Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary al...
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Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary algorithms (SAEAs) in EOPs, we discovered an intriguing phenomenon. Because only a limited number of solutions are evaluated in each iteration, relying solely on these evaluated solutions for evolution can lead to reduced disparity in successive populations. This, in turn, hampers the reproduction operators' ability to generate superior solutions, thereby reducing the algorithm's convergence speed. To address this issue, we propose a strategic approach that incorporates high-quality, un-evaluated solutions predicted by surrogate models during the selection phase. This approach aims to improve the distribution of evaluated solutions, thereby generating a superior next generation of solutions. This work details specific implementations of this concept across various reproduction operators and validates its effectiveness using multiple surrogate models. Experimental results demonstrate that the proposed strategy significantly enhances the performance of surrogate-assisted evolutionary algorithms. Compared to mainstream SAEAs and Bayesian optimization algorithms, our approach incorporating the un-evaluated solution strategy shows a marked improvement.
Evolutionary algorithms are popular optimization tools for real-world applications due to their numerous advantages such as capability of parallel search along multiple directions by maintaining a population of candid...
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Evolutionary algorithms are popular optimization tools for real-world applications due to their numerous advantages such as capability of parallel search along multiple directions by maintaining a population of candidates, invariance to certain mathematical properties (convexity, continuity and hardness) of fitness landscape and ability to handle black-box problems. However, most of the current evolutionary algorithms are loosely based on heuristics inspired by nature and lack the crucial theoretical background. Motivated by the overwhelming advantages of such optimization algorithms and the necessity for theoretical foundation, this paper presents a new evolutionary algorithm - UDE (Uniform Differential Evolution) for solving single- objective optimization problems along with a theoretical analysis of the proposed UDE algorithm. Thus, this paper formally gives insights about the features and properties of the various optimization strategies used. This method is different from traditional Differential Evolution variants as it employs a uniform probability distribution for generating new candidate solutions. UDE is further developed to obtain an adaptive evolutionary algorithm - Adaptive UDE (AUDE), which has shown to obtain significant improvements in the performance and convergence speeds compared to other algorithms on a benchmark set of 19 test problems. The source codes are available at.
According to the Karush-Kuhn-Tucker condition, the Pareto set (PS) of a continuous m-objective optimization problem is a continuous (m - 1)-D piecewise manifold. Based on this regularity property, the ratio of the sum...
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According to the Karush-Kuhn-Tucker condition, the Pareto set (PS) of a continuous m-objective optimization problem is a continuous (m - 1)-D piecewise manifold. Based on this regularity property, the ratio of the sum of the first (m - 1) largest eigenvalue of the population's covariance matrix to the sum of the whole eigenvalue can be employed to illustrate the degree of convergence of the population. This paper proposes a new algorithm, named DE/RM-MEDA, which hybridizes differential evolution (DE) and estimation of distribution algorithm (EDA) for multiobjective optimization problems (MOPs) with the complicated PS. In the proposed algorithm, EDA extracts the population distribution information to sample new trial solutions by establishing a probability model, while DE uses the individual information to create others new individuals through the mutation and crossover operators. At each generation, the number of new solutions generated by the two operators is adjusted by the above-defined ratio. The proposed algorithm is validated on nine tec09 problems. The sensitivity and the scalability have also been experimentally investigated in this paper. The comparison results between DE/RM-MEDA and the other two state-of-the-art evolutionary algorithms, namely NSGA-II-DE and RM-MEDA, show that the proposed algorithm is highly competitive algorithms for solving MOPs with complicated PSs in terms of convergence and diversity metrics.
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