CN102278996B - Ant colony optimization processing method of large-scale multi-target intelligent moving route selection - Google Patents

Abstract

The invention discloses an ant colony optimization processing method of large-scale multi-target intelligent moving route selection; after data of NTSP target logistics delivery addresses, distances between every two addresses, and M price of cost for passing through each route are obtained, a route planning unit is solved by ant colony optimization technology so as to obtain a specific walking route for intelligent mobile-agent delivery, and the route is outputted to an executive mechanism for realization. When the method is used to solve the problem of large-scale multi-target intelligent moving route selection, the invention has good optimization performance, and has the advantages of parallelism, self-organization, strong robustness, and the like, and the obtained solutions are large in quantity, high in quality, and have strong approximation capability to the real Pareto solution set; the obtained solution set has uniform distribution; the calculation speed is high. The invention can be used in intelligent processing units of route planning systems in fields of logistics distribution, intelligent traffic, internet, robots, etc.

Description

The ant group optimization disposal route that a kind of extensive Multiobjective Intelligent mobile route is selected

Affiliated technical field

The present invention relates to intelligent mobile device, the reasonable path technique of especially intelligent mobile agent optimized choice field.

Background technology

Path planning is the logistics distribution field, particularly the key issue in the intelligent logistics under the technology of Internet of things support.Carry out the intelligent mobile agent desire of logistics distribution deliver goods is accomplished in n client's order, and M conflicting cost reaches minimum as far as possible simultaneously to make that cost consumption, route spacing leave etc.From the angle of mathematical processing methods, above problem can abstractly be a typical mathematical problem, promptly so-called multiple goal traveling salesman problem (Multi-objective Traveling Salesman Problem; MTSP), MTSP is generally described as: a given n city and their costs of M between any two, and conflicting between each cost; A certain travelling salesman will visit this n city; From a certain city, visit all the other n-1 city all over and only visit all over once, turn back to the city of setting out at last.The problem that need find the solution is, how this travelling salesman should select the path visited all over, makes M the conflicting cost of visiting all over reach minimum as far as possible simultaneously.

Since practical problems that the reasonable path of the present invention's intelligence mobile agent optimized choice desire solves and the solution indirect correlation of MT reconnaissance SP, the review below we can do the present situation that MTSP finds the solution.

Traditional M TSP solution procedure comprised for two steps: the finding the solution of problem conversion and transfer problem.The method that MTSP is changed mainly contains two types: one type is that MTSP is converted into standard TSP; Representative method for transformation has direct method, multiplication and division, Lamda-weighted method, quadratic sum weighted method, ideal point method, and these class methods exist each target weight setting and ideal point to choose difficult problem; Another kind of is that a plurality of targets among the MTSP are sorted, and finds the solution according to target priority, and representative method has serial method and main target method, and these class methods need some priori cognitions about a plurality of targets.Method for solving to transfer problem also comprises two types: one type is accurate solving method; Representative have branch and bound method, cutting-plane method and a dynamic programming etc.; These methods can guarantee to obtain the optimum solution of transfer problem; But be exponential increase with the problem complexity its operation time, can't in polynomial time, find the solution, thereby be difficult to solve extensive problem; Another kind of is the approximate solution method; These class methods are target in polynomial time, to obtain approximate optimal solution; These class methods can further be divided into three sub-category: the one, and path configuration method, this method are from infeasible solution or not exclusively separate beginning, progressively construct through certain strategy; Up to obtaining a feasible solution, wherein be representative with the nearest neighbor method; The 2nd, the path improved method, it is to adopt certain strategy that feasible solution is improved, example strategy comprises genetic algorithm, limit exchange algorithm, TABU search etc.; The 3rd, the combination of path configuration method and path improved method, wherein the path configuration method produces initial solution, and the path improved method improves initial solution.Because there is not optimum solution in MTSP itself, and traditional MTSP method for solving can only obtain one and separates, and this to separate be a kind of compromise to a plurality of targets, but actual conditions are that different situations should adopt different mean methods.Therefore, how to produce one and comprise the disaggregation that many as far as possible high-qualitys are separated, transferring to the decision-maker is the key that solves multi-objective problem according to different actual conditions separating concentrated the selection.In addition, another problem is that the scale of practical problems is increasing along with the development of producing, and existing method surpasses the non-constant of performance when thousands of in the MTSP scale.Therefore, extensive MTSP is the critical problem in multiple goal combined optimization technique field.

Ant group optimization is a kind of optimisation technique with characteristics such as concurrency, self-organization and strong robustness, and suitable usefulness solves this type of TSP combinatorial optimization problem.At present, adopting ant group optimization to solve in the method for MTSP, representative have a MACS, BIANT and UNBI, but these methods performance degradation when solving extensive MTSP is serious.Thus, a kind of ant colony optimization method that can effectively find the solution extensive MTSP of invention has important and practical meanings.

Summary of the invention

Above shortcoming in view of prior art; The objective of the invention is to obtain the disposal route that a kind of ant group optimization Multiobjective Intelligent mobile route that can effectively find the solution extensive MTSP is selected; Make it to overcome the shortcoming of prior art aspect finding the solution in the path, the more convenient processing power that improves intelligent mobile agent effectively.

The present invention is for solving its technical matters, and the technical scheme that is adopted is:

The ant group optimization disposal route that a kind of extensive Multiobjective Intelligent mobile route is selected is being obtained N _TSPAfter the data of M such as a cost cost in the distance between individual target logistics Shipping Address and two two-addresses, every section path of process; Find the solution with the concrete walking path that obtains intelligent mobile agent deliver goods in the path planning unit and export travel mechanism to and be achieved, adopt following step to be achieved:

1. initialization algorithm parameter;

2. adopt Chebyshev's decomposition method that MTSP is decomposed into N single goal subproblem, the fitness function of n subproblem is:

$g_n\left(\mathrm{\π}\right|{\mathrm{\λ}}^n,z)=\underset{1\≤m\≤M}{\max }\left\{{\mathrm{\λ}}_m^n\right|f_m\left(\mathrm{\π}\right)-z\left|\right\}---\left(1\right)$

In the formula,

Be the target weight vector of n subproblem, and

Be the RP vector, π is the feasible solution of subproblem, f _m(π) be m target function value of this feasible solution, M is a MTSP target data number;

3. the ant crowd who is made up of N ant is divided into N sub-ant crowd according to weight vector with overlap mode, and each sub-ant crowd finds the solution a subproblem; The sub-ant crowd S (n) that finds the solution n subproblem comprises K ant, i.e. S (n)={ i ₁, i ₂, L, i _K, n=1,2, L, N, wherein i _jFor with λ ⁿSubscript with weight vectors λ of j optimum distance;

4. confirm every subproblem set A (k) that ant is found the solution among the ant crowd, A (k)={ n|k ∈ S (n), n=1,2, L, N}, k=1,2, L, N;

5. the pheromones matrix τ of each subproblem of initialization ⁿ, heuristic information matrix η ⁿPlain with initial information

N=1,2, L, N, initialization mode is:

${\mathrm{\τ}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{f}_m\left({\mathrm{\π}}^m\right)---\left(2\right)$

${\mathrm{\η}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{c}_{\mathrm{ij}}^m---\left(3\right)$

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{f}_m\left({\mathrm{\π}}^m\right)---\left(4\right)$

In the formula; π is an initial feasible solution;

is the pheromones amount between city i and the city j in n the subproblem,

be the heuristic information amount between city i and the city j in n the subproblem;

is m target cost between city i and the city j;

is the plain amount of the initial information of n subproblem;

6. cycle index t increases by 1, i.e. t ← t+1, and subproblem index n is taken as 0;

7. subproblem index n increases by 1, i.e. n ← n+1;

8. every ant among the sub-ant crowd S (n) selects a city as the traversal starting point at random;

9.S the ant of the K (n) successively by formula transition rule shown in (5) selects city j to advance, and according to the plain τ of formula (7) lastest imformation ⁿ:

${\mathrm{\τ}}_{\mathrm{ij}}^n=(1-\mathrm{\ξ}){\mathrm{\τ}}_{\mathrm{ij}}^n+\mathrm{\ξ}{\mathrm{\τ}}_0^n---\left(7\right)$

In the formula, α is the pheromones weight, and β is the heuristic information weight, and Ω (i) is the ant that is positioned at city i next addressable city set, and ξ is the plain volatility coefficient of local message, q ₀Be the probability constant;

10. if all ants among the S (n) all do not get back to the city of setting out, then jumped to for the 9th step, otherwise proceed to next step, be i.e. the 11st step;

11. calculate the fitness function value of K ant build path among the sub-ant crowd S (n) according to formula (1), and calculate M desired value of respective path;

12. confirm the optimum ant b among the sub-ant crowd S (n) according to formula (8) _n, promptly

$b_n=\arg \underset{k\∈S\left(n\right)}{\min }\left\{g_n\left({\mathrm{\π}}^k\right|{\mathrm{\λ}}^n,z)\right\}---\left(8\right)$

13. utilize the target function value of separating of ant structure among the S (n) to upgrade the component z of RP z by formula (9) _m, m=1,2, L, M, promptly

$z_m=\underset{k\∈S\left(n\right)}{\min }\left(f_m\left({\mathrm{\π}}^k\right)\right)---\left(9\right)$

14. utilize initial information plain

that ant makes up among the S (n) the target function value of separating upgrades subproblem n by formula (10) promptly

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{\hat{f}}_m^n---\left(10\right)$

${\hat{f}}_m^n=\underset{k\∈S\left(n\right)}{\mathrm{\Σ}}{f}_m\left({\mathrm{\π}}^n\right)/K---\left(11\right)$

15. utilize optimum ant path and upgrade all l ∈ A (b according to formula (12) _n) pheromones matrix τ ^l, promptly

${\mathrm{\τ}}_{\mathrm{ij}}^l=(1-\mathrm{\ρ}){\mathrm{\τ}}_{\mathrm{ij}}^l+\mathrm{\ρ\Δ}{\mathrm{\τ}}^l---\left(12\right)$

$\mathrm{\Δ}{\mathrm{\τ}}^l=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^l{f}_m\left({\mathrm{\π}}^l\right)---\left(13\right)$

16. the target function value of separating that ant among the S (n) is made up joins among the non-domination disaggregation Φ, removes non-domination then and separates concentrated domination and separate;

17. also have subproblem not find the solution in the current circulation, i.e. n ≠ N, then algorithm jumped to for the 7th step, otherwise proceeded to next step, i.e. the 18th step;

18. if this algorithm satisfies termination condition, if i.e. cycle index t >=T, then loop ends, and export non-domination disaggregation Φ, otherwise algorithm jumped to for the 6th step.

Adopt the inventive method, when finding the solution extensive MTSP, it is good to optimize performance, has advantages such as concurrency, self-organization and strong robustness, and many, the Functionality, quality and appealing design of the quantity of separating that is obtained is strong to true Pareto disaggregation approximation capability; The disaggregation that obtains is evenly distributed; Computing velocity is fast.Can be used in the intelligent processing unit of path planning system in the fields such as logistics distribution, intelligent transportation, internet and robot.

The present invention provides a kind of effective technical way of finding the solution extensive MTSP, aspect following three, is superior to three kinds of the most famous in this field methods (MACS, BIANT and UNBI):

1. the disaggregation of the present invention's acquisition is than MACS, and BIANT and UNBI more approach true Pareto disaggregation.Disaggregation is approached true Pareto disaggregation more, and its metric is more little, and quality is high more.Through MTSP being decomposed into a plurality of single goal problems and the ant crowd is decomposed into a plurality of sub-ant crowds with overlap mode, and each sub-ant crowd finds the solution a single goal problem and finds the solution simultaneously with all single goal problems, and the present invention can obtain high-quality disaggregation.Table 1 has provided the present invention when finding the solution 8 typical two objective traveling salesman problems; The disaggregation that obtains is approached true Pareto disaggregation degree and MACS; The contrast of BIANT and three kinds of methods of UNBI; The problem of finding the solution is selected from the TSPLIB database, and the result of four kinds of methods carries out the mean value of 20 independent experiment acquisitions to each problem from every kind of method.In table 1, for 8 problems, the value that the present invention obtains is all much smaller than MACS, and the result of BIANT and three kinds of methods of UNBI shows that the disaggregation that the present invention obtains approaches true Pareto disaggregation most, and that separates is best in quality.

2. the disaggregation degree of being evenly distributed of the present invention's acquisition is superior to MACS, BIANT and UNBI.The disaggregation degree of being evenly distributed is meant the degree of uniformity that the disaggregation of certain method acquisition distributes along the Pareto forward position, and it is even more to distribute, and then the quality of disaggregation is good more, and corresponding metric is big more.Table 2 has provided the present invention when finding the solution 8 typical two objective traveling salesman problems; The disaggregation that obtains be evenly distributed degree and MACS; The contrast of BIANT and three kinds of methods of UNBI, the result carries out the mean value of 20 independent experiment acquisitions in the table to each problem from every kind of method.In table 2, in 8 problems 6, the value that the present invention obtains is all greater than MACS, and BIANT and UNBI show that the disaggregation degree of being evenly distributed that the present invention obtains is superior to MACS, and BIANT and UNBI are best in quality.

Table 1 the present invention and MACS, BIANT, UNBI are in the comparison that approaches on the true Pareto disaggregation degree

Table 2 the present invention and MACS, BIANT and the UNBI comparison on disaggregation is evenly distributed degree

3. computation complexity of the present invention is less than MACS, three kinds of methods of BIANT and UNBI.The method that computation complexity is more little, when finding the solution the problem of identical scale, the computing time that needs is few more, and performance is good more.The present invention when finding the solution 8 typical two objective traveling salesman problems, required computing time and MACS, the comparing result of BIANT and three kinds of methods of UNBI is as shown in table 3.Result in the table 3 carries out the mean value of 20 independent experiment acquisitions to each problem for every kind of method.Can find out from table 3, along with the increase of problem complexity, the present invention and MACS, three kinds of time consuming gaps of method of BIANT and UNBI are big more, and advantage is obvious more.

Table 3 the present invention and MACS, BIANT and the UNBI comparison (unit is second) on computing time

Description of drawings

Fig. 1 be the embodiment of the invention when cycle index is 20, the Pareto forward position of four kinds of methods contrast;

Fig. 2 be the embodiment of the invention when evolutionary generation is 40, the Pareto forward position of four kinds of methods contrast;

Fig. 3 be the embodiment of the invention when evolutionary generation is 60, the Pareto forward position of four kinds of methods contrast;

Fig. 4 be the embodiment of the invention when evolutionary generation is 80, the Pareto forward position of four kinds of methods contrast;

Fig. 5 be the embodiment of the invention when evolutionary generation is 80, the Pareto forward position of four kinds of methods contrast;

In Fig. 1 to Fig. 5; Horizontal ordinate is the numerical value of target 1, and ordinate is the numerical value of target 2, does not all have unit; The Pareto forward position that symbol " " expression the present invention obtains; The Pareto forward position that symbol "+" expression MACS method obtains, the Pareto forward position that symbol " o " expression BIANT method obtains, the Pareto forward position that symbol " * " expression UNBI method obtains.

Embodiment

Below in conjunction with embodiment the present invention is described in further detail.

Embodiment

Adopt the present invention to find the solution the two objective traveling salesman problem of being made up of 200 cities, this problem is constructed by two single goal traveling salesman problem KroA200 among the standard database TSPLIB and KroB200 and is formed.Experiment adopts Matlab as implementation tool, CPU be AMD Sempron 1.6GHz, in save as on the computing machine that 1GB, operating system are Windows XP and find the solution.

The concrete performing step of a kind of ant colony optimization method of finding the solution extensive multiple goal traveling salesman problem provided by the present invention is following:

Step 1: parameter initialization: parameter alpha=1 of algorithm is set, β=2, ρ=0.1, q ₀=0.9, ξ=0.1, K=5, N=20, T=100, Φ=

, weight vectors produces at random, and the weight vectors in the present embodiment is λ ¹=[0.0170 0.9830], λ ²=[0.0541 0.9459], λ ³=[0.2177 0.7823], λ ⁴=[0.2444 0.7556], λ ⁵=[0.2551 0.7449], λ ⁶=[0.2579 0.7421], λ ⁷=[0.3035 0.6965], λ ⁸=[0.3882 0.6118], λ ⁹=[0.4728 0.5272], λ ¹⁰=[0.5002 0.4998], λ ¹¹=[0.5194 0.4806], λ ¹²=[0.5259 0.4741], λ ¹³=[0.5265 0.4735], λ ¹⁴=[0.5289 04711], λ ¹⁵=[0.5533 0.4467], λ ¹⁶=[0.5799 0.4201], λ ¹⁷=[0.6068 0.3932], λ ¹⁸=[0.7459 0.2541], λ ¹⁹=[0.7707 0.2293], λ ²⁰=[0.7851 0.2149], the RP z in the present embodiment is the objective function vector in the path that connected and composed successively by 200 cities, i.e. z=[373,940 327450];

Step 2: adopt Chebyshev's decomposition method that this traveling salesman problem is decomposed into 20 single goal subproblems, the fitness function of n subproblem is described by formula (1), promptly

$g_n\left(\mathrm{\π}\right|{\mathrm{\λ}}^n,z)=\underset{1\≤m\≤2}{\max }\left\{{\mathrm{\λ}}_m^n\right|f_m\left(\mathrm{\π}\right)-z\left|\right\}$

In the formula, λ ¹, λ ², L, λ ²⁰Shown in z such as Step 1, π is the feasible solution of subproblem, f _m(π) be m target function value of this feasible solution;

Step 3: 20 ants are decomposed into 20 sub-ant crowds according to weight vector with overlap mode, and each sub-ant crowd is designated as S (n) and comprises 5 ants, in the present embodiment, and S (1)=[1 234 5]; S (2)=[2 134 5], S (3)=[3 425 1], S (4)=[4 325 1], S (5)=[5 647 3]; S (6)=[6 547 8], S (7)=[7 86 910], S (8)=[8 769 10]; S (9)=[9 10 11 12 13], S (10)=[10 9 11 12 13], S (11)=[11 109 12 13]; S (12)=[12 13 11 10 9], S (13)=[13 12 11 10 9], S (14)=[14 15 16 17 13]; S (15)=[15 14 16 17 13], S (16)=[16 17 15 14 13], S (17)=[17 16 15 14 13]; S (18)=[1,819 17 16 15], S (19)=[19 18 17 16 15], S (20)=[20 9 10 11 8];

Step 4: confirm that every ant is found the solution problem set A (k), k=1,2, L, 20 among the ant crowd.In the present embodiment, A (1)=[1 23 4], A (2)=[1 23 4], A (3)=[1 234 5]; A (4)=[1 2345 6], A (5)=[1 23 45 6], A (6)=[5 67 8], A (7)=[5 67 8]; A (8)=[6 78 20], A (9)=[7 89 10 11 12 13 20], A (10)=[7 89 10 11 12 13 20], A (11)=[9 10 11 12 13 20]; A (12)=[9 10 11 12 13], A (13)=[9 10 11 12 13 14 15 16 17], A (14)=[14 15 16 17]; A (15)=[14 15 16 17 18 19], A (16)=[14 15 16 17 18 19], A (17)=[14 15 16 17 18 19]; A (18)=[18 19], A (19)=[1819], A (20)=[20];

Step 5: according to formula (2), (3) and (4) difference initialization information prime matrix τ ⁿ, heuristic information matrix η ⁿPlain with initial information

N=1,2, L, 20, promptly

${\mathrm{\τ}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{f}_m\left({\mathrm{\π}}^m\right)$

${\mathrm{\η}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{c}_{\mathrm{ij}}^m$

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{f}_m\left({\mathrm{\π}}^m\right)$

In the formula; π is for initially effectively separating;

is the pheromones amount between city i and the city j in n the subproblem,

be the heuristic information amount between city i and the city j in n the subproblem; is m target cost between city i and the city j;

is the plain amount of the initial information of n subproblem;

Step 6: cycle index t increases by 1, i.e. t ← t+1, and subproblem index n is taken as 0;

Step 7: subproblem index n increases by 1, i.e. n ← n+1;

Step 8: 5 ants among the sub-ant crowd S (n) select a city as the traversal starting point at random;

5 ants among the Step 9:S (n) successively by formula (5) select city j to advance, and according to the plain τ of formula (7) lastest imformation ⁿ:

${\mathrm{\τ}}_{\mathrm{ij}}^n=(1-0.1){\mathrm{\τ}}_{\mathrm{ij}}^n+{0.1\mathrm{\τ}}_0^n$

In the formula, Ω (i) is the ant that is positioned at city i next addressable city set;

Step 10: if all ants among the S (n) all do not get back to the city of setting out, then jumped to for the 9th step, otherwise proceed to next step, be i.e. the 11st step;

Step 11: calculate the fitness function value of 5 ant build paths among this sub-ant crowd S (n) that circulates according to formula (1), and calculate 2 desired values of respective path;

Step 12: confirm the optimum ant b among the sub-ant crowd S (n) according to formula (8) _n

$b_n=\arg \underset{k\∈S\left(n\right)}{\min }\left\{g_n\left({\mathrm{\π}}^k\right|{\mathrm{\λ}}^n,z)\right\}$

Step 13: utilize the component z of the target function value of separating of ant structure among the S (n) by formula (9) renewal RP z _m, m=1,2;

$z_m=\underset{k\∈S\left(n\right)}{\min }\left(f_m\left({\mathrm{\π}}^k\right)\right)$

Step 14: utilize the initial information plain

of the target function value of separating of ant structure among the S (n) by formula (10) renewal subproblem n

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{\hat{f}}_m^n$

${\hat{f}}_m^n=\underset{k\∈S\left(n\right)}{\mathrm{\Σ}}{f}_m\left({\mathrm{\π}}^n\right)/5$

Step 15: utilize optimum ant path and upgrade all l ∈ A (b according to formula (12) _n) pheromones matrix τ ^l, promptly

${\mathrm{\τ}}_{\mathrm{ij}}^l=(1-\mathrm{\ρ}){\mathrm{\τ}}_{\mathrm{ij}}^l+\mathrm{\ρ\Δ}{\mathrm{\τ}}^l$

$\mathrm{\Δ}{\mathrm{\τ}}^l=1/\underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^l{f}_m\left({\mathrm{\π}}^l\right)$

Step 16: the target function value of separating that ant among the S (n) is made up joins among the non-domination disaggregation Φ, removes non-domination then and separates concentrated domination and separate;

Step 17: also have subproblem not find the solution in the current circulation, promptly n ≠ 20 then jumped to for the 7th step, otherwise proceed to next step, i.e. the 18th step;

Step 18: if this algorithm satisfies termination condition, if i.e. cycle index t >=100, then loop ends, and export non-domination disaggregation Φ, algorithm jumped to for the 6th step.

Present embodiment is carried out Computer Simulation, Pareto disaggregation evolutionary process such as Fig. 1-shown in Figure 5.These results clearly show that optimization performance of the present invention is superior to MACS, BIANT and three kinds of methods of UNBI, especially have best approaching and distribution the most uniformly in the early stage disaggregation that obtains of evolutionary process.

Obviously; The present invention can mode online or off-line (for example: the intelligent processing unit of the path planning system merchandising machine people) be used for intelligent mobile agent; In view of this name of the game abstractness and the popularity of handling similar object; The inventive method also may be used on many practical field, such as: the data transmission adjustmenting management of the allotment of the vehicles and traffic system, intelligent transportation, internet etc.

Claims (1)

1. the ant group optimization disposal route that extensive Multiobjective Intelligent mobile route is selected is being obtained N _TSPAfter the data of a cost M cost in the distance between individual target logistics Shipping Address and two two-addresses, every section path of process; Find the solution with the concrete walking path that obtains intelligent mobile agent deliver goods in the path planning unit and export topworks to and be achieved, said path planning unit adopts following step:

1. initialization algorithm parameter;

2. adopting Chebyshev's decomposition method is N single goal subproblem with multiple goal routing PROBLEM DECOMPOSITION, and the fitness function of n subproblem is:

$g_n\left(\mathrm{\π}\right|{\mathrm{\λ}}^n,z)=\underset{1\≤m\≤M}{\max }\left\{{\mathrm{\λ}}_m^n\right|f_m\left(\mathrm{\π}\right)-z\left|\right\}---\left(1\right)$

In the formula,

Be the target weight vector of n subproblem, and

Z=(z ₁, z ₂..., z _M) be the RP vector, π is the feasible solution of subproblem, f _m(π) be m target function value of this feasible solution;

3. the ant crowd who is made up of N ant is divided into N sub-ant crowd according to weight vector with overlap mode, and each sub-ant crowd finds the solution a subproblem; The sub-ant crowd S (n) that finds the solution n subproblem comprises K ant, i.e. S (n)={ i ₁, i ₂..., i _K, n=1,2 ..., N, wherein i _jFor with λ ⁿSubscript with weight vectors λ of j optimum distance;

4. confirm every subproblem set A (k) that ant is found the solution among the ant crowd, A (k)=n|k ∈ S (n), and n=1,2 ..., N}, k=1,2 ..., N;

5. the pheromones matrix τ of each subproblem of initialization ⁿ, heuristic information matrix η ⁿPlain with initial information

N=1,2 ..., N, initialization mode is:

${\mathrm{\τ}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{f}_m\left({\mathrm{\π}}^m\right)---\left(2\right)$

${\mathrm{\η}}_{\mathrm{ij}}^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{c}_{\mathrm{ij}}^m---\left(3\right)$

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^k{f}_m\left({\mathrm{\π}}^m\right)---\left(4\right)$

In the formula; π is an initial feasible solution;

is the pheromones amount between city i and the city j in n the subproblem,

be the heuristic information amount between city i and the city j in n the subproblem;

is m target cost between city i and the city j;

is the plain amount of the initial information of n subproblem;

6. cycle index t increases by 1, i.e. t ← t+1, and subproblem index n is taken as 0;

7. subproblem index n increases by 1, i.e. n ← n+1;

8. every ant among the sub-ant crowd S (n) selects a city as the traversal starting point at random;

9.S the ant of the K (n) successively by formula transition rule shown in (5) selects city j to advance, and according to the plain τ of formula (7) lastest imformation ⁿ:

${\mathrm{\τ}}_{\mathrm{ij}}^n=(1-\mathrm{\ξ}){\mathrm{\τ}}_{\mathrm{ij}}^n+\mathrm{\ξ}{\mathrm{\τ}}_0^n---\left(7\right)$

In the formula, α is the pheromones weight, and β is the heuristic information weight, and Ω (i) is the ant that is positioned at city i next addressable city set, and ξ is the plain volatility coefficient of local message, q ₀Be the probability constant, q is the random number between 0 and 1;

10. if all ants among the S (n) all do not get back to the city of setting out, then jumped to for the 9th step, otherwise proceed to next step, be i.e. the 11st step;

11. calculate the fitness function value of K ant build path among the sub-ant crowd S (n) according to formula (1), and calculate M desired value of respective path;

12. confirm the optimum ant b among the sub-ant crowd S (n) according to formula (8) _n, promptly

$b_m=\arg \underset{k\∈S\left(n\right)}{\min }\left\{g_n\left({\mathrm{\π}}^k\right|{\mathrm{\λ}}^n,z)\right\}---\left(8\right)$

13. utilize the target function value of separating of ant structure among the S (n) to upgrade the component z of RP z by formula (9) _m, m=1,2 ..., M, promptly

$z_m=\underset{k\∈S\left(n\right)}{\min }\left(f_m\left({\mathrm{\π}}^k\right)\right)---\left(9\right)$

14. utilize initial information plain

that ant makes up among the S (n) the target function value of separating upgrades subproblem n by formula (10) promptly

${\mathrm{\τ}}_0^n=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^n{\hat{f}}_m^n---\left(10\right)$

${\hat{f}}_m^n=\underset{k\∈S\left(n\right)}{\mathrm{\Σ}}{f}_m\left({\mathrm{\π}}^n\right)/K---\left(11\right)$

15. utilize optimum ant path and upgrade all l ∈ A (b according to formula (12) _n) pheromones matrix τ ^l, promptly

${\mathrm{\τ}}_{\mathrm{ij}}^l=(1-\mathrm{\ρ}){\mathrm{\τ}}_{\mathrm{ij}}^l+\mathrm{\ρ\Δ}{\mathrm{\σ}}^l---\left(12\right)$

$\mathrm{\Δ}{\mathrm{\τ}}^l=1/\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\λ}}_m^l{f}_m\left({\mathrm{\π}}^l\right)---\left(13\right)$

ρ is a rate of evaporation, is a constant;

16. the target function value of separating that ant among the S (n) is made up joins among the non-domination disaggregation Φ, removes non-domination then and separates concentrated domination and separate;

17. also have subproblem not find the solution in the current circulation, i.e. n ≠ N, then algorithm jumped to for the 7th step, otherwise proceeded to next step, i.e. the 18th step;

18. if this algorithm satisfies termination condition, if i.e. cycle index t >=T, then loop ends, and export non-domination disaggregation Φ, otherwise algorithm jumped to for the 6th step.

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