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This article considers a box-constrained global optimization problem for Lipschitz continuous functions with an unknown Lipschitz constant. The well-known derivative-free global search algorithm DIRECT (DIvide RECTangle) is a promising approach for such problems. Several studies have shown that recent two-step (global and local) Pareto selection-based algorithms are very efficient among all DIRECT-type approaches. However, despite its encouraging performance, it was also observed that the candidate selection procedure has two possible shortcomings. First, there is no limit on how small the size of selected candidates can be. Secondly, a balancing strategy between global and local candidate selection is missing. Therefore, it may waste function evaluations by over-exploring the current local minimum and delaying finding the global one. This paper reviews and employs different strategies in a two-step Pareto selection framework (1-DTC-GL) to overcome these limitations. A detailed experimental study has revealed that existing strategies do not always improve and sometimes even worsen results. Since 1-DTC-GL is a DIRECT-type algorithm, the results of this paper provide general guidance for all DIRECT-type algorithms on how to deal with excessive local refinement more efficiently. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA's robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

When solving complex constrained problems, how to efficiently utilize promising infeasible solutions is an essential issue because these promising infeasible solutions can significantly improve the diversity of algorithms. However, most existing constrained multi-objective evolutionary algorithms (CMOEAs) do not fully exploit these promising infeasible solutions. In order to solve this problem, a constrained multi-objective optimization evolutionary algorithm based on the dynamic constraint boundary method is proposed (CDCBM). The proposed algorithm continuously searches for promising infeasible solutions between UPF (the unconstrained Pareto front) and CPF (the constrained Pareto front) during the evolution process by the dynamically changing auxiliary population of the constraint boundary, which continuously provides supplementary evolutionary directions to the main population and improves the convergence and diversity of the main population. Extensive experiments on three well-known test suites and three real-world constrained multi-objective optimization problems demonstrate that CDCBM is more competitive than seven state-of-the-art CMOEAs. [ABSTRACT FROM AUTHOR]

Self-adaptive variants of evolutionary algorithms (EAs) tune their parameters on the go by learning from the search history. Adaptive differential evolution with optional external archive (JADE) and self-adaptive differential evolution (SaDE) are two well-known self-adaptive versions of differential evolution (DE). They are both unconstrained search and optimization algorithms. However, if some constraint handling techniques (CHTs) are incorporated in their frameworks, then they can be used to solve constrained optimization problems (COPs). In an early work, an ensemble of constraint handling techniques (ECHT) is probabilistically hybridized with the basic version of DE. The ECHT consists of four different CHTs: superiority of feasible solutions, self-adaptive penalty, ε -constraint handling technique and stochastic ranking. This paper employs ECHT in the selection schemes, where offspring competes with their parents for survival to the next generation, of JADE and SaDE. As a result, JADE-ECHT and SaDE-ECHT are developed, which are the constrained variants of JADE and SaDE. Both algorithms are tested on 24 COPs and the experimental results are collected and compared according to algorithms' evaluation criteria of CEC'06. Their comparison, in terms of feasibility rate (FR) and success rate (SR), shows that SaDE-ECHT surpasses JADE-ECHT in terms of FR, while JADE-ECHT outperforms SaDE-ECHT in terms of SR. [ABSTRACT FROM AUTHOR]

The heap-based optimizer (HBO) is an innovative meta-heuristic inspired by human social behavior. In this research, binary adaptations of the heap-based optimizer B _ H B O are presented and used to determine the optimal features for classifications in wrapping form. In addition, HBO balances exploration and exploitation by employing self-adaptive parameters that can adaptively search the solution domain for the optimal solution. In the feature selection domain, the presented algorithms for the binary Heap-based optimizer B _ H B O are used to find feature subsets that maximize classification performance while lowering the number of selected features. The textitk-nearest neighbor (textitk-NN) classifier ensures that the selected features are significant. The new binary methods are compared to eight common optimization methods recently employed in this field, including Ant Lion Optimization (ALO), Archimedes Optimization Algorithm (AOA), Backtracking Search Algorithm (BSA), Crow Search Algorithm (CSA), Levy flight distribution (LFD), Particle Swarm Optimization (PSO), Slime Mold Algorithm (SMA), and Tree Seed Algorithm (TSA) in terms of fitness, accuracy, precision, sensitivity, F-score, the number of selected features, and statistical tests. Twenty datasets from the UCI repository are evaluated and compared using a set of evaluation indicators. The non-parametric Wilcoxon rank-sum test was used to determine whether the proposed algorithms' results varied statistically significantly from those of the other compared methods. The comparison analysis demonstrates that B _ H B O is superior or equivalent to the other algorithms used in the literature. [ABSTRACT FROM AUTHOR]