Gregorio Toscano Pulido

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.

A Micro-Genetic Algorithm for Multiobjective Optimization

In this paper, we propose a multiobjective optimization approach based on a micro genetic algorithm (micro-GA) which is a genetic algorithm with a very small population (four individuals were used in our experiment) and a reinitialization process. We use three forms of elitism and a memory to generate the initial population of the micro-GA. Our approach is tested with several standard functions found in the specialized literature. The results obtained are very encouraging, since they show that this simple approach can produce an important portion of the Pareto front at a very low computational cost.

A constraint-handling mechanism for particle swarm optimization

This work presents a simple mechanism to handle constraints with a particle swarm optimization algorithm. Our proposal uses a simple criterion based on closeness of a particle to the feasible region in order to select a leader. Additionally, our algorithm incorporates a turbulence operator that improves the exploratory capabilities of our particle swarm optimization algorithm. Despite its relative simplicity, our comparison of results indicates that the proposed approach is highly competitive with respect to three constraint-handling techniques representative of the state-of-the-art in the area.

Using Clustering Techniques to Improve the Performance of a Multi-objective Particle Swarm Optimizer

In this paper, we present an extension of the heuristic called “particle swarm optimization” (PSO) that is able to deal with multiobjective optimization problems. Our approach uses the concept of Pareto dominance to determine the flight direction of a particle and is based on the idea of having a set of sub-swarms instead of single particles. In each sub-swarm, a PSO algorithm is executed and, at some point, the different sub-swarms exchange information. Our proposed approach is validated using several test functions taken from the evolutionary multiobjective optimization literature. Our results indicate that the approach is highly competitive with respect to algorithms representative of the state-of-the-art in evolutionary multiobjective optimization.

Ranking Methods for Many-Objective Optimization

An important issue with Evolutionary Algorithms (EAs) is the way to identify the best solutions in order to guide the search process. Fitness comparisons among solutions in single-objective optimization is straightforward, but when dealing with multiple objectives, it becomes a non-trivial task. Pareto dominance has been the most commonly adopted relation to compare solutions in a multiobjective optimization context. However, it has been shown that as the number of objectives increases, the convergence ability of approaches based on Pareto dominance decreases. In this paper, we propose three novel fitness assignment methods for many-objective optimization. We also perform a comparative study in order to investigate how effective are the proposed approaches to guide the search in high-dimensional objective spaces. Results indicate that our approaches behave better than six state-of-the-art fitness assignment methods.

The micro genetic algorithm 2: towards online adaptation in evolutionary multiobjective optimization

In this paper, we deal with an important issue generally omitted in the current literature on evolutionary multiobjective optimization: on-line adaptation. We propose a revised version of our micro-GA for multiobjective optimization which does not require any parameter fine-tuning. Furthermore, we introduce in this paper a dynamic selection scheme through which our algorithm decides which is the best crossover operator to be used at any given time. Such a scheme has helped to improve the performance of the new version of the algorithm which is called the micro-GA2 (μGA 2 ), The new approach is validated using several test function and metrics taken from the specialized literature and it is compared to the NSGA-Il and PAES.

A proposal to use stripes to maintain diversity in a multi-objective particle swarm optimizer

In this paper, we propose a new mechanism to maintain diversity in multi-objective optimization problems. The proposed mechanism is based on the use of stripes that are applied on objective function space and that is independent of the search engine adopted to solve the multi-objective optimization problem. In order to validate the proposed approach, we included it in a multi-objective particle swarm optimizer. Our approach was compared with respect to two multi-objective evolutionary algorithms, which are representative of the state-of-the-art in the area. The results obtained indicate that our proposed mechanism is a viable alternative to maintain diversity in the context of multi-objective optimization.

A Memetic PSO Algorithm for Scalar Optimization Problems

In this paper we introduce line search strategies originating from continuous optimization for the realization of the guidance mechanism in particle swarm optimization for scalar optimization problems. Since these techniques are well-suited for-but not restricted to-local search the resulting algorithm can be considered to be memetic. Further, we will use the same techniques for the construction of a new variant of a hill climber. We will discuss possible realizations and will finally present some numerical results indicating the strength of the two algorithms

A comparison on the search of particle swarm optimization and differential evolution on multi-objective optimization

Particle swarm optimization (PSO) and differential evolution (DE) are meta-heuristics which have been found to be successful in a wide variety of optimization tasks. The high speed of convergence and the relative simplicity of PSO make it a highly viable candidate to be used in multi-objective optimization problems (MOPs). Therefore, several PSO approaches capable to handle MOPs (MOPSOs) have appeared in the past. There are some problems, however, where PSO-based algorithms have shown a premature convergence. On the other hand, multi- objective DEs (MODE) have shown lower speed of convergence than MOPSOs but they have been successfully used in problems where MOPSO have mistakenly converged. In this work, we have developed experiments to observe the convergence behavior, the online convergence, and the diversity of solutions of both meta-heuristics in order to have a better understanding about how particles and solutions move in the search space. To this end, MOPSO and MODE algorithms under (to our best effort) similar conditions were used. Moreover, the ZDT test suite was used on all experiments since it allows to observe Pareto fronts in two-dimensional scatter plots (more details on this are presented on the experiments section). Based on the observations found, modifications to two PSO-based algorithms from the state of the art were proposed resulting in a rise on their performance. It is concluded that MOPSO presents a poor distributed scheme that leads to a more aggressive search. This aggressiveness showed to be detrimental for the selected problems. On the other hand, MODE seemed to generate better distributed points on both decision and objective space allowing it to produce better results.

A new mechanism to maintain diversity in multi-objective metaheuristics

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ϵ-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.