Search

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the $\boldsymbol {\varepsilon }$ constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate. [ABSTRACT FROM AUTHOR]

This paper aims to design new strategies to extend traditional multiobjective optimization algorithms to efficiently obtain Pareto-optimal solutions in presence of noise on the objective surfaces. The first strategy, referred to as adaptive selection of sample size, is employed to balance the tradeoff between quality measure of fitness and run-time complexity. The second strategy is concerned with determining statistical expectation, instead of conventional averaging, of fitness samples as the measure of fitness of the trial solutions. The third strategy attempts to extend Goldberg's method to compare slightly worse trial solutions with its competitor by a more statistically viable comparator to examine possible placement of the former solution in the Pareto optimal front. The traditional differential evolution for multiobjective optimization algorithm has been modified by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the extended algorithm reveal that the extended algorithm outperforms its competitors with respect to three performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions. The extended algorithm has been applied on the well known box-pushing problem, where the forces and torques required to shift the box by two robots are evaluated to jointly satisfy the conflicting objectives on task-execution time and energy consumption in presence of noise on range estimates from the sidewalls of the workspace. The application justifies the importance of the proposed noise-handling strategies in practical systems. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]