Salvador Botello Rionda

Constrained optimization with an improved particle swarm optimization algorithm

Purpose – The purpose of this paper is to present a new constrained optimization algorithm based on a particle swarm optimization (PSO) algorithm approach.Design/methodology/approach – This paper introduces a hybrid approach based on a modified ring neighborhood with two new perturbation operators designed to keep diversity. A constraint handling technique based on feasibility and sum of constraints violation is adopted. Also, a special technique to handle equality constraints is proposed.Findings – The paper shows that it is possible to improve PSO and keeping the advantages of its social interaction through a simple idea: perturbing the PSO memory.Research limitations/implications – The proposed algorithm shows a competitive performance against the state‐of‐the‐art constrained optimization algorithms.Practical implications – The proposed algorithm can be used to solve single objective problems with linear or non‐linear functions, and subject to both equality and inequality constraints which can be linea...

A Novel Diversity-based Evolutionary Algorithm for the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard combinatorial optimization problems. In order to deal with large TSP instances, several heuristics and metaheuristics have been devised. In this paper, a novel memetic scheme that incorporates a new diversity-based replacement strategy is proposed and applied to the largest instances of the TSPLIB benchmark. The novelty of our method is that it combines the idea of transforming a single-objective problem into a multi-objective one, by considering diversity as an explicit objective, with the idea of adapting the balance induced between exploration and exploitation to the various optimization stages. In addition, the intensification capabilities of the individual learning method incorporated in the memetic scheme are also adapted by taking into account the stopping criterion. Computational results show the clear superiority of our scheme when compared against state-of-the-art schemes. To our knowledge, our proposal is the first evolutionary scheme that readily solves an instance with more than 30,000 cities to optimality.

PASSSS: an implementation of a novel diversity strategy for handling constraints

In this paper, we introduce PASSSS (PAS/sup 4/), the Pareto archived and dominance selection with shrinkable search space evolutionary computation algorithm. The main contribution of this paper is a diversity control mechanism embedded into the selection operator of an evolutionary algorithm that can be used (with little or no modification) to solve both single-objective and multi-objective optimization problems. We present a detailed description of the PAS/sup 4/ algorithm, and illustrate its capabilities by solving several engineering design problems and some test functions from a well-known benchmark in evolutionary optimization. Additionally, PAS/sup 4/ is also used to solve continuous and discrete multiobjective engineering optimization problems.

IS-PAES: a constraint-handling technique based on multiobjective optimization concepts

This paper introduces a new constraint-handling method called Inverted-Shrinkable PAES (IS-PAES), which focuses the search effort of an evolutionary algorithm on specific areas of the feasible region by shrinking the constrained space of single-objective optimization problems. IS-PAES uses an adaptive grid as the original PAES (Pareto Archived Evolution Strategy). However, the adaptive grid of IS-PAES does not have the serious scalability problems of the original PAES. The proposed constraint-handling approach is validated with several examples taken from the standard literature on evolutionary optimization.

Multiobjective shape optimization using estimation distribution algorithms and correlated information

We propose a new approach for multiobjective shape optimization based on the estimation of probability distributions. The algorithm improves search space exploration by capturing landscape information into the probability distribution of the population. Correlation among design variables is also used for the computation of probability distributions. The algorithm uses finite element method to evaluate objective functions and constraints. We provide several design problems and we show Pareto front examples. The design goals are: minimum weight and minimum nodal displacement, without holes or unconnected elements in the structure.

Why Unary Quality Indicators Are Not Inferior to Binary Quality Indicators

When evaluating the quality of non---dominated sets, two families of quality indicators are frequently used: unary quality indicators (UQI) and binary quality indicators (BQI). For several years, UQIs have been considered inferior to BQIs. As a result, the use of UQIs has been discouraged, even when in practice they are easier to use. In this work, we study the reasons why UQIs are considered inferior. We make a detailed analysis of the correctness of these reasons and the implicit assumptions in which they are based. The conclusion is that, contrary to what is widely believed, unary quality indicators are not inferior to binary ones.

IS-PAES: Multiobjective Optimization with Efficient Constraint Handling

This paper introduces a new constraint-handling method called Inverted-Shrinkable PAES (IS-PAES), which focuses the search e ort of an evolutionary algorithm on specific areas of the feasible region by shrinking the constrained space of single-objective optimization problems. IS-PAES uses an adaptive grid as the original PAES (Pareto Archived Evolution Strategy). However, IS-PAES does not have the serious scalability problems of the PAES. The viability of the proposed approach is validated with several examples taken from the standard evolutionary and engineering optimization literature.

Use of multiobjective optimization concepts to handle constraints in single-objective optimization

In this paper, we propose a new constraint-handling technique for evolutionary algorithms which is based on multiobjective optimization concepts. The approach uses Pareto dominance as its selection criterion, and it incorporates a secondary population. The new technique is compared with respect to an approach representative of the state-of-the-art in the area using a well-known benchmark for evolutionary constrained optimization. Results indicate that the proposed approach is able to match and even outperform the technique with respect to which it was compared at a lower computational cost.

The importance of diversity in the application of evolutionary algorithms to the Sudoku problem

The past few years have seen several variants of Evolutionary Algorithms (EAs) applied to solving Sudoku puzzles. Given that EAs with simple components do not work properly, considerable efforts have gone into designing ad-hoc evolutionary operators that profit from a knowledge of the problem. In this paper, we show that one of the main reasons for the improper behavior of EAs when dealing with difficult Sudoku puzzles is the appearance of premature convergence. Memetic algorithms with readily available genetic operators can be used to solve the hardest known Sudoku puzzles when general and well-known methods for avoiding premature convergence are incorporated. Among the approaches tested, a recently proposed method that is based on adopting multi-objective concepts for the solution of single-objective problems has shown remarkable performance. To our knowledge, the methods presented in this paper are the first EAs capable of solving the three Sudoku puzzles that are regarded as the most difficult ones known to date.

UNIFORMLY DISTRIBUTED PARETO FRONTS THROUGH THE MAXIMIN SELECTION ALGORITHM

This paper introduces the MaxiMin selection algorithm, a deterministic procedure to achieve maximal spread and almost perfectly distributed Pareto fronts. MaxiMin is successful because the measure of uniformity is performed on the set being constructed, not on the source set as most multi-objective algorithms do. For comparison purposes we present results delivered by several MOEAs with and without the MaxiMin selection. Performance metrics and graphical results show that MaxiMin improves the distribution and spread of Pareto fronts, with no negative effects on the convergence performance of the multi-objective algorithm.