Carlos A. Coello

Handling multiple objectives with particle swarm optimization

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.

Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art

Abstract This paper provides a comprehensive survey of the most popular constraint-handling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the immune system, culture or ant colonies. Besides describing briefly each of these approaches (or groups of techniques), we provide some criticism regarding their highlights and drawbacks. A small comparative study is also conducted, in order to assess the performance of several penalty-based approaches with respect to a dominance-based technique proposed by the author, and with respect to some mathematical programming approaches. Finally, we provide some guidelines regarding how to select the most appropriate constraint-handling technique for a certain application, and we conclude with some of the most promising paths of future research in this area.

A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques

This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described with its advantages and disadvantages, its degree of applicability and some of its known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed.This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described with its advantages and disadvantages, its degree of applicability and some of its known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed.

An updated survey of GA-based multiobjective optimization techniques

After using evolutionary techniques for single-objective optimization during more than two decades, the incorporation of more than one objective in the fitness function has finally become a popular area of research. As a consequence, many new evolutionary-based approaches and variations of existing techniques have recently been published in the technical literature. The purpose of this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the operations research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new ways of exploiting the search capabilities of evolutionary algorithms. Furthermore, a summary of the main algorithms behind these approaches is provided, together with a brief criticism that includes their advantages and disadvantages, degree of applicability, and some known applications. Finally, further trends in this area and some possible paths for further research are also addressed.

Use of a self-adaptive penalty approach for engineering optimization problems

Abstract This paper introduces the notion of using co-evolution to adapt the penalty factors of a fitness function incorporated in a genetic algorithm (GA) for numerical optimization. The proposed approach produces solutions even better than those previously reported in the literature for other (GA-based and mathematical programming) techniques that have been particularly fine-tuned using a normally lengthy trial and error process to solve a certain problem or set of problems. The present technique is also easy to implement and suitable for parallelization, which is a necessary further step to improve its current performance.

A simple multimembered evolution strategy to solve constrained optimization problems

This work presents a simple multimembered evolution strategy to solve global nonlinear optimization problems. The approach does not require the use of a penalty function. Instead, it uses a simple diversity mechanism based on allowing infeasible solutions to remain in the population. This technique helps the algorithm to find the global optimum despite reaching reasonably fast the feasible region of the search space. A simple feasibility-based comparison mechanism is used to guide the process toward the feasible region of the search space. Also, the initial stepsize of the evolution strategy is reduced in order to perform a finer search and a combined (discrete/intermediate) panmictic recombination technique improves its exploitation capabilities. The approach was tested with a well-known benchmark. The results obtained are very competitive when comparing the proposed approach against other state-of-the art techniques and its computational cost (measured by the number of fitness function evaluations) is lower than the cost required by the other techniques compared.

A comparative study of differential evolution variants for global optimization

In this paper, we present an empirical comparison of some Differential Evolution variants to solve global optimization problems. The aim is to identify which one of them is more suitable to solve an optimization problem, depending on the problems features and also to identify the variant with the best performance, regardless of the features of the problem to be solved. Eight variants were implemented and tested on 13 benchmark problems taken from the specialized literature. These variants vary in the type of recombination operator used and also in the way in which the mutation is computed. A set of statistical tests were performed in order to obtain more confidence on the validity of the results and to reinforce our discussion. The main aim is that this study can help both researchers and practitioners interested in using differential evolution as a global optimizer, since we expect that our conclusions can provide some insights regarding the advantages or limitations of each of the variants studied.

CONSTRAINT-HANDLING IN GENETIC ALGORITHMS THROUGH THE USE OF DOMINANCE-BASED TOURNAMENT SELECTION

Abstract In this paper, we propose a dominance-based selection scheme to incorporate constraints into the fitness function of a genetic algorithm used for global optimization. The approach does not require the use of a penalty function and, unlike traditional evolutionary multiobjective optimization techniques, it does not require niching (or any other similar approach) to maintain diversity in the population. We validated the algorithm using several test functions taken from the specialized literature on evolutionary optimization. The results obtained indicate that the approach is a viable alternative to the traditional penalty function, mainly in engineering optimization problems.

Improving PSO-Based multi-objective optimization using crowding, mutation and ∈-dominance

In this paper, we propose a new Multi-Objective Particle Swarm Optimizer, which is based on Pareto dominance and the use of a crowding factor to filter out the list of available leaders. We also propose the use of different mutation (or turbulence) operators which act on different subdivisions of the swarm. Finally, the proposed approach also incorporates the ∈-dominance concept to fix the size of the set of final solutions produced by the algorithm. Our approach is compared against five state-of-the-art algorithms, including three PSO-based approaches recently proposed. The results indicate that the proposed approach is highly competitive, being able to approximate the front even in cases where all the other PSO-based approaches fail.

Solving Multiobjective Optimization Problems Using an Artificial Immune System

In this paper, we propose an algorithm based on the clonal selection principle to solve multiobjective optimization problems (either constrained or unconstrained). The proposed approach uses Pareto dominance and feasibility to identify solutions that deserve to be cloned, and uses two types of mutation: uniform mutation is applied to the clones produced and non-uniform mutation is applied to the “not so good” antibodies (which are represented by binary strings that encode the decision variables of the problem to be solved). We also use a secondary (or external) population that stores the nondominated solutions found along the search process. Such secondary population constitutes the elitist mechanism of our approach and it allows it to move towards the true Pareto front of a problem over time. Our approach is compared with three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, three metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is a viable alternative to solve multiobjective optimization problems.