学 | A kind of Urban Road Traffic Accidents emergency management and rescue paths planning method |
| CN117852732A (en) * | 2023-12-06 | 2024-04-09 | 珠海市规划设计研究院 | Multi-target point path searching method, system and medium for ripple thinking from outside to inside |
-
2016
- 2016-01-19 CN CN201610030464.6A patent/CN105488601A/en active Pending
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105956357A (en) * | 2016-04-15 | 2016-09-21 | 北京师范大学 | Method for evaluating anti-interference capability of network system |
| CN105956357B (en) * | 2016-04-15 | 2018-07-17 | 北京师范大学 | A method of assessment network system anti-interference ability |
| CN108549222A (en) * | 2018-04-08 | 2018-09-18 | 黄淮学院 | A kind of device and method solving mathematical programming problem |
| CN110119839A (en) * | 2019-04-24 | 2019-08-13 | 华南理工大学 | A kind of Urban Road Traffic Accidents emergency management and rescue paths planning method |
| CN110119839B (en) * | 2019-04-24 | 2021-05-14 | 华南理工大学 | Urban road traffic accident emergency rescue path planning method |
| CN117852732A (en) * | 2023-12-06 | 2024-04-09 | 珠海市规划设计研究院 | Multi-target point path searching method, system and medium for ripple thinking from outside to inside |
| CN117852732B (en) * | 2023-12-06 | 2024-06-25 | 珠海市规划设计研究院 | Multi-target point path searching method, system and medium for ripple thinking from outside to inside |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Fang et al. | A hybrid of real coded genetic algorithm and artificial fish swarm algorithm for short-term optimal hydrothermal scheduling | |
| Truong et al. | Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem | |
| CN105488601A (en) | Multi-target optimization method for solving complete Pareto frontier | |
| Zheng et al. | Improving the efficiency of multi-objective evolutionary algorithms through decomposition: An application to water distribution network design | |
| CN112491096B (en) | Method and system for generating power grid simulation analysis calculation case | |
| Biazzo et al. | Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs | |
| CN110111010A (en) | A kind of question-answering task distribution method and system based on many intelligence networks | |
| Amigoni et al. | Modeling the management of water resources systems using multi-objective DCOPs | |
| Djedović et al. | Optimization of business processes by automatic reallocation of resources using the genetic algorithm | |
| CN104392317A (en) | Project scheduling method based on genetic culture gene algorithm | |
| Liu et al. | Uniformly bound-growing network models and their spanning trees | |
| CN112115380A (en) | Influence node identification method based on generation countermeasure model | |
| Iguider et al. | Heuristic algorithms for multi-criteria hardware/software partitioning in embedded systems codesign | |
| CN103336876A (en) | Open loop distribution network power flow simulation method based on multi-agents | |
| Ye et al. | Optimizing weight and threshold of BP neural network using SFLA: applications to nonlinear function fitting | |
| Gonçalves et al. | Improved cultural immune systems to solve the economic load dispatch problems | |
| Ntaimo et al. | Expression of a forest cell model in parallel DEVS and Timed Cell-DEVS formalisms | |
| Avila-Melgar et al. | Parallel evolutionary algorithm for Water Distribution Network Design, using the Masters–Students model in distributed environment | |
| Hou et al. | Research on dynamic assignment of satellite communication tasks based on GA algorithm | |
| Das et al. | Optimal scheduling of hydrothermal system considering variable nature of water transportation delay | |
| Zhang et al. | Differential human learning optimization algorithm | |
| Hu et al. | Consensus of a new multi-agent system via multi-task, multi-control mechanism and multi-consensus strategy | |
| Xia et al. | A multi-objective routing scheme for deterministic network | |
| Jun-chun et al. | Optimal network hardening model based on parallel genetic algorithm | |
| Zhao et al. | A MSM-PGA based on Multi-Agent and its application in reactive power optimization of power systems |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| CB02 | Change of applicant information |
Address after: 100088 room 6, unit 7, 8 hospital, new street, Xicheng District, Beijing, 7 Applicant after: Beijing Normal University Applicant after: Liao Jianqin Address before: 100875 room 702, 10 building, Beijing Normal University, 19 new street, Haidian District, Beijing. Applicant before: Beijing Normal University Applicant before: Liao Jianqin |
|
| CB02 | Change of applicant information | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20160413 |
|
| WD01 | Invention patent application deemed withdrawn after publication |