CN111062462A - Local search and global search fusion method and system based on differential evolution algorithm - Google Patents
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Abstract
The invention discloses a local search and global search fusion method and a system based on a differential evolution algorithm, wherein the method comprises the following steps: carrying out initialization configuration on population parameters to generate an initial population; configuring a local search algebra counter and a global search algebra counter; when the population enters a local search stage, determining that a local search algebraic counter is between an upper limit and a lower limit and a sub-population is not converged, and then entering a global search stage; judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, if so, re-executing the global search stage; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm. The invention enhances the convergence and searchability of the population, improves the comprehensiveness of the search, has high efficiency and low complexity, and can be widely applied to the technical field of numerical optimization.
Description
Technical Field
The invention relates to the technical field of numerical optimization, in particular to a local search and global search fusion method and system based on a differential evolution algorithm.
Background
In the fields of science and engineering, some problems of global optimization or combined optimization can be frequently encountered, the problems generally have the characteristics of wide optimization range, nonlinearity and the like, the optimal solution of the problems is often complex to find by utilizing a manual method for optimization, and the global optimal solution of the problems can be conveniently solved by utilizing an optimization algorithm.
The differential evolution algorithm was proposed by r.storm and k.price in 1995, and has now become one of the efficient heuristic search algorithms to solve various continuous optimization problems, and has been widely applied in many fields such as pattern recognition, machine learning, neural network training, intelligent control, and the like. However, the traditional differential evolution algorithm is easy to fall into the problems of local optimization or stagnation and the like, and the optimal parameters need to be obtained by trial and error aiming at different problems, so that the time cost is wasted, and the balance between the development performance and the exploratory performance is difficult to achieve.
When the traditional differential evolution algorithm is used for D-dimensional single-target optimization, the method is specifically realized as follows: firstly, initializing a group of uniformly distributed population P ═ X with Np solution vectors1,G,X2,G,...,XNp,GAnd calculating the objective function value F (X) of the population, and then, iteratively executing mutation, intersection and selecting three operations until the iteration is finished. In the mutation, by combining one or more difference vectors with the basis vector Xi,GCombined to produce mutation vector Vi,G. The mathematical expression for DE/rand/1 is for example: vi,G＝Xr1,G+F·(Xr2,G-Xr3,G) Wherein X isr1,G，Xr2,GAnd Xr3,GIs three different individuals randomly selected, and F belongs to (0, 1)]. In the crossing, vector V is applied to each mutationi,GAnd a base vector Xi,GPerforming intersection to obtain a test vector Ui,G. The process is controlled by a cross rate CR, for binomial crossing, a dimension j is randomly selected at first, a value between 0 and 1 is randomly selected for each dimension of each individual, and if the value is smaller than the value CR or the dimension is the previously selected dimension, V is selected in the dimensioni,GIf not, selecting Xi,GThe value of (c). All test vectors U are then calculatedi,GThe objective function value of (f), (u). In selection, the target function of each test vector and the basic vector is compared, and the small target function is selected as the basic individual of the next generation.
Over the last two decades, a number of efficient differential evolution algorithm variants have been proposed, most of which are globally searchable and many of which are adaptive control parameters and selection strategies that address the time cost of trial and error methods used by traditional differential evolution algorithms. Some differential evolution algorithms are combined with global search and local search, also called modular differential evolution algorithms, and mainly combine the differential evolution algorithm with local search algorithms such as hill climbing method and annealing algorithm.
Disclosure of Invention
In view of this, the embodiments of the present invention provide an efficient and low-complexity local search and global search fusion method and system based on a differential evolution algorithm.
According to an aspect of the present application, an embodiment of the present invention provides a local search and global search fusion method based on a differential evolution algorithm, including the following steps:
carrying out initialization configuration on population parameters to generate an initial population;
configuring a local search algebra counter and a global search algebra counter;
when the population enters a local search stage, determining that a local search algebraic counter is between an upper limit and a lower limit and a sub-population is not converged, and then entering a global search stage;
judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, if so, re-executing the global search stage; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm;
the population parameters comprise population scale, sub-population scale, dimension size, maximum iterative algebra, scale factors, cross rate, local search algebra lower limit, local search algebra upper limit, global search algebra upper limit and the type of differential evolution algorithm variants.
Further, the method also comprises the following steps:
splitting the execution process of the differential evolution algorithm into a plurality of non-overlapping stages; wherein each stage comprises a local search and a global search; the global search includes a transition phase and a global phase.
Further, the method also comprises a local searching step, wherein the local searching step comprises the following steps:
sorting the populations based on the preset selected dimensions;
dividing the population into a plurality of sub-populations according to the sorting result of the population;
and independently evolving each sub-population by taking DE/best/2 as a search engine.
Further, the method also comprises a transition step of global search, wherein the transition step of global search comprises the following steps:
dynamically adjusting the scale factor based on a differential evolution algorithm of the initialization configuration;
the scale factor FiThe dynamic adjustment formula of (2) is:
wherein len ═ Ed (u)i,G,xi,G)/maxlen
Where len represents the distance between the child and the parent after normalization, and abs () represents the absolute value of the number in parentheses; rand represents random generation of a random number in the range of 0,1]A number in between; ed () represents the euclidean distance between two vectors in parentheses; u. ofi,GRepresents xi,GThe sub-individuals after the differential evolution algorithm are represented by vectors; x is the number ofi,GRepresenting the current individual by using a vector with a preset dimension; maxlen represents the maximum distance between the current individuals.
Further, the step of performing initialization configuration on the population parameters to generate the initial population includes the following steps:
carrying out initialization configuration on population parameters;
randomly generating an initial population;
and calculating the objective function value of each individual in the initial population.
Further, the method also comprises the following steps:
when the population enters a local search stage, determining that the local search algebraic counter is not between the upper limit and the lower limit, or after the sub-population is converged, continuing the population to enter the local search stage.
Further, the differential evolution algorithm variants are substituted into the global phase in the step where the population enters the global search phase.
According to another aspect of the present application, a local search and global search fusion system based on a differential evolution algorithm is provided, which includes:
the initialization module is used for carrying out initialization configuration on the population parameters to generate an initial population;
the configuration module is used for configuring a local search algebra counter and a global search algebra counter;
the local search module is used for determining that the local search algebraic counter is between an upper limit and a lower limit and the sub-population does not converge when the population enters a local search stage, and then the population enters a global search stage;
the global search module is used for judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, and if so, the global search stage is executed again; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm;
the population parameters comprise population scale, sub-population scale, dimension size, maximum iterative algebra, scale factors, cross rate, local search algebra lower limit, local search algebra upper limit, global search algebra upper limit and the type of differential evolution algorithm variants.
Further, still include:
the splitting module is used for splitting the execution process of the differential evolution algorithm into a plurality of non-overlapping stages; wherein each stage comprises a local search and a global search; the global search includes a transition phase and a global phase.
According to another aspect of the present application, a local search and global search fusion system based on a differential evolution algorithm is provided, which includes:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the differential evolution algorithm-based local search and global search fusion method.
The technical scheme in the embodiment of the invention at least has the following advantages: when the differential evolution algorithm is executed, the local search stage and the global search stage are fused, when the population is subjected to local search, the convergence of the population is enhanced, and the optimal point in a small range is not easy to leak; then, when the population enters global search, the exploratory property of the population is enhanced, individuals trapped in local optimum can be pulled out, and then large-scale search is carried out; by repeatedly executing the local search and the global search, the comprehensiveness of the search is improved, the efficiency is high, the complexity is low, and the performance of the differential evolution algorithm is improved.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic diagram of the relationship of stages of the evolution process in the method of the present invention;
FIG. 2 is a graph showing the results of several comparative experiments on the basic DE according to the present invention;
FIG. 3 is a graph of the results of comparative experiments with the present invention on several efficient DE variants with a population dimension of 30 dimensions;
fig. 4 is a graph of the results of comparative experiments with the present invention on several efficient DE variants, with a population dimension of 50 dimensions.
Detailed Description
The invention will be further explained and explained with reference to the drawings and the embodiments in the description. The step numbers in the embodiments of the present invention are set for convenience of illustration only, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.
The invention aims to further improve the performance of the existing adaptive control parameter differential evolution algorithm, solve the defects of the traditional modular differential evolution algorithm and provide an efficient local search and global search fusion method and system based on the differential evolution algorithm.
Because the global search and the local search are alternately carried out, the search can be more comprehensive, and the performance of the algorithm is improved. And the local search is only to divide the population based on the value of a certain dimension, so that sub-populations with close distances are obtained by using less computing resources, which may result in the reduction of population diversity, and then the problem is solved by reversely adjusting the scale factor F according to the Euclidean distance between the test vector and the original vector.
The method and system for fusing local search and global search based on differential evolution algorithm of the present invention divides the evolution process into a plurality of non-overlapping stages with the same size, wherein each stage includes local search and global search, and the global search includes a transition stage and a global stage, for a known target function, the maximum or minimum value (i.e. the optimization direction) of the target function in the target interval is required, referring to fig. 1, the steps of this embodiment are as follows:
(1) initialization: setting a population scale Np, a sub-population scale k, a dimension D, a maximum iterative algebra Gmax, a scale factor F, a cross rate CR, a local search algebra lower limit LS _ min, a local search algebra upper limit LS _ max and a global search algebra upper limit GS _ max, and selecting an efficient differential evolution algorithm variant;
(2) randomly generating an initial population P ═ X1,G,X2,G,...,XNp,GWhere G represents the current evolution algebra, X1,G,X2,G,...,XNp,GRepresenting individuals of the population in the G generation, and calculating an objective function value F (X) of each individual;
(3) setting a local search algebra Counter LS _ Counter to 0 and a global search algebra Counter GS _ Counter to 0;
(4) the population enters a local search stage, the segmentation strategy provided by the invention is used in the stage, namely, a certain dimension is randomly selected, the population is sorted according to the value of the dimension, then the population is divided into a plurality of sub-populations, and then each sub-population independently evolves by taking DE/best/2 as a search engine;
(5) and judging whether the termination condition of the algorithm execution is met, if so, storing the result and exiting. Otherwise, judging whether the local search algebra counter is between the upper limit and the lower limit or whether each sub-population converges. If the counter is between the upper limit and the lower limit and the sub-population is not converged, jumping to the step (4), otherwise, jumping to the step (6);
(6) and the population enters a global search stage, and if the local search algebra Counter does not reach the upper limit LS _ max of the local search algebra, the LS _ max-LS _ Counter generation is allocated to the transition stage of the global search. The diversification mechanism provided by the invention is used in the transition stage, namely the diversification strategy is to adjust the value of F according to the following formula on the basis of the selected algorithm:
len＝Ed(ui,G, xi,G) /maxlen (2)
then entering a global stage of global search, and directly substituting the global stage into the selected differential evolution algorithm variant;
where len represents the distance between the child and the parent after normalization, and abs () represents the absolute value of the number in parentheses; randRepresenting random generation of a range of [0,1 ]]A number in between; ed () represents the euclidean distance between two vectors in parentheses; u. ofi,GRepresents xi,GThe sub-individuals after the differential evolution algorithm are represented by vectors; x is the number ofi,GRepresenting the current individual by using a vector with a preset dimension; maxlen represents the maximum distance between the current individuals.
(7) And judging whether the termination condition of the execution of the differential optimization algorithm is met, if so, storing the result and exiting. Otherwise, judging that the value of the global search algebra counter reaches the global search algebra upper limit, if so, skipping to the step (3), otherwise, skipping to the step (6).
In this embodiment, the problem set CEC14 function set is taken as an example, the high dimensional problem of the function set is a problem that is difficult to solve, and if the high dimensional problem (30 dimensions or more) of the function set can be solved efficiently, the generality of the present invention can be demonstrated. In the present invention, these high-dimensional problems are solved and compared with other algorithms. When the population size is set to be 100, selecting a plurality of basic DE and a plurality of efficient DE variants to sleeve the strategy of the patent to be compared with an original algorithm, and independently operating 51 times for 300000 times for evaluation times of an objective function, wherein the algorithm in bold in figures 2, 3 and 4 has better performance.
The results of the comparison graph with two basic DE of DE/rand/1 and DE/best/1 in the case of 30 dimensions are shown in FIG. 2. Wherein, LG-DE/rand/1 has 27 functions with better performance than DE/rand/1, 2 functions with equivalent performance, and 1 function with worse performance than DE/rand/1. And LG-DE/best/1 has 20 functions to show better than DE/best/1, 7 functions have almost the same performance, and 3 functions have worse than DE/best/1. Therefore, the invention can improve the development of DE/rand/1 and the exploratory property of DE/best/1 so as to improve the performance of the two algorithms, and therefore, the invention has the capability of balancing the development property and the exploratory property of the algorithms. Thus, it was confirmed that the present invention can improve the performance of the base DE.
The results of a comparison plot with the four efficient DE variants jDE, SaDE, JADE and CoDE for the 30-dimensional case are shown in FIG. 3. Compared with jDE, LG-jDE performed 19 functions better and 5 functions less well. There are 18 functions that LG-SaDE performs better and 2 functions that perform less well than SaDE. Compared with JADE, LG-JADE has 14 functions which perform better, and 7 functions which perform worse. LG-CoDE performed 27 functions better and 0 functions less well than CoDE. It can be seen that the present invention makes the high efficiency DE variant more efficient.
The results of the comparison plots with the four efficient DE variants jDE, SaDE, JADE and CoDE for the 50-dimensional case are shown in FIG. 4. Compared with jDE, LG-jDE performed 11 functions better and 8 functions less well. There are 17 functions that LG-SaDE performs better and 3 functions that perform worse than SaDE. Compared with JADE, 10 functions have better performance of LG-JADE, and 10 functions have poorer performance. The number of functions that LG-CoDE performs better than CoDE is 22, and the number of functions that perform worse is 3. It follows that the invention can also improve the performance of the algorithm in a higher dimension.
The embodiment of the invention also provides a local search and global search fusion system based on the differential evolution algorithm, which comprises:
the initialization module is used for carrying out initialization configuration on the population parameters to generate an initial population;
the configuration module is used for configuring a local search algebra counter and a global search algebra counter;
the local search module is used for determining that the local search algebraic counter is between an upper limit and a lower limit and the sub-population does not converge when the population enters a local search stage, and then the population enters a global search stage;
the global search module is used for judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, and if so, the global search stage is executed again; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm;
the population parameters comprise population scale, sub-population scale, dimension size, maximum iterative algebra, scale factors, cross rate, local search algebra lower limit, local search algebra upper limit, global search algebra upper limit and species of differential evolution algorithm variants.
Further, as a preferred embodiment, the method further comprises:
the splitting module is used for splitting the execution process of the differential evolution algorithm into a plurality of non-overlapping stages; wherein each stage comprises a local search and a global search; the global search includes a transition phase and a global phase.
The embodiment of the invention also provides a local search and global search fusion system based on the differential evolution algorithm, which comprises:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the differential evolution algorithm-based local search and global search fusion method.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
Finally, the invention provides a local search and global search fusion method and system based on a differential evolution algorithm, mainly provides a dimension-based method to divide a population into a plurality of sub-populations, obtains a high-efficiency and low-complexity local search method by a method of independently evolving each sub-population, and provides a method for reversely adjusting a scale factor F according to the Euclidean distance between a test vector and an original vector when entering a global search stage to improve the diversity of the population in order to solve the problem that the population diversity is lost in the local search.
In alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flow charts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and in which sub-operations described as part of larger operations are performed independently.
Furthermore, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise stated to the contrary, one or more of the described functions and/or features may be integrated in a single physical device and/or software module, or one or more functions and/or features may be implemented in a separate physical device or software module. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary for an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be understood within the ordinary skill of an engineer, given the nature, function, and internal relationship of the modules. Accordingly, those skilled in the art can, using ordinary skill, practice the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative of and not intended to limit the scope of the invention, which is defined by the appended claims and their full scope of equivalents.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. The fusion method of local search and global search based on the differential evolution algorithm is characterized in that: the method comprises the following steps:
carrying out initialization configuration on population parameters to generate an initial population;
configuring a local search algebra counter and a global search algebra counter;
when the population enters a local search stage, determining that a local search algebraic counter is between an upper limit and a lower limit and a sub-population is not converged, and then entering a global search stage;
judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, if so, re-executing the global search stage; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm;
the population parameters comprise population scale, sub-population scale, dimension size, maximum iterative algebra, scale factors, cross rate, local search algebra lower limit, local search algebra upper limit, global search algebra upper limit and the type of differential evolution algorithm variants.
2. The fusion method of local search and global search based on differential evolution algorithm according to claim 1, characterized in that: further comprising the steps of:
splitting the execution process of the differential evolution algorithm into a plurality of non-overlapping stages; wherein each stage comprises a local search and a global search; the global search includes a transition phase and a global phase.
3. The fusion method of local search and global search based on differential evolution algorithm according to claim 1, characterized in that: further comprising a local search step, said local search step comprising the steps of:
sorting the populations based on the preset selected dimensions;
dividing the population into a plurality of sub-populations according to the sorting result of the population;
and independently evolving each sub-population by taking DE/best/2 as a search engine.
4. The fusion method of local search and global search based on differential evolution algorithm according to claim 1, characterized in that: the method also comprises a global search transition step, wherein the global search transition step comprises the following steps:
dynamically adjusting the scale factor based on a differential evolution algorithm of the initialization configuration;
the scale factor FiThe dynamic adjustment formula of (2) is:
wherein len ═ Ed (u)i,G,xi,G)/maxlen
Where len represents the distance between the child and the parent after normalization, and abs () represents the absolute value of the number in parentheses; rand represents random generation of a random number in the range of 0,1]A number in between; ed () represents the euclidean distance between two vectors in parentheses; u. ofi,GRepresents xi,GThe sub-individuals after the differential evolution algorithm are represented by vectors; x is the number ofi,GRepresenting the current individual by using a vector with a preset dimension; maxlen represents the maximum distance between the current individuals.
5. The fusion method of local search and global search based on differential evolution algorithm according to claim 1, characterized in that: the step of performing initialization configuration on the population parameters to generate an initial population comprises the following steps:
carrying out initialization configuration on population parameters;
randomly generating an initial population;
and calculating the objective function value of each individual in the initial population.
6. The fusion method of local search and global search based on differential evolution algorithm according to claim 1, characterized in that: further comprising the steps of:
when the population enters a local search stage, determining that the local search algebraic counter is not between the upper limit and the lower limit, or after the sub-population is converged, continuing the population to enter the local search stage.
7. The fusion method of local search and global search based on differential evolution algorithm according to any one of claims 1-6, characterized in that: substituting the differential evolution algorithm variant into the global phase at the step when the population enters the global search phase.
8. The local search and global search fusion system based on the differential evolution algorithm is characterized in that: the method comprises the following steps:
the initialization module is used for carrying out initialization configuration on the population parameters to generate an initial population;
the configuration module is used for configuring a local search algebra counter and a global search algebra counter;
the local search module is used for determining that the local search algebraic counter is between an upper limit and a lower limit and the sub-population does not converge when the population enters a local search stage, and then the population enters a global search stage;
the global search module is used for judging whether the value of the global search algebra counter is smaller than the upper limit of the global search algebra, and if so, the global search stage is executed again; otherwise, returning to the step of executing and configuring the local search algebra counter and the global search algebra counter until the termination condition of the execution of the initially configured differential evolution algorithm is determined, and ending the differential evolution algorithm;
the population parameters comprise population scale, sub-population scale, dimension size, maximum iterative algebra, scale factors, cross rate, local search algebra lower limit, local search algebra upper limit, global search algebra upper limit and the type of differential evolution algorithm variants.
9. The fusion system of local search and global search based on differential evolution algorithm of claim 8, wherein: further comprising:
the splitting module is used for splitting the execution process of the differential evolution algorithm into a plurality of non-overlapping stages; wherein each stage comprises a local search and a global search; the global search includes a transition phase and a global phase.
10. The local search and global search fusion system based on the differential evolution algorithm is characterized in that: the method comprises the following steps:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the differential evolution algorithm-based local search and global search fusion method of any one of claims 1-7.
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| CN112331315B (en) * | 2020-10-19 | 2023-05-05 | 山东师范大学 | Automatic nurse scheduling method and system based on VBA |
| CN112270957B (en) * | 2020-10-19 | 2023-11-07 | 西安邮电大学 | High-order SNP pathogenic combination data detection method, system and computer equipment |
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