Numerical Constrained Optimization Problems Research Articles

The Performance of Penalty Methods on Tree-Seed Algorithm for Numerical Constrained Optimization Problems

The constraints are the most important part of many optimization problems. The metaheuristic algorithms are designed for solving continuous unconstrained optimization problems initially. The constraint handling methods are integrated into these algorithms for solving constrained optimization problems. Penalty approaches are not only the simplest way but also as effective as other constraint handling techniques. In literature, there are many penalty approaches and these are grouped as static, dynamic and adaptive. In this study, we collect them and discuss the key benefits and drawbacks of these techniques. Tree-Seed Algorithm (TSA) is a recently developed metaheuristic algorithm, and in this study, nine different penalty approaches are integrated with the TSA. The performance of these approaches is analyzed on well-known thirteen constrained benchmark functions. The obtained results are compared with state-of-art algorithms like Differential Evolution (DE), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Genetic Algorithm (GA). The experimental results and comparisons show that TSA outperformed all of them on these benchmark functions

An Improved Centroid-Based Boundary Constraint-Handling Method in Differential Evolution for Constrained Optimization

Differential Evolution (DE) is a population-based Evolutionary Algorithm (EA) for solving optimization problems over continuous spaces. Many optimization problems are constrained and have a bounded search space from which some vectors leave when the mutation operator of DE is applied. Therefore, it is necessary the use of a boundary constraint-handling method (BCHM) in order to repair the invalid mutant vectors. This paper presents a generalized and improved version of the Centroid BCHM in order to keep the search within the valid ranges of decision variables in constrained numerical optimization problems (CNOPs), which has been tested on a robust and comprehensive set of experiments that include a variant of DE specialized in dealing with CNOPs. This new version, named Centroid [Formula: see text], relocates the mutant vector in the centroid formed by K random vectors and one vector taken from the population that is within or near the feasible region. The results show that this new version has a major impact on the algorithm’s performance, and it is able to promote better final results through the improvement of both, the approach to the feasible region and the ability to generate better solutions.

Linear adjustment of a search space in genetic algorithm

The concept of a search space adjustment is developed in order to improve a performance of genetic algorithms (GAs) for solving numerical constrained optimization problems. Implementation of a linear adjustment of a search space size significantly reduces a computational cost to obtain an optimal solution in comparison with other methods of GA. Ability of this approach is demonstrated by using several test cases. Other constrained optimization algorithms are also used to make comparisons with represented approach.

Optimization Method RasID-GA for Numerical Constrained Optimization Problems

This paper proposes Adaptive Random search with Intensification and Diversification combined with Genetic Algorithm (RasID-GA) for constrained optimization. In the previous work, we proposed RasID-GA which combines the best properties of RasID and Genetic Algorithm for unconstrained optimization problems. In general, it is very difficult to find an optimal solution for constrained optimization problems because their feasible solution space is very limited and they should consider the objective functions and constraint conditions. The conventional constrained optimization methods usually use penalty functions to solve given problems. But, it is generally recognized that the penalty function is hard to handle in terms of the balance between penalty functions and objective functions. In this paper, we propose a constrained optimization method using RasID-GA, which solves given problems without using penalty functions. The proposed method is tested and compared with Evolution Strategy with Stochastic Ranking using well-known 11 benchmark problems with constraints. From the Simulation results, RasID-GA can find an optimal solution or approximate solutions without using penalty functions.

A population ecology inspired parent selection strategy for numerical constrained optimization problems

A population ecology inspired parent selection strategy is proposed to improve the searching ability of evolutionary algorithms for numerical constrained optimization problems. This method is mainly used to help find an appropriate number of feasible parents for offspring generation. Based on the similar phenomenon in population ecology, the number of feasible parents has a sigmoid-type relationship with that of the feasible individuals. To implement the novel parent selection strategy, the population is divided into two groups according to the feasibility of the individuals: the feasible group and infeasible group. The evaluation and ranking of these two groups are performed separately. The dynamic penalty method, annealing penalty method and stochastic ranking method are tested with the parent selection strategy on 13 benchmark problems. The results show that the proposed method is capable of improving the searching performance.

Evolutionary algorithm using feasibility-based grouping for numerical constrained optimization problems

Different strategies for defining the relationship between feasible and infeasible individuals in evolutionary algorithms can provide with very different results when solving numerical constrained optimization problems. This paper proposes a novel EA to balance the relationship between feasible and infeasible individuals to solve numerical constrained optimization problems. According to the feasibility of the individuals, the population is divided into two groups, feasible group and infeasible group. The evaluation and ranking of these two groups are performed separately. Parents for reproduction are selected from the two groups by a novel parent selection method. The proposed method is tested using ( μ, λ) evolution strategies with 13 benchmark problems. The results show that the proposed method improves the searching performance for most of the tested problems.