CN107918796A - A kind of more tactful shuffled frog leaping algorithms solved towards nonlinear programming problem - Google Patents
A kind of more tactful shuffled frog leaping algorithms solved towards nonlinear programming problem Download PDFInfo
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Abstract
The invention discloses a kind of more tactful shuffled frog leaping algorithms solved towards nonlinear programming problem（MSSFLA）, based on standard shuffled frog leaping algorithm, use for reference no intelligent agent and intelligent characteristic shown by cooperation, devise a kind of novel rule that leapfrogs, the rule fully excavated change reach during each frog individual positional information.Secondly, devise a kind of embedded cross operator, worst genes of individuals is respectively embedded in local optimum and global optimum's individual, different genes will be uniformly distributed in defect individual to be intersected in worst individual, are conducive to improve the gene quality of original worst frog individual.The regression routine layout strategy used in invention is used for the intermediate result for depositing all evolutionary computations, helps avoid largely computing repeatedly in local search, accelerates the searching process of algorithm.The analysis result that the method for the present invention obtains various criterion test cases, demonstrating MSSFLA described in the invention has stronger robustness and universality.
Description
Technical field
The invention belongs to data mining, artificial intelligence field, more particularly to a kind of solve towards nonlinear programming problem
More strategy shuffled frog leaping algorithms.
Background technology
Data mining is a kind of method that Knowledge Discovery is carried out from mass data.From objective application angle, data
The information flow of excavation must be built upon on the deep understanding to object to be excavated, and difference need to be used for different objects
Excavation treatment technology.
The directions such as the Nonlinear Programming Technique Gong Cheng ﹑ Jing Ji ﹑ Ke Yan ﹑ military affairs in data mining are all widely used,
The instrument of strength is provided for optimized design.Optimize in systematic procedure, in further excavation processing is made to data message,
The Zhi Shi ﹑ of problem are empirical to wait qualitative constraint system goal function is showed phenomena such as Duo Feng ﹑ very lead or is rigid,
Traditional nonlinear programming approach (such as Niu Dun Fa ﹑ interpolation Fa ﹑ gradient method) based on data mining technology is shown necessarily
Fragility, hardly result in the globally optimal solutions of problems, these fragility are shown：(1) single-point computing mode is unfavorable for
Calculate the raising of Real time Efficiency；(2) the improvement movement of local direction is unfavorable for jumping out local optimum region often；(3) optimization is asked
Object function and constraint function in topic model limit the good application of method.Such as Newton method, system is required in practical application
Object function is that high-order can be micro-.Therefore, traditional data digging method towards nonlinear programming problem due to its own
Limitation and the narrow performance of application, though having carried out a degree of processing to problem, still cannot get the complete of synthtic price index
Office's minimax solution.The present invention carries out the information extraction technology in data mining space with other intelligent optimization methods in nature
Organically combine, to solve the Non-Linear Programming computational problem run into data mining process, it will make globally optimal solution can
Reliability and stability are greatly improved.
In data handling procedure, intelligent optimization method is as a kind of effective technology applied to nonlinear programming problem,
It is widely applied in Shuo according to fields such as Wa Jue ﹑ Ren work Zhi Neng ﹑ Ji device Xi ﹑ parallel computations.Such as, Zhang Huiping propose based on
The global optimization approach of data mining technology, information extraction technology is organically combined to jump out with the random perturbation of genetic algorithm
Local extremum trap, so as to obtain globally optimal solution, (Zhang Huiping, wears global optimization approaches of the ripple based on data mining technology
[C] // Chinese process control meeting 2006:485-488).Solution waits greatly idle under focus control mode for substation
Compensation and voltage-controlled problem, it is proposed that based on correlation rule system ant colony idle work optimization method (solution is big, Gong Jinxia,
Xu Jingsong, waits substations of the based on data mining technology idle ant colony optimization algorithm [J] electric power system protection and controls,
2009, 37(10):19-26), ant colony optimization algorithm is improved, established idle complete based on real data Result
Office's optimization overall mathematical model.Bai Shibing proposes that one kind is based on neutral net and particle group optimizing to realize data-optimized excavation
Data mining algorithm (research [J] laser of data mining algorithms of the cypress generation soldier based on neutral net and particle group optimizing
Magazine, 2017,38 (3):88-92), the global kernel function and mixed kernel function of differentiation distributed data digging, structure are calculated
Build Mining Decision model.It is non-with Multi-dimensional constraint that plum great waves etc. proposes that a kind of improved intuitionistic fuzzy genetic algorithm is used to solve
(plum great waves, Hua Jixue, Wang Yi solve the improvement intuitionistic fuzzy genetic algorithm of nonlinear programming problem to linear programming problem
Computer science, 2016,43 (9):250-254), the big little structure phase of individual adaptation degree with genetic algorithm in iteration optimizing
The degree of membership and non-affiliated degree function of feasible solution are answered, it is non-linear that nonlinear programming problem intuitionistic fuzzy is converted into intuitionistic fuzzy
Planning problem expansion solves.Yan Shuaiyin when solving nonlinear programming problem for traditional genetic algorithm local search ability compared with
It is weak, the defects of penalty solving precision is not high, Nonlinear Programming Algorithm is incorporated into genetic algorithm, proposed a kind of based on dynamic
(Yan Shuaiyin, Bao Ruifeng, Li Ruiqin, wait the non-linear rule of dynamic penalty functions to the Non-Linear Programming genetic of state penalty
Draw genetic algorithm and apply machine drivings, 2015 (2) in automotive transmission:146-149).As it can be seen that data mining
Cheng Zhong, intelligent optimization method are suitable for solving nonlinear programming problem, and intelligent optimization method is dug technology with data combines
Nonlinear programming problem is solved, further deeply excavating for information is beneficial to, obtains true statistics meaning and practical significance becomes
In consistent globally optimal solution.
Currently, as a kind of important optimization tool in intelligent optimization method, shuffled frog leaping algorithm is towards complex optimization
Application in system problem is also of increased attention.Shuffled frog leaping algorithm is carried by Eusuff and Lansey etc.
Go out it is a kind of by natural biology imitate and produce based on swarm intelligence collaboratively searching optimization method (Eusuff M M,
Lansey K E. Optimization of Water Distribution Network Design Using the
Shuffled Frog Leaping Algorithm. Journal of Water Sources Planning and
Management, 2003,129(3):210-225).This method simulation frog colony search of food, is thought by kind of a heap sort
Want the process transmitted, the search of global wide area and local careful search are combined closely.The whole search procedures of SFLA reach mode by changing
Progressively evolve towards optimal solution or its region.Local search cause each mould because it is intragroup individual between information obtain fully
Exchange, global search cause community information mutually to be flowed in each Mo Yin colonies, are conducive to the whole evolution of population.With other intelligence
Algorithm is compared, and the feature of SFLA is shown as：Algorithm performs mechanism is concise, algorithm preset parameter is less, arithmetic programming is easier to realize.
Therefore, SFLA is as a kind of novel Optimization Solution instrument towards complicated calculations difficult problem, it is easier to scientific theory and work
Journey application study.Such as, (Zhu Guang space moulds are because of Triangle ID because of Triangle ID probability selection shuffled frog leaping algorithm for a kind of mould of Zhu Guangyu propositions
Probability selection shuffled frog leaping algorithm, 2009,15 (10):1980-1985), new algorithm has than shuffled frog leaping algorithm higher
Efficiency, than Gene hepatitis B vaccine with accuracy more and the convergency factor of higher, efficiently solves the problems, such as sequence optimization.
Deep and clear pellet etc. uses for reference the thought of molecular dynamics simulation, proposes a kind of improvement shuffled frog leaping algorithm based on molecular dynamics simulation
(Zhang Xiaodan, wasp, Zhao Li, wait improvement shuffled frog leaping algorithm data acquisition and processions of the based on molecular dynamics simulation,
2012, 27(3):327-332.), and it is applied to the test process of higher-dimension Solving Multimodal Function, achieves good global optimizing
Effect.Leapfrog algorithm (Zhang Hengwei, Han Jihong, bandit are estimated in the distribution that Zhang Hengwei etc. proposes solution service dynamic select problem
Extensively, service dynamic select algorithm research computer science, 2015,42 (5) in cloud computing environments are waited:251-254.), if
The fitness function for considering reaction time and cost has been counted, has preferably solved the service dynamic optimization under cloud computing environment
Select permeability.Antariksha etc. proposes a kind of shuffled frog leaping algorithm (Antariksha B.A. A based on Immune Clone Selection
Clonal Selection Based Shuffled Frog Leaping Algorithm// IEEE Advance
Computing Congress. New York: IEEE, 2013:125-130.), using clonal selection algorithm in population most
Excellent individual carries out optimizing, carries out optimizing to optimum individual direction to worst individual in population using SFLA, is effectively improved calculation
The global optimizing ability of method.As it can be seen that related complicated optimum problem is widely applied SFLA in numerous engineering fields, and
Achieve preferable engineer application and theory analysis effect.However, from the point of view of the achievement in research consulted both at home and abroad, SFLA is applied
Research report in nonlinear programming problem is extremely rare.Therefore, how with reference to data mining prior art advantage, it is deep
Enter the research process that SFLA is applied to nonlinear programming problem, design a kind of validity suitable for numerous Non―linear programming problems
The shuffled frog leaping algorithm of Hao ﹑ strong robustnesses, can not only theoretically enrich the achievement in research in intelligent optimization field, more can be decision-making
Person provides more broad selective category when being solved towards nonlinear programming problem, for the diversity of its method for solving.
In conclusion from the point of view of the achievement in research consulted both at home and abroad, problem existing in the prior art is：Conventional method and its
When its existing intelligent method is towards nonlinear programming problem, with stronger method directionality, its Real time Efficiency solved and
The precision of solution need to be improved.And it is current, SFLA has been successfully applied to complication system numerous in scientific theory and engineering field
Optimization problem, but the research report that SFLA is applied in nonlinear programming problem is extremely rare.Therefore, how with reference to data
Digging technology, uses for reference the successful case that SFLA is applied to other complicated optimum problems, further gos deep into SFLA and studies the science applied to section
The nonlinear programming problem in engineer application field is referred to, design invention is a kind of towards extensive different type nonlinear programming problem
More tactful shuffled frog leaping algorithms, make it have good robustness and succinct operability, can not only be policymaker in face
When being solved to nonlinear programming problem, there is provided more diversified selection approach, moreover it is possible to deeply to enrich SFLA in intelligent optimization
The achievement in research in method field provides referential theory and using foundation.
The content of the invention
In view of the problems of the existing technology, the present invention provides a kind of strategy more solved towards nonlinear programming problem
Shuffled frog leaping algorithm,
The present invention is achieved in that a kind of more tactful shuffled frog leaping algorithms solved towards nonlinear programming problem, including：
The present invention first introduces a kind of novel rule that leapfrogs, uses for reference biocenose on the basis of standard shuffled frog leaping algorithm
Middle no intelligent agent shows the characteristic of intelligent behavior by cooperation, using data mining information extractive technique, fully excavates
During repeatedly reaching in population each frog body position full detail；
Secondly, a kind of embedded cross operator is devised, before performing the crossover operation, worst frog genes of individuals is respectively embedded into
Into local optimum and global optimum's individual, using the individual architectural difference of itself of part and global optimum, by worst individual from
Each gene of body has been evenly distributed in excellent individual, is carried out worst individual depth and is evolved；
Finally, computing repeatedly for the individual adaptation degree inside Mo Yin colonies is avoided using regression routine layout strategy.
Further, the novel true environment mixed inside the regular fully simulation frog colony that leapfrogs, every frog individual are being jumped
Mould is because of the full detail of remaining intragroup frog body position where itself will be fully excavated during jump；Meanwhile mixing leapfrogs
Rule has incorporated biological motion inertia characteristics.
Further, embedded cross operator, utilizes global optimum's individualWith local optimum individualExcellent letter
Architecture is ceased, based on the two individual architectural differences of itself, worst frog genes of individuals is embedded into two individuals and performs intersection
Computing, is conducive to strengthen worst individual tachytelic evolution degree.
Further, regression routine layout strategy, is grasped for only renewal is performed to worst frog individual in each Mo Yin colonies
Make, and when remaining frog individual adaptation degree does not change, its original adaptation is retained to remaining frog individual after rearrangement
Degree, and newly-generated frog individual is inserted into external archive in bubble sort method.
Further, the novel rule that leapfrogs includes：
The futuramic rule that leapfrogs：In each Mo Yin colonies of standard SFLA, repeatedly reach according to the best green grass or young crops determined every time
Frog individual updates worst frog individual, and only the worst individual in the Mo Yin colonies is updated, and renewal policy depiction is：
In formula,rand() is the random number of a distribution between zero and one；IfFitness value better than original, thenSubstitution；Otherwise, then with global optimum's individualInstead of；Repeat more new strategy (1)
(2), if the new explanation produced is still inferior to, then randomly generate a new solution and substitute originally；
Above-mentioned more new strategy is laid particular emphasis onWithTo worst individual humidification.However, just residing for biology itself
For ecological behavioural environment, every frog, to varying degrees also can be by group in addition to being influenced by part and global optimum's individual
The influence of interior other frogs.The promotion behavior of cooperating with each other of biocenose is a kind of mutually beneficial situation of instinct, this cooperation
All-win situation to a certain extent perhaps can exceed optimum individual influence, can by it is a kind of it is uninterrupted in a manner of promote it is worst
Frog individual moves quickly into new position from current location towards optimal solution direction.Therefore, it is fully excavation frog individual office
Portion's information, extracts favourable information, devises a kind of novel more new strategy that leapfrogs in MSSFLA algorithms in the following manner:
Above formula,s(wm, n) represent to be centered around in a Mo Yin colony'sn- 1 frog colony,hRepresent frog group
Internal specific numbers,It is a normalization factor；
Formula (3) Section 2, which has taken into full account, to be looped aroundMo Yin colonies inside other frogs influence degree；Meanwhile formula
(3) it have also contemplated that frog individual keeps conduct in moving process to a kind of of self inertia state in, this design is shown；It isk- 1 step-length that leapfrogs to change when reaching, is counted as the speed of current worst frog, parameterwIt is one used
Property coefficient；The variation pattern of the inertia coeffeicent is changed in a manner of a kind of dynamic linear, i.e.,：
Wherein,w min Withw max It is the minimum value and maximum of inertia coeffeicent.iterIt is that current change reaches number,iter maxRepeatedly reach most
Big figure.
Further, the embedded cross operator, including：
In standard SFLA, ifThe position of worst frog individual cannot be substituted, random generation can be used at that time
New positionSubstitute worst frog individual；However, this random substitution mode can substantially weaken Mo Yin colonies it is overall into
Change, and random fashion and the superiority that can guarantee that new individual.And global optimum's individualWith local optimum individualHave
Excellent information architecture, makes full use of the architectural difference of its own, it will contributes to worst individual depth to evolve.Cause
This, using embedded cross operator, replaces random substitution mode in standard SFLA, will ensure that the position of new individual is completely superior to
Worst individual current location；The process is described using with 4 gene position sequences corresponding individual.
Further, it is described to be included using corresponding individual description process with 4 gene bit sequences：
First, by worst individualp w Gene be respectively embedded in local optimum individualp l With local optimum individualp g , so as to generate
The individual new to twoC 1,C 2.The selection of embedded point, which uses, to be correspondingly embedded in, or is embedded in since first position of gene；
Secondly, crosspoint is selectedoc, to individualC 1WithC 2Crossover operation is performed, the process is left partly using crosspoint is intercoursed
Portion or right side, or corresponding left and right are intercoursed, individual Diversity after being intersected with enhancing.In addition, this interleaved mode
Multiple-spot detection mode can also be selected；
Finally, individual intersection obtained is divided into left and right two parts by gene point, compares left halfL 1WithL 2Gene order, is selected
It is preferred that going out excellent genes sequence replaces worst individualp w 。
Further, regression routine strategy is designed, is specifically included：
For true environment, for each mould because it is intragroup every time circulation in, except worst frog individual position generation
Become outside the pale of civilization, remaining frog individual does not change, remaining individual fitness of itself does not change；Then utilize
Regression routine layout strategy can avoid repeating for computing resource, specifically include：
Step 1, using data mining information extractive technique, in area of feasible solutions centerU(Z,r), withZCentered on,rFor half
Footpath, constructs initial population, and calculates the Shi Ying Du ﹑ sequences of individual and be grouped and be sequentially completed；
Step 2, according to packetm 1,m 2, the more new strategy that leapfrogs in equation (3) is performed, improves worst frog individualP 5,P 4, point
Two corresponding new individuals have not been obtainedP 5_new, P 4_newIf new individualP 5_new, P 4_newIt is inferior to individualP 5,P 4, then perform embedding
Enter formula crossover operator, it is ensured that new individual is better than old individual；
Step 3, storagem 1In in addition to worst frog remaining individual enter external archive.Meanwhile willP 4_newBy bubble sort side
Method is inserted into external archive concentration；Similarly, storem 2In in addition to worst frog remaining individual enter external archive, and
WillP 5_newExternal archive is inserted into by bubble sort method；
Step 4, obtains a final external archive collection comprising new individual.Whether EOT end of test condition meets, if meeting defeated
Go out as a result, algorithm performs terminate；Otherwise, it is grouped againm 1,m 2, and go to step 2.
Further, design MSSFLA algorithm flows include：
1）Wanted using data mining information extraction skill, generation includesmThe initial population of frog, and calculate every frog individual
Fitnessf；
2）All frogs are divided into W subgroup, each Mo Yin colonies includenSub- frog；
3）Each Mo Yin colonies are tested；
Further, each Mo Yin colonies are tested, specifically included：
A) first, in different Mo Yin colonies, the rule execution that leapfrogs that frog individual is determined according to above-mentioned equation (3) was jumped
Journey, is moved to new position；
If b) new position is better than old position, worst frog individual is moved to new position, and shifts and move d);Otherwise, insertion is performed
Formula crossover operator；
If c) frog offspring individual is better than the worst frog of parent, replacement operation is performed, otherwise, a frog is generated at random, turns
To b);
D) whether current mould terminates because of intragroup local search, if search terminates, performs regression routine layout strategy;
4) T local search whether is completed, most office's optimal result is exported if completing, otherwise, is transferred to step 2).
Advantages of the present invention and good effect are：The method of the present invention is applied to solution Non-Linear Programming in data mining and asks
Topic, its processing procedure have the characteristics that illustrative simplicity, universality are strong.To make worst a physical efficiency efficiently extract having for search space
Information is imitated, the method for the present invention introduces a kind of novel rule that leapfrogs, and realizes characterization of the individual to search space, fully excavates
The full detail of each frog body position during repeatedly reaching.Secondly, it is poor fully to excavate global and local optimum individual structure
It is different, a kind of embedded cross operator is devised in invention, worst frog genes of individuals is respectively embedded in local optimum and the overall situation
In optimum individual, then crossover operation is performed, be conducive to worst individual depth and evolve.To accelerate convergence speed of the algorithm, this hair
The bright regression routine layout strategy that introduces avoids computing repeatedly for Mo Yin colonies Personal fitness, is conducive to data message
Good application.In addition, proposed inventive method enhances algorithm pair using data mining information extractive technique structure initial population
The search spread ability of feasible zone, is conducive to the depth excavation of data message during algorithm iteration.By being surveyed to various criterion
The interpretation of result that examination case obtains, the method for the present invention, can towards all kinds of different types of linear programmings or nonlinear programming problem
Fully excavate search space in useful information, be conducive to accelerate solution search speed, improve globally optimal solution credibility and
Stability, makes the globally optimal solution in statistical significance and practical significance reach unanimity.
Brief description of the drawings
Fig. 1 be it is provided in an embodiment of the present invention solved towards nonlinear programming problem more tactful shuffled frog leaping algorithms the step of show
It is intended to；
Fig. 2 is the schematic diagram of embedded cross operator provided in an embodiment of the present invention；
Fig. 3 is the schematic diagram of regression routine layout strategy provided in an embodiment of the present invention；
Fig. 4 is the schematic diagram of test function provided in an embodiment of the present invention；
Fig. 5 is the schematic diagram of the evolution curve procedures between algorithms of different provided in an embodiment of the present invention；
Fig. 6 is the schematic diagram of test result provided in an embodiment of the present invention；
Fig. 7 is the test result after 100 independent operatings such as MSSFLA ﹑ SFLA ﹑ LPSO and MSFLA that inventive embodiments provide
Structure diagram；
Fig. 8 is the result schematic diagram that SFLA and MSSFLA provided in an embodiment of the present invention solve multiple target 0-1 problems 1；
Fig. 9 is the result schematic diagram that MSSFLA and SFLA provided in an embodiment of the present invention are applied to multi-Objective 0-1 Knapsack Problems 1；
Figure 10 is the result schematic diagram that SFLA and MSSFLA provided in an embodiment of the present invention solve multiple target 0-1 problems 2；
Figure 11 is the result schematic diagram that MSSFLA and SFLA provided in an embodiment of the present invention are applied to multi-Objective 0-1 Knapsack Problems 2.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, the present invention is carried out
It is further described.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit
The present invention.
From the point of view of the achievement in research consulted both at home and abroad, research SFLA being applied in nonlinear programming problem is reported extremely
It is rare, and SFLA is towards having many successful stories in other complex systems optimization problems, its method for solving compared with compared to
Traditional optimization method has more preferable real-time and validity.Therefore, how to go deep into SFLA and be applied to nonlinear programming problem
Research process have more challenge.Currently, the existing solution technique applied to nonlinear programming problem, majority have stronger
Method directionality, and during towards nonlinear programming problem, the Real time Efficiency of its method and the precision of solution all have much room for improvement.Therefore,
It is a kind of towards extensive different types of nonlinear programming problem method for solving to design invention, can not only be that policymaker is non-thread in solution
Property planning problem when, there is provided the variation of system of selection approach, moreover it is possible to for deeply enrich SFLA intelligent optimization field research
Achievement provides necessary theory and using foundation.
Below in conjunction with the accompanying drawings and specific embodiment is further described the application principle of the present invention.
As shown in Figure 1-Figure 3, the more strategy mixing frogs provided in an embodiment of the present invention solved towards nonlinear programming problem
Jump algorithm, including：
1) it is novel to mix the regular true environment fully simulated inside frog colony that leapfrogs, every frog in MSSFLA
Body will make full use of where itself remaining frog individual information in Mo Yin colonies in jump.Meanwhile this mixing leapfrogs rule
Biological motion inertia characteristics are then also incorporated.Compared with standard SFLA movement rules, objectivity and authenticity are had more.
2) embedded cross operator, the crossover operator in genetic algorithm different from the past, embedded cross operator it is excellent
Point is：Using the excellent information architecture of global optimum's individual and local optimum individual, based on the two individual structures of itself
Difference, worst frog genes of individuals is embedded into two individuals perform crossing operation will may consequently contribute to it is worst it is individual it is quick into
Change.
3) regression routine layout strategy, it is contemplated that standard SFLA, only performs worst frog individual in each Mo Yin colonies
Renewal operation, and remaining frog individual adaptation degree does not change.Therefore, it is retained to remaining frog individual after rearrangement
Original fitness, and newly-generated frog individual is inserted into external archive with prosperous bubble sort method.The advantages of strategy, is
Be conducive to the Fast Convergent of population entirety, greatly saved computing resource, avoid computing repeatedly for fitness.It is intended to protect
Point：
It is novel to mix leapfrog Gui Ze ﹑ embedded cross operators and regression routine layout strategy, all it is other intelligent optimization methods
In unexistent technology, these three technical tactics are form the described more tactful shuffled frog leaping algorithms of the method for the present invention important
Part, important influence is produced to the optimal solution optimizing ability for strengthening nonlinear programming problem.
With reference to specific embodiment, the invention will be further described,
Fig. 4 is one group of standard nonlinear planning function test set.
Fig. 5 is the evolution curve procedures figure that MSSFLA is obtained in the standard test functions collection.
The more tactful shuffled frog leaping algorithms proposed in the present invention are referred to as MSSFLA, and with SFLA (Eusuff. M.M,
Lansey.K, Pasha.F. Shuffled Frog Leaping Algorithm: a memetic meta- heuristic
for discrete optimization. Enginering Optimization, 2006, 38:129-154.) ﹑ LPSO
(Poli. R, Kennedy. J, Blackwell. T. Particle swarm optimization. Swarm
intelligence, 2007,1(1):33-57.) and MSFLA (Li. X, Lou. J.P, Chen. M.R, Wang.N. An
improved shuffled frog-leaping algorithm with external optimization for
continuous optimization. Information Sciences, 2012, 192:143-151.) etc. all kinds of mixing
The algorithm that leapfrogs carries out test and comparison, and the collection of functions description for test is as shown in Figure 4.
Non―linear programming function is respectively divided into two groups in Fig. 4, no mode and multi-modal function.These functions are feasible at its
There are multiple local best points in region mostly.The feature of these test functions is not quite similar, such as multi-modal function local optimum number
Mesh can be with the increase of problem dimension, its optimizing cost can exponentially form increase, and this fabulous the testing out of feature energy is answered
Search performance for all kinds of shuffled frog leaping algorithms of multi-modal function.Different shuffled frog leaping algorithms are being tested applied to function
During, if the solution that some algorithm is found is better than acceptable solution, the execution of the algorithm, which is considered as, to be run successfully.For test ratio
Compared with fairness, all functions are arranged at 30 dimensions.
In the present invention, the parameter of MSSFLA is arranged to：Maximum repeatedly reaches number 2 × 105, frog individual sum 200, group's number
For 10, the frog number of each group is 20, and in group is repeatedly 1 up to number, and maximum leapfrogs step-length as maximum search scope
0.5 times.It is local to be repeatedly arranged to 2 and 1000 up to number and global number repeatly.Similarly, other comparison algorithms use its citation
The parameter setting offered, and global change up to number maximum is arranged to 1000.Fig. 5 shows MSSFLA methods described in the invention at six
The fitness obtained on test function is averagely evolved curve procedures.
Fig. 6 shows average optimum solution (Average) and its corresponding standard variance (SD) after each function test, this two
Item data is used for the convergence efficiency for testing institute's comparison algorithm.All kinds of algorithms are applied to average suitable after 100 execution of different functions
Response curve is as shown in Figure 5.Just as shown in fig. 6, for Average and SD, compared to other shuffled frog leaping algorithms,
MSSFLA substantially has extraordinary superior function, and the performance indicator on test function is better than other comparison algorithms.This
Outside, for the overall situation of the evolution curve procedures of Fig. 5 repeatedly reaches number, MSSFLA can comparatively fast converge to globally optimal solution.Such as, scheme
In 5 (a), MSSFLA converges to optimal solution when repeatedly reaching number and being 500, than 1000 times predetermined efficiency for accelerating one times.To the greatest extent
Average optimal solution can also be converged to by managing other algorithms, but the required number that repeatedly reaches will substantially be more than MSSFLA, and thus convergence rate will
It is inferior to MSSFLA.Forf 2For function, MSSFLA converged to for about 700 generations；Forf 3Withf 5For function, MSSFLA convergences
To about 900 generations；Forf 6For, MSSFLA converged to for about 750 generations.Obviously, compared to other comparison algorithms, MSSFLA to
Optimal solution region can be quickly converged on the function test set gone out.
For the validity of further check algorithm, MSSFAL and other comparison algorithms are distinguished into execution 100 times again, such as
Fruit certain hold process obtain optimal valuefMeetf≤γ(γRepresent an acceptable value), this time simulation calculating is considered as holding
Go successfully.Test result is shown in the figure 7, in the figureS r Represent success rate and optimizing average time respectively with AVT.
In six test functions, MSSFLA existsf 1﹑f 2﹑f 3Deng obtaining complete success on function.Especially functionf 3's
Test result will be substantially better than other comparison algorithms.Although SFLA and LPSO obtain optimal solution very on multi-modal function
Difficulty, but MSSFLA but can optimizing success.Further it should be noted that：Success rates of the MSSFLA on six test functions
It is higher than 90%.As it can be seen that justS r For AVT, MSSFLA, which solves the performance without mode and multi-modal function, will be substantially better than it
Its three kinds of algorithms.
In conclusion MSSFLA and other several comparison algorithms existf 1~f 6Test result compare, show this hair
Bright described MSSFLA can be obtained preferably as a result, either Average ﹑ SD ﹑S r And AVT, MSSFLA can be obtained
Preferably as a result, having obvious advantage.This is because more tactful shuffled frog leaping algorithms (MSSFLA) that the present invention describes incorporate
A kind of novel mixing leapfrogs rule, and the rule is from biological behavior characteristic angle, by the win-win cooperation between biocenose
Thought has incorporated frog individual moving process.It is different from simple crossover process individual in genetic algorithm, embedded cross algorithm
The difference of the excellent information architecture of global optimum's individual and local optimum individual has been used, worst frog genes of individuals is embedding
Enter and perform crossing operation into two individuals, accelerate worst individual evolutionary rate.Regression routine layout strategy is in frog optimizing
A large amount of computing resources have greatly been saved in the application of process, accelerate the convergence rate of population entirety,
For application process of the description the method for the present invention in Practical Project field, by taking multi-Objective 0-1 Knapsack Problems as an example, the problem
It is a kind of typical multiobjective non linear programming problem, research and solution problems not only have its actual application value, and
More important theory analysis value.MSSFLA is applied in multi-Objective 0-1 Knapsack Problems, may compare before and after SFLA is improved
As a result.It is described as follows：
Knapsack problem 1:There are 100 articles, 2 knapsacks, initial population individual amount is arranged to 400, and sub- population invariable number is 20.
The Evolution of Population Policy Result obtained using two kinds of different optimization methods of MSSFLA and SFLA is as shown in Figure 8 and Figure 9.
Knapsack problem 2:There are 100 articles, 3 knapsacks, initial population individual amount is arranged to 400, sub- population invariable number
For 20.In this case, Evolution of Population Policy Result Figure 10 for being obtained using two kinds of different optimization methods of MSSFLA and SFLA and
Shown in Figure 11.
From Fig. 8 and Fig. 9 as it can be seen that in same problem test, based on identical experimental setup parameters, using MSSFLA than
To be got well using initial SFLA effects.The former can find solution more more preferable than the latter at the very start in algorithm, reach process with changing
Progress, the solution that MSSFLA is found at the end of the later stage is more satisfactory than the solution that original SFLA is found.Figure 10 is transparent to show that
Go out that the convergence rate of MSSFLA is faster than original SFLA algorithms, and MSSFLA begins to restrain when 600 generation, and SFLA
Repeatedly there is the sign for being absorbed in local optimum up to initial stage, gradually convergence searches out globally optimal solution until the 800th beginning, Figure 11
The adaptive value that the results show goes out the solution that MSSFLA is obtained is better than the solving result of SFLA.
As seen from the above analysis, compared to other optimization methods, the method for the present invention is better than simple SFLA, described
Algorithm MSSFLA be a kind of optimal most optimum distribution of resources scheme.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of more tactful shuffled frog leaping algorithms solved towards nonlinear programming problem, it is characterised in that described towards non-thread
Property more tactful shuffled frog leaping algorithms for solving of planning problem, including：
The present invention first introduces a kind of novel rule that leapfrogs, has used for reference biota on the basis of standard shuffled frog leaping algorithm
The characteristic of intelligent behavior is shown by cooperation without intelligent agent in body, takes full advantage of during repeatedly reaching each frog in population
The full detail of body position；
Secondly, a kind of embedded cross operator is devised, which is respectively embedded in local optimum and complete by worst genes of individuals
In office's optimum individual gene, then perform crossing operation；Using the individual architectural difference of itself of part and global optimum, by worst
Different genes are uniformly distributed in excellent individual in body, are carried out worst individual depth and are evolved；
Finally, computing repeatedly for the individual adaptation degree inside Mo Yin colonies is avoided using regression routine layout strategy.
2. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
The novel true environment mixed inside the regular fully simulation frog colony that leapfrogs, every frog individual will be abundant in jump
Using mould where itself because of remaining intragroup frog individual information；Meanwhile mix the rule that leapfrogs and incorporated biological motion inertia
Feature.
3. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
Embedded cross operator, utilizes global optimum's individualWith local optimum individualExcellent information architecture difference,
Gene in worst frog individual is respectively embedded in two individuals and performs crossing operation, this is beneficial to accelerate worst frog individual
Evolutionary rate.
4. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
Regression routine layout strategy, only renewal operation is performed for previous in each Mo Yin colonies to worst frog individual, and remaining is blue or green
Present situation when frog individual adaptation degree does not change, retains its original fitness, no to remaining frog individual after rearrangement
Compute repeatedly；And newly-generated frog individual is inserted into external archive in bubble sort method.
5. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
The novel algorithm that leapfrogs includes：
The futuramic rule that leapfrogs：In each Mo Yin colonies of standard SFLA, repeatedly reach every time according to best determined
Body updates worst individual, and only worst individual in the Mo Yin colonies is updated, and renewal policy depiction is：
In formula,rand() is the random number of a distribution between zero and one；IfFitness value better than original,
ThenSubstitution；Otherwise, then with global optimum's individualInstead of；More new strategy (1) and (2) are repeated,
If the new explanation produced is still inferior to, then randomly generate a new solution and substitute originally；
Above-mentioned more new strategy is laid particular emphasis onWithTo worst individual humidification；However, the just residing life of biology itself
For state behavioural environment, every frog, to varying degrees also can be by addition to being influenced by part and global optimum frog individual
The influence of other frog individuals in group；Biocenose is this by a kind of mutually beneficial evolution characteristic that shows of cooperation instinct
Win-win cooperation situation to a certain extent perhaps can exceed optimum individual influence, by it is a kind of it is uninterrupted in a manner of promote most
Poor frog individual moves quickly into new position from current location towards optimal solution direction.In view of such a biobehavioral is special
Property, a kind of novel more new strategy that leapfrogs is devised in MSSFLA algorithms in the following manner:
Above formula,s(wm, n) represent to be centered around in a Mo Yin colony'sn- 1 frog colony,hRepresent frog colony
Interior specific numbers,It is a normalization factor；
Formula (3) Section 2, which has taken into full account, to be looped aroundMo Yin colonies inside other frogs influence degree；Meanwhile formula
(3) frog individual is considered in show a kind of retention performance of self inertia state, this design in moving process；It isk- 1 step-length that leapfrogs to change when reaching, is counted as the speed of current worst frog, parameterwIt is one used
Property coefficient；The variation pattern of the inertia coeffeicent is changed in a manner of a kind of dynamic linear, i.e.,：
Wherein,w min Withw max It is the minimum value and maximum of inertia coeffeicent.iterIt is that current change reaches number,iter maxRepeatedly reach
Maximum number.
6. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
The embedded cross operator, including：
In standard SFLA, ifThe position of worst frog individual cannot be substituted, at that time can be with generating at random
New positionSubstitute worst frog individual；However, this random substitution mode can substantially weaken the whole evolution of Mo Yin colonies,
And random fashion does not ensure that the superiority of new individual；In view of global optimum's individualWith local optimum individual
There is excellent information architecture, make full use of its respective architectural difference, it will contribute to worst individual depth to evolve；
Therefore, the random substitution mode in standard SFLA is fallen using the embedded cross policy replacement of design, it is ensured that the position of new individual
It is completely superior to worst individual current location, which is described using the corresponding individual with 4 gene bit sequences.
7. the more tactful shuffled frog leaping algorithms solved as claimed in claim 6 towards nonlinear programming problem, it is characterised in that
The individual of the use with 4 gene bit sequences, which describes the process, to be included：
First, by worst individualp w Gene be respectively embedded in local optimum individualp l With global optimum's individualp g In, so as to generate
Obtain two new individualsC 1,C 2.The selection of the insertion point is used and is correspondingly embedded in, or is embedded in since first position of gene；
Secondly, crosspoint is selectedoc, to individualC 1WithC 2Crossover operation is performed, which uses and intercourse crosspoint left side
Or right side, or correspond to left and right and intercourse, individual Diversity, this interleaved mode can also be selected after being intersected with enhancing
Multiple crosspoints；
Finally, individual intersection obtained is divided into left and right two parts by gene point, compares left halfL 1WithL 2Gene order, is selected
It is preferred that going out excellent genes sequence replaces worst individualp w 。
8. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
Regression routine strategy is designed, is specifically included：
For true environment, for each mould because it is intragroup every time circulation in, except worst frog individual position generation
Become outside the pale of civilization, remaining frog individual does not change, remaining individual fitness of itself does not also change.Therefore, may be used
Repeating for computing resource is avoided using regression routine layout strategy.Specifically include：
Step 1, similar to standard SFLA, generates initial population, and the Shi Ying Du ﹑ sequences and packet for calculating individual are sequentially completed；
Step 2, according to packetm 1,m 2, the more new strategy that leapfrogs in equation (3) is performed, improves worst frog individualP 5,P 4, respectively
Two corresponding new individuals are obtainedP 5_new, P 4_newIf new individualP 5_new, P 4_newIt is inferior to individualP 5,P 4, then insertion is performed
Formula crossover operator, it is ensured that new individual is better than old individual；
Step 3, storagem 1In in addition to worst frog remaining individual enter external archive, meanwhile, generalP 4_newBy bubble sort
Method is inserted into external archive concentration；Similarly, storem 2In in addition to worst frog remaining individual enter external archive,
And willP 5_newExternal archive is inserted into by bubble sort method；
Step 4, obtains a final external archive collection comprising new individual.Whether EOT end of test condition meets, if meeting defeated
Go out as a result, algorithm performs terminate；Otherwise, it is grouped againm 1,m 2, and go to step 2.
9. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, it is characterised in that
Design MSSFLA algorithm flows include：
1）Generation includesmThe initial population of frog, calculates the fitness of every frog individualf；
2）All frogs are divided into W subgroup, each Mo Yin colonies includenSub- frog；
3）Each Mo Yin colonies are tested.
10. the more tactful shuffled frog leaping algorithms solved as claimed in claim 1 towards nonlinear programming problem, its feature exist
In testing each Mo Yin colonies, specifically include：
A) first, in different Mo Yin colonies, the rule execution that leapfrogs that frog individual is determined according to above-mentioned equation (3) was jumped
Journey, is moved to new position；
If b) new position is better than old position, worst frog individual is moved to new position, and is transferred to d);Otherwise, insertion is performed
Formula crossover operator；
If c) frog offspring individual is better than the worst frog of parent, replacement operation is performed;Otherwise, a frog is generated at random, is turned
To b);
D) whether current mould terminates because of intragroup local search, if search terminates, performs regression routine layout strategy.
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