CN106611217A - Weighted genetic local search algorithm for multi-objective flow shop scheduling - Google Patents
Weighted genetic local search algorithm for multi-objective flow shop scheduling Download PDFInfo
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Abstract
The invention provides a weighted genetic local search algorithm for multi-objective flow shop scheduling. The algorithm comprises the following steps: first stage, a preparation stage: generating an initial solution, entitling a weight value to each target function and constructing a temporary group to store a non-dominated solution; second stage: performing global search by using a genetic operator, namely performing selection, intersection and mutation; third stage: local search: searching a specified number of neighborhood solutions of each solution in a current population; fourth stage: performing an elitist strategy; and then performing optimal solution iteration (the initial solution is only generated in the first generation) search, and obtaining a scheduling scheme according to the solution after the iteration. The algorithm improves the genetic local search algorithm, and the local search direction and the elitist strategy are determined by a random weighting method, the local search of only detecting a part of neighborhood solutions and a target function weight value of a parent generation solution, so that the performance of the algorithm is greatly improved.
Description
Art
Type patent of the present invention is used for the production scheduling plan for working out the scheduling of multiple target Flow Shop.
Background technology
Genetic algorithm is a kind of efficient full search algorithm, the combination of itself and local search algorithm, i.e., hereditary office
Portion's searching algorithm so that algorithm is greatly improved for the search capability of non-domination solution.At present, this global search
The algorithm combined with Local Search has been widely deployed among Optimizing manufacture, and achieves effect well
Really.However, existing local search algorithm is often difficult to non-of whole for simply and efficiently finding multi-objective problem
With solution.
The content of the invention
This algorithm is made improvements for traditional Genetic local search algorithm, simply and efficiently to find multiple target stream
Whole non-domination solutions of scheduling problem between waterwheel.This algorithm enters in terms of three below to conventional genetic Local Search
Row is improved：First, the weighted value of each object function is difficult to determine；Second, to producing in local search procedure
A large amount of neighborhood solutions relatively tend to take up the substantial amounts of calculating time；3rd, Local Search direction is not comprehensive enough；
4th, the excellent solution obtained in search procedure may be lost during algorithm iteration afterwards.
Type of the present invention solves the technical scheme adopted by its technical problem：First, it is every by stochastic weighted method
Individual object function gives weighted value；Second, the neighborhood solution each current solution searched in limiting local search procedure
Number；3rd, the weighted value used using the parent solution that produces filial generation solution is as filial generation solution in Local Search
Object function weighted value；4th, using elitism strategy, the non-domination solution in every generation is stored in and temporarily organize simultaneously
Update by generation.
The beneficial effect of type of the present invention：First, make the process of determination object function weighted value no longer difficult；Second,
Balance global search and Local Search；3rd, each solution in Local Search has the searcher of oneself uniqueness
To so that the direction variation of Local Search；4th, it is to avoid iteration of the excellent solution for producing in algorithm afterwards
During be lost.
Description of the drawings
With reference to the accompanying drawings and examples type of the present invention is further illustrated.
Fig. 1 is the schematic diagram of Flow Shop scheduling.
Fig. 2 is the schematic diagram in Local Search direction.
Fig. 3 is the schematic diagram of non-domination solution.
Fig. 4 is the schematic diagram of elitism strategy.
Fig. 5 is the schematic diagram of Weighting type Genetic local search flow process.
Fig. 6 is two-point crossover operator schematic diagram.
Fig. 7 is mobile mutation schematic diagram.
Fig. 8 is the schematic diagram of algorithm detailed process
Specific embodiment
First, the expression of production information
Such as Fig. 1, it is located in Flow Shop, has n workpiece J to be produced1, J2..., Jn, have m platform machines
Device M1, M2..., Mm, workpiece JiRelease time be ri, workpiece JiIn machine MjThe front waiting time is
wij, workpiece JiTime of delivery：di。
2nd, the method for expressing of scheduling scheme：
Scheduling scheme on machine i is expressed as Xi=(s1, s2..., sn), 1≤i≤m (siRepresent that workpiece is compiled
Number, 1≤i≤n), then total activation scheme is expressed as X=(X1, X2..., Xm)
3rd, stochastic weighted method
Assignment method to the weighted value of n target：
1. n and weighted value random for 1 are randomly generated1, random2..., randomn；
2. weighted value w of i-th object functioniFor
wi=randomi/(random1+…randomn), i=1,2 ..., n.
4th, the local search algorithm of a detection part neighborhood solution
Specified neighborhood solution detects number k, will produce the object function weighted value of the parent solution of current solution X as
(this is by the Local Search for making each current solution have oneself uniqueness for the object function weighted value of current solution X
Direction, so that Local Search direction is diversified, its feature is vividly described out by Fig. 2), local
Search produces neighborhood solution by the way of mobile mutation.
So, it is as follows for the local search procedure of solution X：
1. neighborhood solution X of current solution X is detected '；
If 2. X ' is the solution more excellent than X, current solution X is substituted with X ' and return 1；Under otherwise performing
One step；
3. if the randomly selected k neighborhood solution of current solution X is detected, i.e. X's is detected
There is no more excellent solution in k neighborhood solution, then EP (end of program)；1 is returned otherwise.
5th, non-domination solution
For n object function f of maximization1(x), f2(x) ..., fnX (), solves x, y when two full
Foot
And
fj(x)<fjWhen (y), then claim solution y domination solution x.If a solution is not asked by multiple-objection optimization
Any other solution domination of topic, that solution are referred to as a non-domination solution.For two objective optimisation problems
The non-domination solution of (maximization object function) can be vividly described out by Fig. 3.
6th, elitism strategy
Such as Fig. 4, in the implementation procedure of this algorithm, contain two groups of solutions, respectively current population and storage non-domination solution
Temporary transient group.
Temporary transient group is updated with the non-domination solution in this population first per generation population, and randomly choose specified number
Solution；Then, the population will add current population by randomly selected non-domination solution before Jing after genetic operator process,
Carry out jointly Local Search；The population that Local Search is produced after terminating continues executing with said process as the next generation.
7th, Weighting type Genetic local search
Such as Fig. 5, this algorithm is after initialization population, it is first determined object function weighted value, then passes through something lost
Passing operator carries out global search to population, then carries out Local Search, is then protected using elitism strategy
Non-domination solution, finally by iterating to find whole non-domination solutions to said process.
8th, two-point crossover operator
Such as Fig. 6
9th, mobile mutation
Such as Fig. 7
Tenth, algorithm detailed process is as follows
Such as Fig. 8
Step one --- initialization (generation initial solution)
1. m sequence (m is number of machines) is produced, and each sequence is a randomly ordered sequence (n of several 1-n
For workpiece number to be produced).
2. according to population scale Npop, produce the initial solution of corresponding number.
Step 2 --- calculating target function value
1. calculating target function f1(x), f2(x) ..., fnThe value of (x).
Step 3 --- update the non-domination solution of temporarily group
1. the non-domination solution in initial population is found.
2. the non-domination solution in initial solution is copied into into temporary transient group.
Step 4 --- calculate fitness function value
To each solution ---
1. weighted value is determined
wi=randomi/(random1+…randomn), i=1,2 ..., n.
2. fitness function value is calculated：
F (x)=w1f1(x)+w2f2(x)+…+wnfn(x).
Step 5 --- select defect individual
1. the select probability of each individual (solution) is calculated
Wherein Ψ represents current population, and f (x) is the fitness value for solving x, fmin(Ψ)=min { f (x)
|x∈Ψ}。
2. according to select probability, (the N for selecting select probability bigpop-Nelite) individual (solution).
Step 6 --- intersect
1. the number of the solution intersected is calculated according to crossover probability, the solution of corresponding number is selected immediately.
2. it is random using it is selected it is individual two-by-two one group as a pair of parent solutions, carry out with two-point crossover operator
Intersect.When intersecting to each pair parent solution, respectively the often row of two solutions is intersected, then result
It is reassembled into filial generation solution.
Step 7 --- mutation
1. the number of the solution intersected is calculated according to mutation probability, the solution of corresponding number is selected immediately.
2. pair selected individuality moves mutation.When being mutated to each pair parent solution, respectively to every row
Mutation, then result is reassembled into filial generation solution.
Step 8 --- Local Search
1. from temporary transient group (step 3 generation) middle random selection NeliteIndividual solution, addition have (Npop-Nelite) individual solution
Current population, construction one have NpopThe population of individual solution.
2. (to each solution) randomly generates k neighborhood solution by mobile mutation.
3. (each is solved) by selecting the fitness function weighted value of the parent solution of the solution to construct the solution
Fitness function, then calculates the fitness function value of this k neighborhood solution.
4. (to each solution), if having the solution more excellent than the solution in this k neighborhood solution, replaces the solution with it；
Otherwise, the solution is not done and is changed.
Step 9 --- iteration
If 1. algorithm has searched for the solution of specified number, algorithm terminates；Otherwise return to step two.
Step 10 --- produce scheduling scheme
1., after iteration terminates, it is excellent that the as algorithm of the solution in the optimal solution and temporary transient group in current population is tried to achieve
Solution, according to the representation of scheduling scheme, you can these solutions are converted to corresponding scheduling scheme.
Claims (5)
1. a kind of Weighting type Genetic local search algorithm for Flow Shop scheduling, it is characterised in that including following several steps：Step one：Weighted value is given for each object function by stochastic weighted method；Step 2：The number of the neighborhood solution each current solution searched in limiting local search procedure；Step 3：To produce object function weighted value of the weighted value that used of parent solution of filial generation solution as filial generation solution in Local Search；Step 4：Using elitism strategy, the non-domination solution in every generation is stored in into temporary transient group and is updated by generation.
2. algorithm according to claim 1, is characterized in that：Specified neighborhood solution detects number k, will produce the object function weighted value of the object function weighted value of the parent solution of current solution X as current solution X.
3. algorithm according to claim 1, is characterized in that：Local Search produces neighborhood solution by the way of mobile mutation.
4. algorithm according to claim 1, is characterized in that：Using elitism strategy, contain temporary transient group of two groups of solutions, respectively current population and storage non-domination solution in the implementation procedure of this algorithm, specific practice is as follows：
1）Temporary transient group is updated with the non-domination solution in this population first per generation population, and randomly choose the solution for specifying number；
2）The population Jing after genetic operator process will add current population by randomly selected non-domination solution before, carry out jointly Local Search；
3）The population that Local Search is produced after terminating continues executing with said process as the next generation.
5. algorithm according to claim 1, is characterized in that：Using stochastic weighted method, it is that each object function gives weighted value, the assignment method to the weighted value of n target：
Randomly generate n and weighted value random for 11, random2..., randomn；
Weighted value w of i-th object functioniFor
wi=randomi/（random1+...+randomn）, i=1,2 ..., n..
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109164766A (en) * | 2018-08-22 | 2019-01-08 | 上海交通大学 | The production control system in multiplexing kind workshop |
| CN112487345A (en) * | 2019-09-12 | 2021-03-12 | 富士通株式会社 | Optimization device, optimization program, and optimization method |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109164766A (en) * | 2018-08-22 | 2019-01-08 | 上海交通大学 | The production control system in multiplexing kind workshop |
| CN109164766B (en) * | 2018-08-22 | 2019-09-24 | 上海交通大学 | The production control system in multiplexing kind workshop |
| CN112487345A (en) * | 2019-09-12 | 2021-03-12 | 富士通株式会社 | Optimization device, optimization program, and optimization method |
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