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• A parallel EA with primary-auxiliary knowledge is proposed, using our improved cuckoo search algorithm as the primary knowledge and integrating several other EA as the auxiliary knowledge, which fundamentally enables the hybrid of different algorithms and greatly enhances algorithmic diversity. • The way of acting of the evolutionary strategy change from the traditional greedy selection to the balanced primary-auxiliary approach in this paper, which allows each strategy to work in iteration. • A novel knowledge migration strategy is proposed, which allows the primary knowledge to learn the excellent knowledge from the auxiliary knowledge through a novel topology designed for knowledge migration. The development of hybrid algorithms or the application of multiple strategies is one of the focal points for research on improving evolutionary algorithms. However, since most of the evolutionary equations of different algorithms can be transformed into each other, it is difficult to change the established properties of the given algorithm through a hybrid algorithm based on a mixture of evolutionary equations. In addition, multi-strategy methods tend to adopt the best strategy for the current local domain through greedy strategies in the solution process, which does not ensure validity in the global domain. Recently, Federated Learning has achieved remarkable results in machine learning, where the idea of model independence, parallelism and data sharing can essentially compensate for the weaknesses of hybrid and multi-strategy algorithms. Inspired by the idea of Federated Learning, this paper proposes an evolutionary algorithm named as parallel based Evolutionary Algorithm with primary-auxiliary knowledge. Specifically, a Spark-based primary-auxiliary knowledge model is developed, with different evolutionary algorithms used on each parallel sub-model. Then, an effective topological knowledge (individual) migration method is devised, which enables the primary knowledge model to learn the best knowledge from different auxiliary knowledge models through a topological structure. In this way, the best knowledge on the auxiliary knowledge models can be transferred to the primary knowledge model. Through a test conducted on the CEC2013 test set, it can be found out that the proposed algorithm clearly outperforms the 10 algorithms compared, which demonstrates the excellent performance of our proposed parallel based evolutionary algorithm with primary-auxiliary knowledge. [ABSTRACT FROM AUTHOR]

• A parallel EA with primary-auxiliary knowledge is proposed, using our improved cuckoo search algorithm as the primary knowledge and integrating several other EA as the auxiliary knowledge, which fundamentally enables the hybrid of different algorithms and greatly enhances algorithmic diversity. • The way of acting of the evolutionary strategy change from the traditional greedy selection to the balanced primary-auxiliary approach in this paper, which allows each strategy to work in iteration. • A novel knowledge migration strategy is proposed, which allows the primary knowledge to learn the excellent knowledge from the auxiliary knowledge through a novel topology designed for knowledge migration. The development of hybrid algorithms or the application of multiple strategies is one of the focal points for research on improving evolutionary algorithms. However, since most of the evolutionary equations of different algorithms can be transformed into each other, it is difficult to change the established properties of the given algorithm through a hybrid algorithm based on a mixture of evolutionary equations. In addition, multi-strategy methods tend to adopt the best strategy for the current local domain through greedy strategies in the solution process, which does not ensure validity in the global domain. Recently, Federated Learning has achieved remarkable results in machine learning, where the idea of model independence, parallelism and data sharing can essentially compensate for the weaknesses of hybrid and multi-strategy algorithms. Inspired by the idea of Federated Learning, this paper proposes an evolutionary algorithm named as parallel based Evolutionary Algorithm with primary-auxiliary knowledge. Specifically, a Spark-based primary-auxiliary knowledge model is developed, with different evolutionary algorithms used on each parallel sub-model. Then, an effective topological knowledge (individual) migration method is devised, which enables the primary knowledge model to learn the best knowledge from different auxiliary knowledge models through a topological structure. In this way, the best knowledge on the auxiliary knowledge models can be transferred to the primary knowledge model. Through a test conducted on the CEC2013 test set, it can be found out that the proposed algorithm clearly outperforms the 10 algorithms compared, which demonstrates the excellent performance of our proposed parallel based evolutionary algorithm with primary-auxiliary knowledge. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm (UMDA) for a class of parametric functions with isolated global optima. We prove a number of results that are used to model the evolution of UMDA probability distributions for this class of functions. We show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of UMDA. We also introduce for the first time a long string limit analysis of UMDA. Finally, we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints. [Copyright &y& Elsevier]