CN103020307A - Non-dominated solution sorting method based on depth search and high-frequency mutation strategy - Google Patents
Non-dominated solution sorting method based on depth search and high-frequency mutation strategy Download PDFInfo
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- CN103020307A CN103020307A CN 201310000853 CN201310000853A CN103020307A CN 103020307 A CN103020307 A CN 103020307A CN 201310000853 CN201310000853 CN 201310000853 CN 201310000853 A CN201310000853 A CN 201310000853A CN 103020307 A CN103020307 A CN 103020307A
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Abstract
The invention provides a non-dominated solution sorting method based on a depth search and high-frequency mutation strategy. The method comprises the following steps: processing constrains in a multi-objective optimization problem by using a sorting method; operating the obtained non-dominated solutions, obtaining more excellent individuals by using excellent individual information, and performing deep searching optimization in a better excellent direction; and performing clone mutation operation on existing non-dominated individuals so as to obtain non-dominated individuals nearby. According to the invention, in the multi-objective optimization problem, accuracy of a non-dominated solution group is improved, and the continuity of the non-dominated solution group is increased to find all the non-dominated solutions as much as possible, so as to enable decision-makers to have more decision space.
Description
Technical field
What the present invention relates to is a kind of Multiobjective Intelligent optimization method, specifically a kind of method that obtains non-domination solution under the Complex Constraints condition.
Background technology
Optimization problem is the hot issue in engineering practice and the scientific research.Wherein, only have the optimization problem of an objective function to be called as single-object problem, objective function is above one and need simultaneously treated optimization problem be called as multi-objective optimization question.Multi-objective optimization question originates from design, modeling and the planning problem of actual complex system, related field comprises industry manufacturing, city transportation, capital budget, energy distribution, city layout etc., all has multi-objective optimization question in engineering practice and real-life decision process.Originally, multi-objective optimization question often is converted into the single goal problem by modes such as weightings, then finds the solution with the method for mathematical programming, can only obtain the optimum solution in a kind of weights situation at every turn.Yet for most of multi-objective optimization question, often have this situation: namely a solution is optimum for certain target, is relatively poor for other targets.Therefore, the set that exists a compromise to separate is called as non-domination disaggregation.Simultaneously, because objective function and the constraint function of multi-objective optimization question may be non-linear, non-differentiability or discontinuous, traditional mathematic programming methods often efficient is lower, and they are responsive for the given order of weighted value or target.
For breaking through the limitation of weighted value algorithm, Goldberg from the angle of non-domination solution, has proposed the non-dominated sorting algorithm take genetic algorithm as the basis, and is used for finding the solution non-domination disaggregation.But from practical application effect, there are two major defects in this algorithm: 1) resulting non-domination solution out of true; 2) resulting non-domination solution is disperseed, and discontinuous, the non-domination solution that namely obtains is not comprehensive.
Summary of the invention
The object of the present invention is to provide a kind ofly when processing the multi-objective problem of Complex Constraints, can search out the non-dominated sorting method based on deep search and high frequency Mutation Strategy of more excellent more fully non-domination solution.
The object of the present invention is achieved like this:
(1) produces at random initial population, satisfy first non-domination solution of constraint condition in the storing initial population;
(2) according to constraint condition, the individuality that satisfies constraint condition is divided into a class, the individuality that does not satisfy constraint condition is divided into another kind of;
(3) to satisfying the individuality of constraint condition, determine non-domination solution, make it share same adaptive value A
1, and from remaining individuality, determine the non-domination solution of second batch, and distribute corresponding adaptive value, continue this process, until satisfying the constraint condition individuality, all are assigned with adaptive value;
(4) formation sequence: to not satisfying the individuality of constraint condition, the number according to not satisfying constraint condition sorts from less to more, and satisfies the identical individuality of number, comes in the same sequence;
(5) according to the individual adaptive value that is assigned with, adopt the roulette criterion to choose the parent individuality and hybridize, of future generation individual to produce; In the offspring individual that produces, randomly draw the individual variation that participates in;
(6) calculate offspring individual target function value and constraint function value, obtain satisfying in the offspring individual first non-domination solution of constraint condition, and upgrade the non-domination disaggregation of storing;
(7) calculate institute's non-domination solution of store and concentrate distance between each non-domination solution, two the individual hybridization farthest of order distance produce newly individuality; If new individuality satisfies constraint condition, and more outstanding than parent individuality, then point to the optimizing of the filial generation direction degree of depth along parent, keep more excellent individuality, and upgrade non-domination disaggregation;
(8) will have the individual clone of non-domination solution now, all individualities behind the variation clone, calculate individual goal functional value and constraint functional value behind the clonal vaviation, and obtain satisfying in the clonal vaviation individuality first non-domination solution of constraint condition by sort method, and upgrade the non-domination solution group who is stored with this;
(9) individual weight multiple bank order of future generation, hybridization, variation and clonal vaviation process are until reach when specifying algebraically iter the non-domination solution group that output is stored.
The present invention can also comprise:
1, described adaptive value is calculated as follows,
A
n＝A
1-(n-1)*δA
In the formula: A
nBe the adaptive value that n criticizes non-domination solution, δ A is the adaptive value difference between arithmetic number, adjacent batch of non-domination solution of representative.
2, in the described formation sequence, the First ray individual fitness is by formula B
1=A
1-N* δ A calculates, and other sequence individual fitness is by formula B
m=B
1-(m-1) * δ A calculates,
In the formula: B
1Be the First ray individual fitness, N is total batch of number of non-domination Xie in (3) step, B
mBe m batch of individual fitness.
3, the distance between described each non-domination solution is by formula
Calculate,
In the formula: dis is the distance between two non-domination solutions, x
i, y
iRepresent respectively two non-domination solution optimized variables, p is the optimized variable number.
Technological improvement mainly is among the present invention:
(1) adopt the method that sorts, process the constraint in the multi-objective optimization question, processing for constraint provides a kind of new effective ways.
(2) resulting non-domination solution is operated, utilize excellent individual information to go to obtain more excellent individual, and along the optimizing of the more excellent direction degree of depth, thereby arithmetic accuracy improved;
(3) individual to existing non-domination, carry out the clonal vaviation operation, it is individual to obtain according to this near its non-domination, thereby makes resulting non-domination solution more comprehensive; Simultaneously, the high frequency Mutation Strategy has also improved the precision of algorithm.
Technical scheme among the present invention and technological improvement have following outstanding beneficial effect:
(1) in multi-objective optimization question, improves non-domination solution group's precision;
(2) in multi-objective optimization question, improve non-domination solution group's continuity, find as much as possible all non-domination solutions, so that the decision maker has more decision space.
Description of drawings
Fig. 1 is the process flow diagram based on the non-dominated sorting method of deep search and high frequency Mutation Strategy;
Fig. 2 is the contrast of the present invention and Goldberg institute algorithm.
Embodiment
Below in conjunction with Fig. 1 the present invention is done more specifically description:
(1) produces at random initial population, satisfy first non-domination solution of constraint condition in the storing initial population;
(2) according to constraint condition, the individuality that satisfies constraint condition is divided into a class, the individuality that does not satisfy constraint condition is divided into another kind of;
(3) to satisfying the individuality of constraint condition, determine non-domination solution, make it share same adaptive value A
1, and from remaining individuality, determine the non-domination solution of second batch, distribute corresponding adaptive value, continue this process, be assigned with adaptive value until all satisfy the constraint condition individuality, in this step, the adaptive value computing method as shown in the formula;
A
n＝A
1-(n-1)*δA
In the formula: A
nBe the adaptive value that n criticizes non-domination solution, δ A is arithmetic number, represents the adjacent batch of adaptive value difference between non-domination solution.
(4) to not satisfying the individuality of constraint condition, the number according to not satisfying constraint condition sorts from less to more, and satisfies the identical individuality of number, comes in the same sequence; First ray ideal adaptation value calculating method is suc as formula B
1=A
1-N* δ A, other sequence ideal adaptation value calculating method is suc as formula B
m=B
1-(m-1) * δ A;
In the formula: B
1Be the First ray individual fitness, N is total batch of number of non-domination Xie in (3) step, B
mBe m batch of individual fitness.
(5) according to the individual adaptive value that is assigned with, adopt the roulette criterion to choose the parent individuality and hybridize, of future generation individual to produce; In the offspring individual that produces, randomly draw the individual variation that participates in;
(6) calculate offspring individual target function value and constraint function value, obtain satisfying in the offspring individual first non-domination solution of constraint condition, and upgrade the non-domination disaggregation of being stored with this;
(7) according to formula
Calculate institute's non-domination solution of store and concentrate, two the individual hybridization farthest of the distance between each non-domination solution, order distance produce newly individuality; If new individuality satisfies constraint condition, and more outstanding than parent individuality, then point to the optimizing of the filial generation direction degree of depth along parent, keep more excellent individuality, and upgrade non-domination disaggregation;
In the formula: dis is the distance between two non-domination solutions; x
i, y
iRepresent respectively two non-domination solution optimized variables; P is the optimized variable number.
(8) will have the individual clone of non-domination solution now, all individualities behind the variation clone, calculate individual goal functional value and constraint functional value behind the clonal vaviation, and obtain satisfying in the clonal vaviation individuality first non-domination solution of constraint condition by sort method, and upgrade the non-domination solution group who is stored with this;
(9) individual weight multiple bank order of future generation, hybridization, variation and clonal vaviation process are until reach when specifying algebraically iter the non-domination solution group that output is stored.
Fig. 2 is for the Bi-objective function:
min f
1＝-25(x
1-2)
2-(x
2-2)
2-(x
3-1)
2-(x
4-4)
2-(x
5-1)
2 (1)
min f
2＝(x
1-1)
2+(x
2-1)
2+(x
3-1)
2+(x
4-1)
2+(x
5-1)
2 (2)
In constraint condition:
g
1＝x
1+x
2-2≥0 (3)
g
2＝6-x
1-x
2≥0 (4)
g
3＝2+x
1-x
2≥0 (5)
g
4＝2-x
1+3x
2≥0 (6)
g
5＝4-(x
3-3)
2-x
4≥0 (7)
g
6＝(x
5-3)
2+x
6-4≥0 (8)
10≥x
i≥0，i＝1,2,3,4,5,6 (9)
Lower, the contrast of the present invention and Goldberg institute algorithm.
To realize the functional value f of function (1) in the accompanying drawing 2
1And the functional value f of function (2)
2Minimum is target, and satisfy in formula (3)-(9) be constrained to the example the invention will be further described:
(1) setting the population number is 800, and the condition of convergence is that the evolution number of times reaches 400 times, and is initial population optimized variable assignment at random.Calculate each individual goal functional value in the population according to function (1) and (2); Calculate each individual constraint function value according to constraint condition (3)-(9).Satisfy first non-domination solution of constraint condition in the storing initial population;
The individuality that (2) will satisfy constraint condition is divided into class A, and the individuality that does not satisfy constraint condition is divided into class B;
(3) individual for category-A, determine non-domination solution, make it share same adaptive value 800, from the individuality of remainder, determine the non-domination solution of second batch, and make their adaptive value less by 20 than the non-domination solution of last consignment of individual fitness, this process of continuing is until all individualities that satisfy constraint condition are assigned with adaptive value;
(4) individual for category-B, do not satisfy the number of constraint condition according to it, be divided into from less to more different sequences, and satisfy constraint condition number same individual, list same sequence in.To first individuality in the category-B colony, its adaptive value is less by 20 than the last batch of individual fitness in the category-A individuality; To other batch individuality in the category-B colony, its adaptive value is than inferior individual little by 20 of its last consignment of;
(5) according to the individual adaptive value that is assigned with, adopt the roulette criterion to choose the parent individuality and hybridize, and choose at random offspring individual participation variation;
(6) calculate offspring individual target function value and constraint function value, obtain satisfying in the offspring individual first non-domination solution of constraint condition by sort method, and upgrade the non-domination disaggregation of being stored with this;
(7) distance between resulting non-domination solution in the calculation procedure (6), selected distance two non-domination solutions are farthest hybridized, produce new individual, if new individuality satisfies constraint condition, and more outstanding than parent individuality, then point to the optimizing of the filial generation direction degree of depth along parent, keep more excellent individuality, and upgrade non-domination disaggregation;
(8) the non-domination solution of all storages is carried out the operation of 10 time clonings, and the colony behind the variation clone, individual goal functional value and constraint functional value behind the calculating clonal vaviation, and obtain satisfying in the clonal vaviation individuality first non-domination solution of constraint condition by sort method, and upgrade the non-domination solution group who is stored with this;
(9) individual weight multiple bank order of future generation, hybridization, variation and clonal vaviation process, until when reaching the condition of convergence, the non-domination solution group that output is stored.
Claims (5)
1. non-dominated sorting method based on deep search and high frequency Mutation Strategy is characterized in that:
(1) produces at random initial population, satisfy first non-domination solution of constraint condition in the storing initial population;
(2) according to constraint condition, the individuality that satisfies constraint condition is divided into a class, the individuality that does not satisfy constraint condition is divided into another kind of;
(3) to satisfying the individuality of constraint condition, determine non-domination solution, make it share same adaptive value, and from remaining individuality, determine the non-domination solution of second batch, distribute corresponding adaptive value, continue this process, until satisfying the constraint condition individuality, all are assigned with adaptive value;
(4) formation sequence: to not satisfying the individuality of constraint condition, the number according to not satisfying constraint condition sorts from less to more, and satisfies the identical individuality of number, comes in the same sequence;
(5) according to the individual adaptive value that is assigned with, adopt the roulette criterion to choose the parent individuality and hybridize, of future generation individual to produce; In the offspring individual that produces, randomly draw the individual variation that participates in;
(6) calculate offspring individual target function value and constraint function value, obtain satisfying in the offspring individual first non-domination solution of constraint condition, and upgrade the non-domination disaggregation of storing;
(7) calculate institute's non-domination solution of store and concentrate distance between each non-domination solution, two the individual hybridization farthest of order distance produce newly individuality; If new individuality satisfies constraint condition, and more outstanding than parent individuality, then point to the optimizing of the filial generation direction degree of depth along parent, keep more excellent individuality, and upgrade non-domination disaggregation;
(8) will have the individual clone of non-domination solution now, all individualities behind the variation clone, calculate individual goal functional value and constraint functional value behind the clonal vaviation, and obtain satisfying in the clonal vaviation individuality first non-domination solution of constraint condition by sort method, and upgrade the non-domination solution group who is stored with this;
(9) individual weight multiple bank order of future generation, hybridization, variation and clonal vaviation process are until reach when specifying algebraically iter the non-domination solution group that output is stored.
2. the non-dominated sorting method based on deep search and high frequency Mutation Strategy according to claim 1 is characterized in that described adaptive value is calculated as follows:
A
n＝A
1-(n-1)*δA
In the formula: A
nBe the adaptive value that n criticizes non-domination solution, δ A is the adaptive value difference between arithmetic number, adjacent batch of non-domination solution of representative.
3. the non-dominated sorting method based on deep search and high frequency Mutation Strategy according to claim 1 and 2 is characterized in that: in the described formation sequence, the First ray individual fitness is by formula B
1=A
1-N* δ A calculates, and other sequence individual fitness is by formula B
m=B
1-(m-1) * δ A calculates,
In the formula: B
1Be the First ray individual fitness, N is total batch of number of non-domination Xie in (3) step, B
mBe m batch of individual fitness.
4. the non-dominated sorting method based on deep search and high frequency Mutation Strategy according to claim 1 and 2 is characterized in that: the distance between described each non-domination solution is by formula
Calculate,
In the formula: dis is the distance between two non-domination solutions, x
i, y
iRepresent respectively two non-domination solution optimized variables, p is the optimized variable number.
5. the non-dominated sorting method based on deep search and high frequency Mutation Strategy according to claim 3 is characterized in that: the distance between described each non-domination solution is by formula
Calculate,
In the formula: dis is the distance between two non-domination solutions, x
i, y
iRepresent respectively two non-domination solution optimized variables, p is the optimized variable number.
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Application publication date: 20130403 |