Hybrid Simulated Annealing: An Efficient Optimization Technique

Genetic Algorithm falls under the category of evolutionary algorithm that follows the principles of natural selection and genetics, where the best adapted individuals in a population are more likely to survive and reproduce, passing on their advantageous traits to their offsprings. Crossover is a crucial operator in genetic algorithms as it allows the genetic material of two or more individuals in the population to combine and create new individuals. Optimizing it can potentially lead to better solutions and faster convergence of the genetic algorithm. The proposed crossover operator gradually changes the alpha value as the search proceeds, similar to the temperature in simulated annealing. The performance of the proposed crossover operator is compared with the simple arithmetic crossover operator. The experiments are conducted using Python and results show that the proposed crossover operator outperforms the simple arithmetic crossover operator. This paper also emphasizes the importance of optimizing genetic operators, particularly crossover operators, to improve the overall performance of genetic algorithms

Dynastic Potential Crossover Operator

An optimal recombination operator for two parent solutions provides the best solution among those that take the value for each variable from one of the parents (gene transmission property). If the solutions are bit strings, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. Exploring this hyperplane is computationally costly, in general, requiring exponential time in the worst case. However, when the variable interaction graph of the objective function is sparse, exploration can be done in polynomial time. In this paper, we present a recombination operator, called Dynastic Potential Crossover (DPX), that runs in polynomial time and behaves like an optimal recombination operator for low-epistasis combinatorial problems. We compare this operator, both theoretically and experimentally, with traditional crossover operators, like uniform crossover and network crossover, and with two recently defined efficient recombination operators: partition crossover and articulation points partition crossover. The empirical comparison uses NKQ Landscapes and MAX-SAT instances. DPX outperforms the other crossover operators in terms of quality of the offspring and provides better results included in a trajectory and a population-based metaheuristic, but it requires more time and memory to compute the offspring.This research is partially funded by the Universidad de M\'alaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under grant number UMA18-FEDERJA-003 (PRECOG); under grant PID 2020-116727RB-I00 (HUmove) funded by MCIN/AEI/10.13039/501100011033; and TAILOR ICT-48 Network (No 952215) funded by EU Horizon 2020 research and innovation programme. The work is also partially supported in Brazil by São Paulo Research Foundation (FAPESP), under grants 2021/09720-2 and 2019/07665-4, and National Council for Scientific and Technological Development (CNPq), under grant 305755/2018-8

Dynastic potential crossover operator

An optimal recombination operator provides an optimal solution fulfilling the gene transmission property: the value of any variable in the offspring must be inherited from one of the parents. In the case of binary variables, the offspring of an optimal recombination operator is optimal in the smallest hyperplane containing the two parent solutions. In general, exploring this hyperplane is computationally costly, but if the objective function has a low number of nonlinear interactions among the variables, the exploration can be done in $O(4^{\beta}(n+m)+n^2)$ time, for problems with $n$ decision variables, $m$ subfunctions composing the objective function and where $\beta$ is a constant. In this talk, we present a quasi-optimal recombination operator, called Dynastic Potential Crossover (DPX), that runs in $O(4^{\beta}(n+m)+n^2)$ time in any case and is able to act as an optimal recombination operator for low-epistasis combinatorial problems. We show some experimental results where the operator is integrated in DRILS (an ILS with recombination) and standard EA solving NKQ Landscapes and MAX-SAT.This research is funded by the Spanish Ministry of Economy and Competitiveness and FEDER under contract TIN2017-88213-R, and the University of Malaga. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Genetic Algorithm with 3-parent Uniform Crossover

A new genetic algorithm which uses a 3-parent uniform crossover operator is developed and analyzed. Uniform crossover operators are shown to be based on the premise that all bit-level genetic information should be passed from parents to children. The 3-parent uniform crossover operator is shown to adhere to this premise. The 3-parent uniform crossover operator is shown to be better than the 2-parent uniform crossover operator on the De Jong test functions. Two new genetic algorithms which use 3-parent traditional crossover operators are developed and analyzed. The first uses a strategy of randomly selecting 3 of the 6 children resulting from 3-parent reproduction. The second uses a strategy of selecting the best 3 of the 6 children resulting from 3-parent reproduction. Each of the 3-parent traditional crossover operators is shown to be superior to the 2-parent traditional crossover operator on the De Jong test functions. The strategy of selecting the best 3 out of 6 children is shown to be superior to the strategy of randomly selecting 3 out of 6 children. In addition to these 3-parent genetic algorithms, a relationship between the Metropolis algorithm from simulated annealing and the two-membered evolution strategy is developed. The Metropolis algorithm is shown to be a special case of the two- membered evolution strategy

CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods

A COMPARATIVE STUDY OF CROSSOVER OPERATORS FOR GENETIC ALGORITHMS TO SOLVE TRAVELLING SALESMAN PROBLEM

Genetic algorithms (GAs) represent a method that mimics the process of natural evolution in effort to find good solutions. In that process, crossover operator plays an important role. To comprehend the genetic algorithms as a whole, it is necessary to understand the role of a crossover operator. Today, there are a number of different crossover operators that can be used , one of the problems in using genetic algorithms is the choice of crossover operator Many crossover operators have been proposed in literature on evolutionary algorithms, however, it is still unclear which crossover operator works best for a given optimization problem. This paper aims at studying the behavior of different types of crossover operators in the performance of genetic algorithm. These types of crossover are implemented on Traveling Salesman Problem (TSP); Whitley used the order crossover (OX) depending on specific parameters to solve the traveling salesman problem, the aim of this paper is to make a comparative study between order crossover (OX) and other types of crossover using the same parameters which was Whitley used