CN110222812A - A kind of improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy - Google Patents

A kind of improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy Download PDF

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CN110222812A
CN110222812A CN201910516393.4A CN201910516393A CN110222812A CN 110222812 A CN110222812 A CN 110222812A CN 201910516393 A CN201910516393 A CN 201910516393A CN 110222812 A CN110222812 A CN 110222812A
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chestnut
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赵世杰
高雷阜
徒君
于冬梅
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Liaoning Technical University
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Abstract

The invention discloses a kind of periodically to successively decrease the improvement chestnut wing hawk optimization algorithm of regulating strategy with energy, step are as follows: generate the initial position of N chestnut wing hawk in solution space using random generation strategy；Update prey energy state and Jump intensity；Energy is updated periodically to successively decrease regulatory factor and prey energy；According to the relative size of prey energy and success rate of escaping, the location updating and solution validity check of chestnut wing hawk population at individual are executed；The fitness value of chestnut wing hawk population at individual is calculated, and determines current optimal solution and optimal objective value by principle of optimality；Step S2~S6 is repeated, until the number of iterations t reaches T；Return to optimal solution and optimal objective value.The present invention introduces the regulatory factor that periodically successively decreases in prey ENERGY E decrementing procedure, to guarantee that prey energy successively decreases with iterative process in cycle dynamics, to effectively multicycle optimizing of the enhancing chestnut wing hawk optimization algorithm between global search and local search and more be approached the accurate solution of the true optimal solution of problem to be optimized.

Description

A kind of improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy
Technical field
Periodically successively decrease regulating strategy the invention belongs to the technical field of intelligent optimization algorithm more particularly to a kind of band energy Improvement chestnut wing hawk optimization algorithm.
Background technique
Intelligent optimization algorithm (Intelligence Optimization Algorithm, IOA) is a kind of inspires in specific The random optimization technology based on group of natural phenomena, with initial value insensitivity, mechanism it is simple it can be readily appreciated that and independent of The advantages that gradient information and become solve higher-dimension, non-linear, challenge a kind of important algorithm, be successfully applied at present The engineering mathematics such as Machine Design optimization, intelligent control and scheduling, Model Parameter Optimization field.It is inspired at present according to suffered nature The difference of mechanism, intelligent algorithm can be divided into 3 major class: the evolutional programming (Evolutionary based on genetic evolution mechanism Programming, EP), genetic algorithm (Genetic Algorithms, GA) etc.；The population for simulating biological cluster behavior is excellent Change algorithm (Particle Swarm Optimization, PSO), ant group algorithm (Ant Colony Optimization, ACO) Deng；Simulated annealing (Simmulated Annealing, SA), multiverse optimization based on specific physical-chemical principle Algorithm (Multi-Verse Optimizer, MVO) etc..In view of the preferable iterative search performance, relatively strong steady of intelligent optimization algorithm Robustness etc., the intelligent optimization algorithm for simulating new inspiration mechanism also continue to bring out, chestnut wing hawk optimization algorithm (Harris hawks Optimization, HHO) it is a kind of new intelligent optimization algorithm based on biological cluster behavior.
Chestnut wing hawk optimization algorithm is equal to 2019 based on the cooperation row during Li Chi hawk group capture prey by Heidari For and propose, by modelling chestnut wing hawk and prey escape during hawk underriding capture with prey energy linearity weaken etc. inspire Mechanism represents the feasible solution of institute's optimization problem with chestnut wing hawk, represents optimal solution obtained by problem current iteration with prey, passes through more Chestnut wing hawk is by successive ignition parallel search and finally seeks obtaining Optimum Solution (approximate optimal solution).
4 kinds of dimensions (30 dimensions, 100 dimensions, 500 peacekeepings that chestnut wing hawk optimization algorithm (HHO) passes through 29 groups of benchmark test functions 1000 dimension) comparative experiments demonstrate its iteration optimization performance better than genetic algorithm, particle swarm algorithm, biogeography optimization calculate Method, flower pollination algorithm, grey wolf optimization algorithm, bat algorithm, glowworm swarm algorithm, cuckoo searching algorithm, the optimization of moth flame 11 kinds of intelligent optimization algorithms such as algorithm, learning aid optimization algorithm and differential evolution algorithm；Simultaneously with three-bar truss, drawing-pressing spring, It is preferable that 6 groups of engineering design optimization problems such as pressure vessel, welded grider, multidisc clutch brake and rolling bearing verify it Engineering practical value.
Currently, chestnut wing hawk optimization algorithm is in starting developing stage, needs to be carried out exploratory research and incorporate more Nature Self-configuring is explored performance drawn game portion exploitation performance further to improve the global of chestnut wing hawk optimization algorithm, and is expanded Applied to more application fields to embody its preferable practical value and realistic meaning.
In chestnut wing hawk optimization algorithm, the size of prey ENERGY E reflects chestnut wing hawk to the capture ability of Optimum Solution, energy The more big underriding for more easily escaping hawk is measured to surround and seize, on the contrary it is easier to be captured.Prey ENERGY E is from maximum value to most in traditional HHO algorithm The small linear decrement states of value, i.e. alternation process between maximum value-minimum value of tradition HHO algorithm Exactly-once energy.When When prey ENERGY E is larger, HHO algorithm mainly carries out global search to solution space；And when prey ENERGY E is smaller, then algorithm Local search is substantially carried out with the optimal solution of determination problem to be optimized.Therefore, prey ENERGY E directly influence HHO algorithm and Row iteration optimizes performance, and original definition formula is
Wherein, T indicates maximum number of iterations, E0Indicate the original state of ENERGY E and with iterative process in section (- 1,1) Interior dynamic change.The dynamic of prey ENERGY E of escaping controls the iterative search process of algorithm: when | E | when >=1, HHO algorithm is executed Heuristic process, i.e. chestnut wing hawk search for the different zones of solution space to explore the position of prey rabbit；When | E | when < 1, HHO algorithm Search solution neighborhood is to execute recovery process.
In existing HHO algorithm, only linear decrease is primary from peak to peak for prey ENERGY E.And in practical nature In, it is not that will once be captured successfully with greater probability that chestnut wing hawk, which surrounds and seize prey (rabbit),；Prey rabbit is not yet simultaneously The chestnut wing hawk that can leave captures but tries one's best to escape surrounding and seize for chestnut wing hawk, i.e. prey rabbit always seeks during escaping Bushes, cave etc. is asked to hide object to avoid the underriding of chestnut wing hawk and surround and seize, but the process will disappear because prey rabbit actively escapes Its big energy is consumed, prey will rest and reorganize a period of time after ENERGY E is restored and wait for an opportunity to hide from currently if escaping successfully Object is kept away to leave it is expected that that jumps out chestnut wing hawk as early as possible surrounds and seize circle；Hide object once should leave, will be opened between chestnut wing hawk and prey rabbit The life and death gambling process of a beginning new round " surround and seize-escape ", each round of prey rabbit, which is hidden, always consumes a large amount of energy, so After several wheels, prey rabbit is finally just captured due to ENERGY E is depleted by chestnut wing hawk.I.e. the ENERGY E of prey rabbit " is being enclosed Catch-escape " it is not in the process that disposably just decrease is minimum value, but shows periodical decreasing energy changing rule, And the prior art of tradition HHO algorithm is then difficult to portray the dynamic process, therefore, it is necessary to the prey energy in existing HHO algorithm The mathematic(al) representation of amount E improves.
Summary of the invention
Based on the above the deficiencies in the prior art, periodically passed the problem to be solved by the present invention is that providing a kind of band energy Subtract the improvement chestnut wing hawk optimization algorithm of regulating strategy, it can be under the conditions of same chestnut wing hawk population scale and maximum number of iterations more The optimal solution of function is approached well, is effectively enhanced the global of algorithm and is explored performance drawn game portion exploitation performance.
In order to solve the above-mentioned technical problem, the present invention is achieved through the following technical solutions:
The present invention provides a kind of improvement chestnut wing hawk optimization algorithm of regulating strategy that periodically successively decreases with energy, including following step It is rapid:
S1: the initial position of N chestnut wing hawk is generated at solution space [LB, UB] using random generation strategy；
S2: prey energy state E is updated0With Jump intensity J；
S3: it updates energy and periodically successively decreases regulatory factor CD and prey ENERGY E；
S4: according to the relative size of prey ENERGY E and the success rate p that escapes, the location updating of chestnut wing hawk population at individual is executed And solution validity check；
S5: the fitness value of chestnut wing hawk population at individual is calculated, and determines current optimal solution and optimal objective by principle of optimality Value；
S6: repeating step S2~S6, until the number of iterations t reaches T；
S7: optimal solution x* and optimal objective value f (x*) is returned.
Optionally, in the step S1, the initialized location of chestnut wing hawk population at individual is denoted as xi=[xi,1, xi,2..., xi,D], and have:
xi,j=LB (j)+(UB (j)-LB (j)) × rand ()
Wherein, i=1,2 ..., N indicate i-th chestnut wing hawk in chestnut wing hawk population, and j=1,2 ..., D indicate to be optimized and ask J-th of dimension of variable is inscribed, LB (j) and UB (j) are respectively indicated under effective value of the solution variable to be optimized in jth dimension Limit and the upper limit, rand () indicate the random real number generated at random in section [0,1].
Optionally, in the step S2, the energy state E of prey0With the number of iterations t, dynamic is more in section [- 1,1] Newly, and have:
E0,t=2 × rand () -1
Wherein, t=1,2 ..., T indicate the current number of chestnut wing hawk population iterative search, and prey Jump intensity J is simulated The behavior of prey rabbit in nature, indicate prey avoid by chestnut wing hawk capture when and the random skip for the during of escaping is strong Degree, and dynamic updates in section [- 2,2], calculating formula Jt=2 × (rand () -1).
Further, in the step S3, energy periodically successively decrease regulatory factor CD with iteration in periodically dynamic reduce To guarantee that prey ENERGY E generally shows reduction trend, and have:
Wherein, k=0, the number of cycles that 1,2 ... expression energy periodically successively decreases, is a default integer value；The smaller table of k Show chestnut wing hawk optimization algorithm global search process more easy to carry out, the bigger expression chestnut wing hawk optimization algorithm of k part more easy to carry out Search process；
The regulatory factor CD that periodically successively decreased according to energy can must improve the prey ENERGY E iteration in chestnut wing hawk optimization algorithm more New calculating formula are as follows:
Further, in the step S4,
In the absolute value of prey ENERGY E | E | when >=1, chestnut wing hawk optimization algorithm executes global heuristic process, i.e. chestnut wing hawk Body is inhabited at random in solution space [LB, UB], and carries out location updating referring to other chestnut wing hawks or prey position according to probability, and Have:
Wherein, the position vector of chestnut wing hawk, x when x (t+1) and x (t) respectively indicate (t+1) secondary and the t times iterationrabbit And xrandIt respectively indicates current prey rabbit and chooses the position vector of chestnut wing hawk, r at random1、r2、r3、r4With p be section [0, 1] random number in；
It indicates the position average vector of all individuals in chestnut wing hawk population when current iteration, and works as and hunt Object energy | E | when < 1, chestnut wing hawk optimization algorithm then executes local recovery process, i.e., chestnut wing hawk individual is with prey ENERGY E and 0.5 Relative size and escape success rate p ∈ [0,1] and 0.5 relative size relationship common property give birth to 4 kinds and different surround and seize prey strategy.
Further, 4 kinds different to surround and seize prey strategy as follows:
(1) when p >=0.5 and | E | when >=0.5, chestnut wing hawk individual execute it is soft surrounds and seize strategy, i.e. prey has enough ENERGY Es And attempt to escape dangerous circumstances by random skip, but finally still captured by chestnut wing hawk individual, mathematical expression are as follows:
X (t+1)=Δ x (t)-E | Jxrabbit(t)-x(t)|
Wherein, △ x (t)=xrabbit(t)-x (t) indicates position difference when the t times iteration between chestnut wing hawk and prey；
(2) when p>=0.5 and | E | when<0.5, chestnut wing hawk individual executes and surrounds and seize strategy firmly, i.e., prey ENERGY E is lower and chestnut wing Hawk individual, which directly dives, attacks and captures prey suddenly, mathematicization expression are as follows:
X (t+1)=xrabbit(t)-E|Δx(t)|
(3) when p<0.5 and | E | when>=0.5, chestnut wing hawk individual execute with it is progressive quickly dive it is soft surround and seize, i.e., prey has Enough ENERGY Es simultaneously attempt to escape dangerous circumstances by random skip, but chestnut wing hawk individual takes surprise attack with optimal underriding direction Mode execute it is soft surround and seize, mathematicization expression are as follows:
Wherein, S indicates that D ties up random row vector, and LF indicates Levy flight function, and has:
Wherein, u and v indicates the random number in section (0,1), and q indicates preset constant 1.5,It indicates Gamma function；
(4) when p < 0.5 and | E | when < 0.5, chestnut wing hawk individual execute with it is progressive quickly dive surround and seize strategy, i.e. prey firmly ENERGY E is lower and chestnut wing hawk individual is executed in such a way that surprise attack is taken in optimal underriding direction and surrounded and seize firmly, mathematicization expression are as follows:
After new chestnut wing hawk population generation, examine whether solution is located in solution valid interval [LU, UB], if solution x, which exceeds, to be had Imitate section then random generation again.
Optionally, in the step S5, according to the objective function of problem to be optimized, it is right to calculate each individual in chestnut wing hawk population The target function value answered, and according to target minimization principle determines when current iteration t the corresponding optimal solution x* of prey and its optimal Target value f (x*), and have:
Optionally, in the step S6 and step S7, judge whether current iteration number t reaches maximum number of iterations T, if It is the optimal solution x* and optimal objective value f for then exporting the resulting problem to be optimized of chestnut wing hawk optimization algorithm parallel iteration optimizing (x*), on the contrary then current iteration number t increases 1 and continues to execute step S2 to step S6.
By upper, the improvement chestnut wing hawk optimization algorithm of the regulating strategy of the invention that periodically successively decreases with energy is in prey ENERGY E The regulatory factor CD that periodically successively decreases is introduced in decrementing procedure, to guarantee that prey ENERGY E is successively decreased with iterative process in cycle dynamics, To effective multicycle optimizing of the enhancing chestnut wing hawk optimization algorithm between global search and local search and more approached to The accurate solution of the true optimal solution of optimization problem；Meanwhile embodiment the result shows that, compared with traditional HHO algorithm, using the algorithm into When row high-dimensional function optimization, low optimization accuracy, algorithm robustness and higher-dimension applicability are significantly superior to chestnut in the prior art Wing hawk optimization algorithm.
The above description is only an overview of the technical scheme of the present invention, in order to better understand the technical means of the present invention, And it can be implemented in accordance with the contents of the specification, and in order to allow above and other objects, features and advantages of the invention can It is clearer and more comprehensible, below in conjunction with preferred embodiment, and cooperates attached drawing, detailed description are as follows.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, the attached drawing to embodiment is simply situated between below It continues.
Fig. 1 is that the improvement chestnut wing hawk optimization algorithm of the regulating strategy of the invention that periodically successively decreases with energy solves objective optimization The execution flow chart of problem；
Fig. 2 is that prey energy of the invention periodically successively decreases energy alternation when being respectively 0,1 and 2 of periodicity in regulating strategy The contrast schematic diagram that curve and tradition HHO algorithm operate twice；
Fig. 3 is periodically global between chestnut wing hawk and prey-part under successively decreasing regulating strategy the prey energy period of the invention Search for schematic diagram；
Fig. 4 is to improve the average fitness value fluctuating change that HHO algorithm 10 times are tested under different cycles number k in the present invention to show It is intended to；
Fig. 5 is the average fitness for improving HHO algorithm and tradition HHO algorithm in the present invention and tieing up on test function at 4 group 30 It is worth iteration contrast schematic diagram (every 10 iteration draw a contrast points)；
Fig. 6 is the average fitness for improving HHO algorithm and tradition HHO algorithm in the present invention and tieing up on test function at 4 group 200 It is worth iteration contrast schematic diagram (every 10 iteration draw a contrast points)；
Fig. 7 is the average adaptation for improving HHO algorithm and tradition HHO algorithm in the present invention and tieing up on test function at 4 group 1000 Angle value iteration contrast schematic diagram (every 20 iteration draw a contrast points)；
Fig. 8 is the average adaptation for improving HHO algorithm and tradition HHO algorithm in the present invention and tieing up on test function at 4 group 10000 Angle value iteration contrast schematic diagram (every 30 iteration draw a contrast points).
Specific embodiment
The embodiment of the invention will now be described in detail with reference to the accompanying drawings, and as part of this specification passes through Embodiment illustrates the principle of the present invention, and other aspects of the present invention, feature and its advantage will become by the detailed description It is very clear.In the attached drawing of institute's reference, the same or similar component is indicated using identical drawing reference numeral in different figures.
In the present invention, more wheels between preferably simulation prey-hawk surround and seize-escape process, change to the ENERGY E of prey Journey introduces periodical decline characteristic and proposes that prey energy periodically successively decreases regulatory mechanism: i.e. hawk is hunted when prey is surrounded and seize in underriding Object consumes a large amount of ENERGY E always to seek to hide object as far as possible and avoid surrounding and seize for hawk, and hawk then realizes to hiding object at this time The search of neighborhood；For prey after hiding a period of time of resting and reorganizing in object, primary energy is restored but be still below to ENERGY E simultaneously, That is prey ENERGY E generally tapers off situation, and prey can then wait for an opportunity to escape to jump out hawk as early as possible after energy centainly restores Environment is surrounded and seize, and hawk then can execute again underriding and surround and seize, and recycle several wheels with this, the periodicity that prey ENERGY E will occur is successively decreased Changing rule.The Optimization Mechanism that the process contains is temporarily to hide object to be equivalent to the local extremum of problem to be optimized to guarantee prey The capture of hawk, while hawk then search of the synchronously simulating to the local extremum neighborhood are escaped according to probability；And prey waits for an opportunity to escape again Hide object to another, be then equivalent to the part that hawk carries out another extreme value neighborhood and search again for, until prey energy finally exhausts And it is captured and guaranteed algorithm and seek obtaining Optimum Solution by hawk.This hawk-surrounding and seize between prey-is shown in by the directviewing description for process of escaping Fig. 3.
The periodicity of prey ENERGY E, which successively decreases to change, is conducive to HHO algorithm in the global friendship explored between part exploitation performance It is jumped for property, to realize that the overall situation-local search balances and finally seeks obtaining the true globally optimal solution of problem according to probability.The mechanism pair The mathematicization description answered, which is equivalent to, to be introduced the periodicity of ENERGY E on the basis of existing HHO algorithm and successively decreases regulatory factor CD, mathematics Expression are as follows:
Wherein, k=0, the periodicity that 1,2 ... expression prey ENERGY E is successively decreased.Fig. 2 is illustrated random two when different cycles k The prey ENERGY E variation comparison signal of secondary operation.It can be seen from the figure that the bigger HHO algorithm of periodicity k carry out it is global explore with Conversion operation between the exploitation of part is more frequent, is more easy to carry out local search procedure and global search performance is weaker；On the contrary, if The global search performance of the smaller then algorithm of periodicity k is stronger and local search performance is weak, therefore k needs reasonable set with preferably Exploit performance in the global performance drawn game portion of exploring of balanced algorithm.
The improvement chestnut wing hawk optimization algorithm of the regulating strategy that periodically successively decreases with energy of the invention the following steps are included:
S1: the initial position of N chestnut wing hawk is generated at solution space [LB, UB] using random generation strategy, wherein chestnut wing hawk The initialized location of population at individual is denoted as xi=[xi,1, xi,2..., xi,D], and have:
xi,j=LB (j)+(UB (j)-LB (j)) × rand ()
Wherein, i=1,2 ..., N indicate i-th chestnut wing hawk in chestnut wing hawk population, and j=1,2 ..., D indicate to be optimized and ask J-th of dimension of variable is inscribed, LB (j) and UB (j) are respectively indicated under effective value of the solution variable to be optimized in jth dimension Limit and the upper limit, rand () indicate the random real number generated at random in section [0,1].
S2: prey energy state E is updated0With Jump intensity J, the energy state E of prey0With the number of iterations t section [- 1, 1] dynamic updates in, and has:
E0,t=2 × rand () -1
Wherein, t=1,2 ..., T indicate the current number of chestnut wing hawk population iterative search, and prey Jump intensity J is simulated The behavior of prey rabbit in nature, indicate prey avoid by chestnut wing hawk capture when and the random skip for the during of escaping is strong Degree, and dynamic updates in section [- 2,2], calculating formula Jt=2 × (rand () -1).
S3: updating energy and periodically successively decrease regulatory factor CD and prey ENERGY E, energy periodically successively decrease regulatory factor CD with Iteration reduces in periodically dynamic to guarantee that prey ENERGY E generally shows reduction trend, and has:
Wherein, k=0, the number of cycles that 1,2 ... expression energy periodically successively decreases, is a default integer value；The smaller table of k Show chestnut wing hawk optimization algorithm global search process more easy to carry out, the bigger expression chestnut wing hawk optimization algorithm of k part more easy to carry out Search process；
The regulatory factor CD that periodically successively decreased according to energy can must improve the prey ENERGY E iteration in chestnut wing hawk optimization algorithm more New calculating formula are as follows:
S4: according to the relative size of prey ENERGY E and the success rate p that escapes, the location updating of chestnut wing hawk population at individual is executed And solution validity check；In the absolute value of prey ENERGY E | E | when >=1, chestnut wing hawk optimization algorithm executes global heuristic process, i.e., Chestnut wing hawk individual is inhabited at random in solution space [LB, UB], and carries out position referring to other chestnut wing hawks or prey position according to probability It updates, and has:
Wherein, the position vector of chestnut wing hawk, x when x (t+1) and x (t) respectively indicate (t+1) secondary and the t times iterationrabbit And xrandIt respectively indicates current prey rabbit and chooses the position vector of chestnut wing hawk, r at random1、r2、r3、r4With p be section [0, 1] random number in；
It indicates the position average vector of all individuals in chestnut wing hawk population when current iteration, and works as and hunt Object energy | E | when < 1, chestnut wing hawk optimization algorithm then executes local recovery process, i.e., chestnut wing hawk individual is with prey ENERGY E and 0.5 Relative size and the success rate p ∈ [0,1] that escapes it is different from raw 4 kinds of 0.5 relative size relationship common property surround and seize prey strategy.
4 kinds different, and to surround and seize prey strategy as follows:
(1) when p >=0.5 and | E | when >=0.5, chestnut wing hawk individual execute it is soft surrounds and seize strategy, i.e. prey has enough ENERGY Es And attempt to escape dangerous circumstances by random skip, but finally still captured by chestnut wing hawk individual, mathematical expression are as follows:
X (t+1)=Δ x (t)-E | Jxrabbit(t)-x(t)|
Wherein, △ x (t)=xrabbit(t)-x (t) indicates position difference when the t times iteration between chestnut wing hawk and prey；
(2) when p>=0.5 and | E | when<0.5, chestnut wing hawk individual executes and surrounds and seize strategy firmly, i.e., prey ENERGY E is lower and chestnut wing Hawk individual, which directly dives, attacks and captures prey suddenly, mathematicization expression are as follows:
X (t+1)=xrabbit(t)-E|Δx(t)|
(3) when p<0.5 and | E | when>=0.5, chestnut wing hawk individual execute with it is progressive quickly dive it is soft surround and seize, i.e., prey has Enough ENERGY Es simultaneously attempt to escape dangerous circumstances by random skip, but chestnut wing hawk individual takes surprise attack with optimal underriding direction Mode execute it is soft surround and seize, mathematicization expression are as follows:
Wherein, S indicates that D ties up random row vector, and LF indicates Levy flight function, and f (Y) and f (Z) then indicate corresponding function It is worth (fitness value), and has:
Wherein, u and v indicates the random number in section (0,1), and q indicates preset constant 1.5,It indicates Gamma function；
(4) when p < 0.5 and | E | when < 0.5, chestnut wing hawk individual execute with it is progressive quickly dive surround and seize strategy, i.e. prey firmly ENERGY E is lower and chestnut wing hawk individual is executed in such a way that surprise attack is taken in optimal underriding direction and surrounded and seize firmly, mathematicization expression are as follows:
After new chestnut wing hawk population generation, examine whether solution is located in solution valid interval [LU, UB], if solution x, which exceeds, to be had Imitate section then random generation again.
S5: the fitness value of chestnut wing hawk population at individual is calculated, and determines current optimal solution and optimal objective by principle of optimality Value calculates the corresponding target function value of each individual in chestnut wing hawk population, and according to target most according to the objective function of problem to be optimized Smallization principle determines prey corresponding optimal solution x* and its optimal objective value f (x*) when current iteration t, and has:
S6: repeating step S2~S6, until the number of iterations t reaches T；
S7: returning to optimal solution x* and optimal objective value f (x*), judges whether current iteration number t reaches greatest iteration time Number T, if so, the optimal solution x* and optimal objective of the output resulting problem to be optimized of chestnut wing hawk optimization algorithm parallel iteration optimizing Value f (x*), on the contrary then current iteration number t increase 1 and continue to execute step S2 to step S6.
In the present invention periodicity of energy successively decrease regulating strategy be by cosine function carry out mathematicization description, can complete The alternative solution of same goal of the invention mainly includes following several respects:
(1) prey energy periodically successively decreases the initial phase of the cosine function in regulatory factor CD in the present inventionBe set as π/ 2, in addition it is also possible to be set as other initial phasesSuch asWithCorresponding CD mathematic(al) representation is respectively
WithWherein, K=0,1,2 ... indicate the number of cycles that energy periodically successively decreases.
(2) present invention in prey energy periodically successively decrease regulatory factor CD be by cosine function carry out mathematical expression, Mathematical expression, the regulatory factor at this point, the corresponding prey energy of SIN function periodically successively decreases can also be carried out by SIN function CD is mathematically represented as
Wherein, initial phaseAny value can be still taken, such asDeng.
(3) prey energy of the invention periodically successively decreases regulatory factor CD mathematical expression except above-mentioned SIN function and cosine letter Number definition is outer, can also be portrayed by the combination of SIN function and cosine function, corresponding mathematical expression are as follows:
Wherein, m ∈ [0,1] indicates that the weighting compromise factor is acted on the compromise for regulating and controlling SIN function and cosine function,WithRespectively indicate the initial phase of cosine function and SIN function.
(4) the prey energy of the invention regulating strategy that periodically successively decreases can effectively realize the multiple overall situation of intelligent optimization algorithm Periodicity between search and local search jumps, in addition, the periodicity is successively decreased, regulating strategy is also introduced into other intelligent optimizations Primary " global search+local search " process, i.e. period is usually only carried out in traditional intelligence optimization algorithm to break in algorithm It is primary " global search+local search " process of traditional intelligence optimization algorithm when number k=0, and the bigger expression intelligence of periodicity k " global search+local search " number that energy optimization algorithm executes is more.
It is applicable in test the preferable of effective and higher-dimension situation of method optimization performance improvement provided in an embodiment of the present invention Property, carry out 2 groups of experiments altogether: experiment 1 probes into energy periodicity decrement factor to HHO algorithm optimization with 4 groups of benchmark test functions The otherness of the regulation validity and its different cycles that can improve influences；Experiment 2 is improved with the comparative experiments of HHO algorithm with verifying Preferable well-posedness of the algorithm to 200D, 1000D and 10000D higher-dimension situation.Each experimental group experiment is all made of 4 groups of benchmark test letters Number is shown in Table 1, wherein F1 and F2 is unimodal function with part the exploitation performance and convergence efficiency etc. of testing algorithm；F3~F4 is more Peak function explores evading property of performance drawn game portion's extreme value etc. to test the global of algorithm.
Table 1: benchmark test function
Experiment 1 is test different-energy periodicity regulatory factor CD to the difference of chestnut wing hawk optimization algorithm (HHO) performance improvement The opposite sex influences, and is tested using function dimension D=30 in table 1 as experimental subjects with periodicity k=0,1,2 ..., 20, each to test It is respectively 30 and 500 that chestnut wing hawk population scale N and maximum number of iterations T are set in group.For guarantee experimental result fairness, Equal independent operating 10 times of each experimental group, and energy is drawn with the average value of 10 experimental results and is periodically successively decreased in regulatory factor CD not Fig. 4 is shown on the influence of the optimization performance of HHO (chestnut wing hawk optimization algorithm) with period k.
It is analyzed by Fig. 4 it is found that the average optimization performance for improving HHO algorithm changes with period k in dynamic fluctuation, in period k Odd number value and even number value between improve HHO algorithm iteration result generally show " V " type variation, i.e. period k be even number value Opposite its odd number value situation mutually closed on that is superior to of optimization performance；In periodicity k >=2, the average suitable of HHO algorithm is improved Angle value is answered almost to be superior to traditional HHO algorithm, and optimal with its performance when k=6.
The preferable optimization performance of HHO algorithm is improved when in view of k=6, is set k=6 as HHO is improved in subsequent experimental and is calculated The periodicity of method, using average value, standard deviation, worst-case value and the optimal value of 10 experiment gained optimal objective values as algorithm performance Evaluation index, then the experimental result comparison statistics for improving HHO algorithm and tradition HHO algorithm are shown in Table 2.
Table 2:30 ties up experimental result comparison statistics
It is analyzed by table 2 and is calculated it is found that improving HHO algorithm and being significantly better than traditional HHO in 4 evaluation index values of 4 groups of functions Method, improves more than ten to tens orders of magnitude, and the worst-case value of especially improvement HHO algorithm is also better than tradition HHO algorithm Optimal value reach several orders of magnitude, demonstrate improve HHO algorithm have superior parallel iteration optimizing performance.Optimal " average value " Show that improving HHO algorithm shows higher low optimization accuracy and ensemble average superior performance in 10 independent repetition experiments； Optimal " standard deviation " illustrates that improving HHO algorithm has compared with strong algorithms robustness (robustness)；Optimal " optimal value " examines improvement HHO algorithm is to the abundant exploration of problem solution space and exploits and seeks obtaining the target-seeking approximate optimal solution of higher precision；And it is optimal " worst Value " then implies that problem of implementation will be carried out with lesser optimizing error by improving HHO algorithm in the potential application field of no priori knowledge Preferably solve and seek and to obtain more preferably approximate optimal solution.Under same experimental condition, improves HHO algorithm and letter is tested to unimodal-multimodal Number all has optimal low optimization accuracy, show to improve HHO algorithm have preferable local producing capacity, compared with strong convergence precision, compared with Good ability of searching optimum and evading property of local extremum etc..
For the further intuitive iterative process contrast effect for showing improvement HHO algorithm and tradition HHO algorithm, tested with 10 times Average fitness value draw Fig. 5 (significantly to show iterative process difference, each 10 iteration draw a contrast points).
It is analyzed by Fig. 5 and is better than passing always it is found that improving Average Iteration fitness value of the HHO algorithm on 4 groups of test functions System HHO algorithm；In the iterative process mid-early stage of intelligent optimization, improves HHO algorithm and be always maintained at powerful Dynamic iterations optimization property Can and convergence precision interval between traditional HHO algorithm be in increase tendency；And in the iteration later period, it has been fallen due to improving HHO algorithm Enter the small neighborhood of the true globally optimal solution of problem to be optimized and seek higher precision optimal solution, and lead to the flat of iterativecurve Straight state can still seek obtaining high-precision result in table 2 even if showing to improve HHO algorithm and reducing certain the number of iterations.
The above results sufficiently demonstrate the mentioned energy of the present invention and periodically successively decrease regulating strategy to improvement HHO algorithm performance Validity and the superior optimizing performance for improving HHO algorithm.
It is as follows to the resulting optimal solution of 4 groups of test function parallel iteration optimizing and optimal objective value example to improve HHO algorithm:
(1) 3 groups of data of F1 function are as follows:
First group of solution information: optimal objective value is 3.784E-70, and corresponding optimal solution is 2.103E-71 6.765E-72
Second group of solution information: optimal objective value is 7.699E-68, and corresponding optimal solution is-1.991E-70-7.086E-70
Third group solution information: optimal objective value is 2.571E-74, and corresponding optimal solution is 4.705E-76 1.691E-76
(2) 3 groups of data of F2 function are as follows:
First group of solution information: optimal objective value is 2.653E-164, and corresponding optimal solution is -8.884E-84 1.815E-84
Second group of solution information: optimal objective value is 3.243E-142, and corresponding optimal solution is-1.977E-72-2.687E-74
Third group solution information: optimal objective value is 1.189E-130, and corresponding optimal solution is -5.200E-67 3.620E-67
(3) 3 groups of data of F3 function are as follows:
First group of solution information: optimal objective value is 1.161E-87, and corresponding optimal solution is 1.313E-88-1.033E-87
Second group of solution information: optimal objective value is 1.298E-74, and corresponding optimal solution is -5.449E-75 1.769E-76
Third group solution information: optimal objective value is 2.342E-72, and corresponding optimal solution is -1.041E-73 7.234E-73
(4) 3 groups of data of F4 function are as follows:
First group of solution information: optimal objective value is 1.755E-80, and corresponding optimal solution is-2.075E-81-1.906E-80
Second group of solution information: optimal objective value is 1.223E-72, and corresponding optimal solution is 4.654E-73-2.347E-73
Third group solution information: optimal objective value is 1.774E-65, and corresponding optimal solution is 2.224E-65 1.700E-65
By 12 groups of solution information analyses of above-mentioned 4 groups of functions, the optimal solution of improvement HHO algorithm is the small neighborhood in optimal solution It is interior there are certain fluctuation, solve fluctuation be substantially due to intelligent optimization algorithm as random optimization technology it is intrinsic with Caused by machine, and then lead to due to the randomness of optimal solution the randomness of optimal objective value, the data in table 2 Certain minor fluctuations will be generated under same test condition, but will be significantly better than traditional HHO algorithm.
Experiment 2, further to probe into the optimization performance for improving HHO algorithm under more higher-dimension situation, with 4 groups of tests in table 1 The dimension of function is respectively set as 200,1000 and 10000, and chestnut wing hawk population scale N is still 30 and corresponding maximum number of iterations T is respectively set to 500,1000 and 1500, improves HHO algorithm and the equal independent operating of HHO algorithm 10 times, comparison statistical result point It is not shown in Table 3~table 5.
Table 3:200 ties up experimental result comparison statistics
Table 4:1000 ties up experimental result comparison statistics
Table 5:10000 ties up experimental result comparison statistics
It is analyzed by 3~table of table 5 it is found that improving optimization of the HHO algorithm under same experiment condition in high-dimensional optimization Performance is still significantly superior to traditional HHO algorithm, and convergence precision evaluation index is promoted a to tens orders of magnitude up to more than ten.It is right The multimodal F3 function of 10000 dimension situations improves HHO and calculates even if averagely optimizing the order of magnitude that precision reaches 1.0E-269 in HHO algorithm Method still can further seek more preferably Optimum Solution and corresponding " worst index value " also have reached the order of magnitude of 1.0E-301, The outstanding higher-dimension for sufficiently demonstrating improvement HHO algorithm extremely optimizes performance.Meanwhile in function dimension D increasing process, improve The limited times the number of iterations increase of HHO algorithm, which can be synchronized preferably, catches up with and surpasses in the increasing velocity of function dimension, and seeks more Excellent problem optimal solution, intuitive consecutive mean iteration comparing result are shown in that (in iteration correlation curve, 200 tie up every 10 to Fig. 6~Fig. 8 Secondary iteration, every 20 iteration of 1000 dimensions and 10000 every 30 iteration of dimension draw a contrast points), the above results effectively demonstrate Improving HHO algorithm compared to traditional HHO algorithm there are better higher-dimension Dynamic iterations to optimize performance.
The above is a preferred embodiment of the present invention, cannot limit the right model of the present invention with this certainly It encloses, it is noted that for those skilled in the art, without departing from the principle of the present invention, may be used also To make several improvement and variation, these, which improve and change, is also considered as protection scope of the present invention.

Claims (8)

1. a kind of improvement chestnut wing hawk optimization algorithm of regulating strategy that periodically successively decreases with energy, which is characterized in that including following step It is rapid:
S1: the initial position of N chestnut wing hawk is generated at solution space [LB, UB] using random generation strategy；
S2: prey energy state E is updated0With Jump intensity J；
S3: it updates energy and periodically successively decreases regulatory factor CD and prey ENERGY E；
S4: according to the relative size of prey ENERGY E and the success rate p that escapes, the location updating and solution of chestnut wing hawk population at individual are executed Validity check；
S5: the fitness value of chestnut wing hawk population at individual is calculated, and determines current optimal solution and optimal objective value by principle of optimality；
S6: repeating step S2~S6, until the number of iterations t reaches T；
S7: optimal solution x* and optimal objective value f (x*) is returned.
2. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist In in the step S1, the initialized location of chestnut wing hawk population at individual is denoted as xi=[xi,1, xi,2..., xi,D], and have:
xi,j=LB (j)+(UB (j)-LB (j)) × rand ()
Wherein, i=1,2 ..., N indicate i-th chestnut wing hawk in chestnut wing hawk population, and j=1,2 ..., D indicate that problem to be optimized becomes J-th of dimension of amount, LB (j) and UB (j) respectively indicate effective value lower limit of the solution variable to be optimized in jth dimension and The upper limit, rand () indicate the random real number generated at random in section [0,1].
3. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist In, in the step S2, the energy state E of prey0With the number of iterations t, dynamic updates in section [- 1,1], and has:
E0,t=2 × rand () -1
Wherein, t=1,2 ..., T indicate the current number of chestnut wing hawk population iterative search, and prey Jump intensity J simulates nature The behavior of prey rabbit in boundary indicates prey random skip intensity for the during of escaping when avoiding being captured by chestnut wing hawk, and Dynamic updates in section [- 2,2], calculating formula Jt=2 × (rand () -1).
4. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist In, in the step S3, energy periodically successively decrease regulatory factor CD with iteration in periodically dynamic reduce to guarantee prey ENERGY E Reduction trend is generally showed, and is had:
Wherein, k=0, the number of cycles that 1,2 ... expression energy periodically successively decreases, is a default integer value；The smaller expression chestnut of k Wing hawk optimization algorithm global search process more easy to carry out, the bigger expression chestnut wing hawk optimization algorithm of k local search more easy to carry out Process；
The regulatory factor CD that periodically successively decreased according to energy can must improve the update of the prey ENERGY E iteration in chestnut wing hawk optimization algorithm Calculating formula are as follows:
5. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist In, in the step S4,
In the absolute value of prey ENERGY E | E | when >=1, chestnut wing hawk optimization algorithm executes global heuristic process, i.e., chestnut wing hawk individual with Machine is inhabited in solution space [LB, UB], and carries out location updating referring to other chestnut wing hawks or prey position according to probability, and have:
Wherein, the position vector of chestnut wing hawk, x when x (t+1) and x (t) respectively indicate (t+1) secondary and the t times iterationrabbitWith xrandIt respectively indicates current prey rabbit and chooses the position vector of chestnut wing hawk, r at random1、r2、r3、r4It is section [0,1] with p Interior random number；
It indicates the position average vector of all individuals in chestnut wing hawk population when current iteration, and works as prey energy Amount | E | when < 1, chestnut wing hawk optimization algorithm then executes local recovery process, i.e., chestnut wing hawk individual with prey ENERGY E with 0.5 it is opposite Size and escape success rate p ∈ [0,1] and 0.5 relative size relationship common property give birth to 4 kinds and different surround and seize prey strategy.
6. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as claimed in claim 5, feature exist In 4 kinds different, and to surround and seize prey strategy as follows:
(1) when p >=0.5 and | E | when >=0.5, chestnut wing hawk individual execute it is soft surrounds and seize strategy, i.e. prey has enough ENERGY Es and tries Figure escapes dangerous circumstances by random skip, but is finally still captured by chestnut wing hawk individual, mathematical expression are as follows:
X (t+1)=Δ x (t)-E | Jxrabbit(t)-x(t)|
Wherein, △ x (t)=xrabbit(t)-x (t) indicates position difference when the t times iteration between chestnut wing hawk and prey；
(2) when p>=0.5 and | E | when<0.5, chestnut wing hawk individual executes and surrounds and seize strategy firmly, i.e., prey ENERGY E is lower and chestnut wing hawk Body, which directly dives, attacks and captures prey suddenly, mathematicization expression are as follows:
X (t+1)=xrabbit(t)-E|Δx(t)|
(3) when p<0.5 and | E | when>=0.5, chestnut wing hawk individual execute with it is progressive quickly dive it is soft surround and seize, i.e., prey has enough ENERGY E and attempt to escape dangerous circumstances by random skip, but chestnut wing hawk individual is in such a way that surprise attack is taken in optimal underriding direction Execute it is soft surround and seize, mathematicization expression are as follows:
Wherein, S indicates that D ties up random row vector, and LF indicates Levy flight function, and has:
Wherein, u and v indicates the random number in section (0,1), and q indicates preset constant 1.5,Indicate Gamma Function；
(4) when p < 0.5 and | E | when < 0.5, chestnut wing hawk individual execute with it is progressive quickly dive surround and seize strategy, i.e. prey energy firmly E is lower and chestnut wing hawk individual is executed in such a way that surprise attack is taken in optimal underriding direction and surrounded and seize firmly, mathematicization expression are as follows:
After new chestnut wing hawk population generates, examine whether solution is located in solution valid interval [LU, UB], if solution x exceeds effective district Between then again random generate.
7. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist According to the objective function of problem to be optimized, calculating the corresponding objective function of each individual in chestnut wing hawk population in the step S5 Value, and according to target minimization principle determines prey corresponding optimal solution x* and its optimal objective value f (x*) when current iteration t, And have:
8. the improvement chestnut wing hawk optimization algorithm for the regulating strategy that periodically successively decreases with energy as described in claim 1, feature exist In, in the step S6 and step S7, judge whether current iteration number t reaches maximum number of iterations T, if so, output chestnut The optimal solution x* and optimal objective value f (x*) of the resulting problem to be optimized of wing hawk optimization algorithm parallel iteration optimizing, it is on the contrary then when Preceding the number of iterations t increases 1 and continues to execute step S2 to step S6.
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