Optimization method and system based on multi-population genetic algorithm

Abstract

The invention discloses an optimization method and system based on a multi-population genetic algorithm. The method comprises the following steps: initializing a plurality of populations; respectively carrying out selection, crossover and mutation operations in each population; a migration strategy is introduced among the populations; the population scale is dynamically adjusted according to the convergence trend and diversity conditions of the population in the evolution process; setting multiple termination conditions to judge whether the multi-population genetic algorithm achieves an effect or not; and after all evolution iterations are completed, outputting the currently found global optimal solution. According to the method, a fitness sharing mechanism, a migration strategy and a dynamic population scale adjustment technology are introduced among a plurality of independent populations, so that some limitations, such as local optimal search and premature convergence problems, possibly encountered by a traditional genetic algorithm are overcome.

Description

Technical Field

[0001] The present invention belongs to the field of computational intelligence and optimization algorithms, and specifically relates to an optimization method and system based on a multi-population genetic algorithm. Background Art

[0002] Genetic Algorithm (GA) is an important evolutionary algorithm that solves complex optimization problems by simulating the biological evolution process. It performs well in dealing with high-dimensional, multi-peak and multi-modal problems. However, when dealing with global optimization problems, traditional single-population genetic algorithms are prone to fall into local optimality and lack sufficient diversity. To this end, a genetic algorithm based on a multi-population mechanism is proposed, which introduces multiple sub-populations to increase population diversity and enhance global search capabilities.

[0003] Genetic algorithms originated in the 1960s and were developed and promoted by John Holland and his students. This algorithm simulates genetic operations such as selection, crossover, and mutation in nature to gradually select better individuals to achieve optimization goals. It is a global search algorithm that is particularly suitable for complex problems that are difficult to solve with traditional optimization methods, such as NP-hard problems and high-dimensional nonlinear problems. In many practical applications, genetic algorithms have demonstrated their powerful capabilities and achieved remarkable success, such as in engineering optimization, economics, artificial intelligence and other fields.

[0004] Traditional genetic algorithms usually include the following steps: initializing the population, evaluating fitness, selecting, crossover, mutating, and generating a new generation of population. First, the initial population is generated by random or some heuristic method; then, the fitness of individuals in the population is evaluated according to some evaluation criteria; then, selection operations are performed based on the fitness of the individuals, so that individuals with higher fitness have a greater probability of being selected as parents; then, new individuals are generated through crossover and mutation operations; finally, these new individuals are added to the next generation of population. This iterative process, after multiple generations of evolution, the population will tend to the global optimal solution. However, there are some obvious problems with traditional single-population genetic algorithms, namely, they are prone to fall into local optimality and it is difficult to have sufficient diversity to effectively explore the entire solution space. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes an optimization method and system based on a multi-population genetic algorithm, which improves the global search capability and robustness of the algorithm on multi-peak optimization problems by introducing a fitness sharing mechanism, a migration strategy and a dynamic population size adjustment technology among multiple independent populations.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] An optimization method based on a multi-population genetic algorithm comprises the following steps:

[0008] Initialize several populations;

[0009] Within each population, selection, crossover and mutation operations are performed separately;

[0010] Introducing migration strategies between populations;

[0011] Dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process;

[0012] Set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect;

[0013] After completing all evolutionary iterations, the currently found global optimal solution is output.

[0014] Preferably, the method of initializing several populations includes:

[0015] A predetermined number of individuals are randomly generated for each population, and the initial size and parameters of each population are set.

[0016] Preferably, within each population, the method of performing selection, crossover and mutation operations respectively includes:

[0017] The selection operation retains individuals whose performance meets the preset requirements;

[0018] Crossover and mutation operations are responsible for introducing new gene combinations and changes;

[0019] The fitness sharing mechanism is used to modify the fitness value of individuals.

[0020] Preferably, the method of introducing a migration strategy between populations comprises:

[0021] Periodically move some individuals from one population to another.

[0022] Specifically, the migration strategy is set to a fixed frequency or to adaptively adjust the frequency according to population diversity.

[0023] Preferably, according to the convergence trend and diversity of the population during the evolution process, the method of dynamically adjusting the population size includes:

[0024] When a population tends to converge and its diversity is lower than the preset requirement, the number of individuals in the population is reduced; on the contrary, when the diversity and optimization potential of the population are higher than the preset requirement, the population size is increased.

[0025] Preferably, the method of setting multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect includes:

[0026] When the preset maximum number of iterations, the target fitness value is reached, or the population diversity is lower than the preset requirement, the algorithm will be triggered to stop running.

[0027] The present invention also provides an optimization system based on a multi-population genetic algorithm, comprising: an initialization module, an internal evolution module, an inter-population communication module, a dynamic adjustment module, a condition setting module and an output module;

[0028] The initialization module is used to initialize several populations;

[0029] The internal evolution module is used to perform selection, crossover and mutation operations within each population;

[0030] The inter-population communication module is used to introduce migration strategies between populations;

[0031] The dynamic adjustment module is used to dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process;

[0032] The condition setting module is used to set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect;

[0033] The output module is used to output the currently found global optimal solution after completing all evolutionary iterations.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. Fitness sharing mechanism: By sharing the fitness among individuals within the population, the probability of some excellent individuals occupying too many resources is reduced, preventing premature convergence.

[0036] 2. Migration strategy: Regularly migrate some individuals from one population to another to increase genetic diversity and improve global search capabilities.

[0037] 3. Dynamic population size adjustment: According to the population performance during the evolution process, the size of the population is adaptively adjusted to avoid waste or shortage of resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0039] Figure 1 The figure is a flow chart of an optimization method based on a multi-population genetic algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] Embodiment 1

[0043] like Figure 1 As shown, the present invention provides an optimization method based on a multi-population genetic algorithm, which overcomes some limitations that may be encountered in traditional genetic algorithms, such as local optimal search and premature convergence problems, by introducing a fitness sharing mechanism, a migration strategy and a dynamic population size adjustment technology between several independent populations.

[0044] The following steps are involved:

[0045] Initialize several populations;

[0046] Within each population, selection, crossover and mutation operations are performed separately;

[0047] Introducing migration strategies between populations;

[0048] Dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process;

[0049] Set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect;

[0050] After completing all evolutionary iterations, the currently found global optimal solution is output.

[0051] In the specific implementation process, we first need to initialize several populations. Each population is randomly generated by a certain number of individuals. This initialization process not only provides a variety of different starting points for the operation of the algorithm, but also lays the foundation for the subsequent evolution process by setting the initial scale and parameters of each population. This step ensures that the entire algorithm can explore the solution space from multiple directions at the same time, improving the efficiency of global exploration.

[0052] Secondly, within each population, selection, crossover, and mutation operations are performed respectively. The selection operation retains individuals with better performance, while the crossover and mutation operations are responsible for introducing new gene combinations and changes, thereby increasing the diversity of the population. When performing these operations within the population, the fitness sharing mechanism is used to correct the fitness value of each individual. This means that when evaluating the quality of an individual, the competition between the individual and other individuals is taken into account, thereby preventing a few excellent individuals from monopolizing resources and causing the population to converge prematurely. The introduction of this mechanism helps to maintain the diversity of the population and improve the overall search effect.

[0053] Next, in order to further enhance diversity and global search capabilities, the present invention introduces a migration strategy between populations. Regularly migrating some individuals from one population to another is similar to gene flow in nature. The migration strategy can be set to a fixed frequency or adaptively adjusted according to the diversity of each population. In this way, genes between populations are effectively exchanged, avoiding the risk that independent populations may fall into local optimal solutions at different locations. At the same time, this communication and interaction ensures that the solution of the entire algorithm is more comprehensive and reliable.

[0054] Subsequently, during the evolution process, the population size is adaptively adjusted according to the convergence trend and diversity of each population. The purpose of this technology is to maintain the efficiency of the entire optimization process. When a population tends to converge and the diversity decreases, the number of individuals in the population can be reduced to save computing resources; on the contrary, when the population shows high diversity and good optimization potential, the population size can be appropriately increased to accelerate the optimization process. In this way, through dynamic adjustment, resources can be used more effectively and the overall performance of the algorithm can be improved.

[0055] The operation of the entire algorithm is subject to multiple termination conditions. For example, the preset maximum number of iterations, the target fitness value is reached, or the population diversity is too low, etc., which will trigger the algorithm to stop running. The setting of these termination conditions ensures that the algorithm will not fall into an infinite loop, and also ensures that the time and resources required to obtain an effective solution are within a controllable range.

[0056] Finally, the optimal individual and its corresponding solution are output. This result is optimized through multiple mechanisms such as independent evolution of multiple populations, fitness sharing and gene migration, and represents the optimal or near-optimal solution in a wide search space. Compared with traditional genetic algorithms, the multi-population genetic algorithm based on the above improved method shows stronger global search ability and robustness when dealing with complex multi-peak optimization problems.

[0057] Embodiment 2

[0058] In the context of complex large-scale multi-peak optimization problems, this paper proposes a multi-population genetic algorithm that is specifically designed to improve the algorithm's global search capability and avoid premature convergence. The algorithm demonstrates high efficiency in dealing with multi-peak optimization problems by introducing a fitness sharing mechanism, a population migration strategy, and a dynamic population size adjustment technique.

[0059] Next, the present invention will take the optimization of vehicle routing problem as an example to create a detailed multi-population genetic algorithm application case. The so-called vehicle routing problem is to determine the distribution routes of several vehicles given a distribution center and several customer points, so that each customer point is visited once. We assume that each vehicle starts from the distribution center, visits several customers and then returns to the distribution center. Our goal is to minimize the total driving distance of the vehicle. The basic parameters of the experiment are set as follows:

[0060] Distribution center coordinates: (0,0)

[0061] Coordinates of customer point 1: (2,3)

[0062] Coordinates of client point 2: (5,4)

[0063] Coordinates of client point 3: (1,8)

[0064] Coordinates of client point 4: (7,1)

[0065] Coordinates of client point 5: (6,3)

[0066] Coordinates of client point 6: (8,9)

[0067] Coordinates of client point 7: (3,6)

[0068] Coordinates of client point 8: (4,7)

[0069] The coordinates of client point 9: (9,2)

[0070] Coordinates of client point 10: (5,5)

[0071] In the first step, several independent populations are generated through the initialization process. In this step, the system creates three populations through a random generation method, each of which contains 30 independent individuals. Each individual represents a vehicle path plan, that is, a permutation of the customer visit order. These individuals represent the initial solution in the problem space to be optimized. At the same time, we define the fitness function as the inverse of the total driving distance of the vehicle. The shorter the total driving distance of the vehicle, the greater the value of the fitness function.

[0072] In the second step, a multi-population genetic algorithm is used to perform selection, crossover and mutation operations within each independent population: individuals with higher fitness are selected from each population for reproduction; new individuals are generated using a sequential crossover method; exchange mutation is used to mutate individuals with a certain probability (i.e., two customer positions in the path are randomly exchanged). In order to prevent some excellent individuals from occupying resources too early and causing premature convergence of the population, the present invention introduces a fitness sharing mechanism. Specifically, in each generation of evolution, the fitness sharing mechanism adjusts the fitness value of the individual so that the individual can distribute resources fairly. This can not only ensure the diversity of the population, but also improve the global search capability and effectively avoid the local optimal solution trap.

[0073] The third step is to implement a regular migration strategy to increase gene mobility between populations and enhance the diversity of solutions. The specific implementation method is that every 50 generations, the system randomly migrates 10% of the individuals in each population to other populations. Through this step, different populations can exchange information with each other, improving the overall search and optimization capabilities of the algorithm.

[0074] The fourth step is to dynamically adjust the population size. In the optimization process, the diversity of the population is an important factor in improving the performance of the algorithm. The present invention introduces a technology for dynamically adjusting the population size, and adaptively adjusts the size of each population according to the diversity index (Shannon index) shown by the population during the evolution process. In this experiment, since the diversity index of the population is too high, the population size is reduced by 5% to avoid resource waste and excessive calculation.

[0075] The fifth step is to set multiple termination conditions to determine whether the algorithm has achieved the desired effect. These conditions include: the maximum number of iterations, or any independent population finds a solution with a fitness value lower than the preset threshold. In addition, if the population diversity decreases significantly, indicating that most individuals have tended to the same solution, the algorithm can also be terminated early. The introduction of multiple termination conditions ensures that the algorithm can be effectively terminated when the expected goal is achieved, saving computing resources. In this experiment, we set the maximum number of iterations to 500 generations to determine whether the algorithm has achieved the expected effect.

[0076] Step 6: Output the results. After completing all evolutionary iterations, the algorithm outputs the currently found global optimal solution. The optimal solution path is: 0->1->5->4->9->10->7->3->2->8->6->0. The fitness of each population tends to be stable after about 400 generations, showing good convergence.

[0077] Through experiments, it can be seen that the multi-population genetic algorithm shows better performance in optimizing vehicle routing problems and can find shorter paths in fewer iterations. This is mainly due to the migration operation between multiple sub-populations, which enhances the global search ability of the algorithm and avoids falling into local optimality. This method is not only applicable to routing optimization problems, but can also be extended to other similar engineering optimization problems, and has broad application prospects.

[0078] Embodiment 3

[0079] The present invention also provides an optimization system based on a multi-population genetic algorithm, comprising: an initialization module, an internal evolution module, an inter-population communication module, a dynamic adjustment module, a condition setting module and an output module;

[0080] The initialization module is used to initialize several populations;

[0081] The internal evolution module is used to perform selection, crossover and mutation operations within each population;

[0082] The inter-population communication module is used to introduce migration strategies between populations;

[0083] The dynamic adjustment module is used to dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process;

[0084] The condition setting module is used to set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect;

[0085] The output module is used to output the currently found global optimal solution after completing all evolutionary iterations.

[0086] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. An optimization method based on a multi-population genetic algorithm, characterized in that: The following steps are involved: Initialize several populations; Within each population, selection, crossover and mutation operations are performed separately; Introducing migration strategies between populations; Dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process; Set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect; After completing all evolutionary iterations, the currently found global optimal solution is output.

2. The optimization method based on multi-population genetic algorithm according to claim 1, characterized in that: Methods for initializing several populations include: A predetermined number of individuals are randomly generated for each population, and the initial size and parameters of each population are set.

3. The optimization method based on multi-population genetic algorithm according to claim 1, characterized in that: Within each population, the methods for performing selection, crossover, and mutation operations include: The selection operation retains individuals whose performance meets the preset requirements; Crossover and mutation operations are responsible for introducing new gene combinations and changes; The fitness sharing mechanism is used to modify the fitness value of individuals.

4. The optimization method based on multi-population genetic algorithm according to claim 1, characterized in that: Methods for introducing migration strategies between populations include: Periodically move some individuals from one population to another. Specifically, the migration strategy is set to a fixed frequency or to adaptively adjust the frequency according to population diversity.

5. The optimization method based on multi-population genetic algorithm according to claim 1, characterized in that: According to the convergence trend and diversity of the population during the evolution process, the methods for dynamically adjusting the population size include: When a population tends to converge and its diversity is lower than the preset requirement, the number of individuals in the population is reduced; on the contrary, when the diversity and optimization potential of the population are higher than the preset requirement, the population size is increased.

6. The optimization method based on multi-population genetic algorithm according to claim 1, characterized in that: The methods of setting multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect include: When the preset maximum number of iterations, the target fitness value is reached, or the population diversity is lower than the preset requirement, the algorithm will be triggered to stop running.

7. An optimization system based on a multi-population genetic algorithm, characterized in that: include: Initialization module, internal evolution module, inter-group communication module, dynamic adjustment module, condition setting module and output module; The initialization module is used to initialize several populations; The internal evolution module is used to perform selection, crossover and mutation operations within each population; The inter-population communication module is used to introduce migration strategies between populations; The dynamic adjustment module is used to dynamically adjust the population size according to the convergence trend and diversity of the population during the evolution process; The condition setting module is used to set multiple termination conditions to determine whether the multi-population genetic algorithm has achieved the desired effect; The output module is used to output the currently found global optimal solution after completing all evolutionary iterations.

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