Michael N. Vrahatis

Recent approaches to global optimization problems through Particle Swarm Optimization

This paper presents an overview of our most recent results concerning the Particle Swarm Optimization (PSO) method. Techniques for the alleviation of local minima, and for detecting multiple minimizers are described. Moreover, results on the ability of the PSO in tackling Multiobjective, Minimax, Integer Programming and ℓ1 errors-in-variables problems, as well as problems in noisy and continuously changing environments, are reported. Finally, a Composite PSO, in which the heuristic parameters of PSO are controlled by a Differential Evolution algorithm during the optimization, is described, and results for many well-known and widely used test functions are given.

On the computation of all global minimizers through particle swarm optimization

This paper presents approaches for effectively computing all global minimizers of an objective function. The approaches include transformations of the objective function through the recently proposed deflection and stretching techniques, as well as a repulsion source at each detected minimizer. The aforementioned techniques are incorporated in the context of the particle swarm optimization (PSO) method, resulting in an efficient algorithm which has the ability to avoid previously detected solutions and, thus, detect all global minimizers of a function. Experimental results on benchmark problems originating from the fields of global optimization, dynamical systems, and game theory, are reported, and conclusions are derived.

Particle swarm optimization method in multiobjective problems

This paper constitutes a first study of the Particle Swarm Optimization (PSO) method in Multiobjective Optimization (MO) problems. The ability of PSO to detect Pareto Optimal points and capture the shape of the Pareto Front is studied through experiments on well-known non-trivial test functions. The Weighted Aggregation technique with fixed or adaptive weights is considered. Furthermore, critical aspects of the VEGA approach for Multiobjective Optimization using Genetic Algorithms are adapted to the PSO framework in order to develop a multi-swarm PSO that can cope effectively with MO problems. Conclusions are derived and ideas for further research are proposed.

Particle Swarm Optimization and Intelligence: Advances and Applications

Particle Swarm Optimization and Intelligence: Advances and Applications examines modern intelligent optimization algorithms proven as very efficient in applications from various scientific and technological fields. Providing distinguished and unique research, this innovative publication offers a compendium of leading field experiences as well as theoretical analyses and complementary techniques useful to academicians and practitioners.

Particle swarm optimization for integer programming

The investigation of the performance of the particle swarm optimization (PSO) method in integer programming problems, is the main theme of the present paper. Three variants of PSO are compared with the widely used branch and bound technique, on several integer programming test problems. Results indicate that PSO handles efficiently such problems, and in most cases it outperforms the branch and bound technique.

Enhancing Differential Evolution Utilizing Proximity-Based Mutation Operators

Differential evolution is a very popular optimization algorithm and considerable research has been devoted to the development of efficient search operators. Motivated by the different manner in which various search operators behave, we propose a novel framework based on the proximity characteristics among the individual solutions as they evolve. Our framework incorporates information of neighboring individuals, in an attempt to efficiently guide the evolution of the population toward the global optimum, without sacrificing the search capabilities of the algorithm. More specifically, the random selection of parents during mutation is modified, by assigning to each individual a probability of selection that is inversely proportional to its distance from the mutated individual. The proposed framework can be applied to any mutation strategy with minimal changes. In this paper, we incorporate this framework in the original differential evolution algorithm, as well as other recently proposed differential evolution variants. Through an extensive experimental study, we show that the proposed framework results in enhanced performance for the majority of the benchmark problems studied.

Parallel differential evolution

Parallel processing has emerged as a key enabling technology in modern computing. Recent software advances have allowed collections of heterogeneous computers to be used as a concurrent computational resource. In this work we explore how differential evolution can be parallelized, using a ring-network topology, so as to improve both the speed and the performance of the method. Experimental results indicate that the extent of information exchange among subpopulations assigned to different processor nodes, bears a significant impact on the performance of the algorithm. Furthermore, not all the mutation strategies of the differential evolution algorithm are equally sensitive to the value of this parameter.

Effective backpropagation training with variable stepsize

The issue of variable stepsize in the backpropagation training algorithm has been widely investigated and several techniques employing heuristic factors have been suggested to improve training time and reduce convergence to local minima. In this contribution, backpropagation training is based on a modified steepest descent method which allows variable stepsize. It is computationally efficient and posseses interesting convergence properties utilizing estimates of the Lipschitz constant without any additional computational cost. The algorithm has been implemented and tested on several problems and the results have been very satisfactory. Numerical evidence shows that the method is robust with good average performance on many classes of problems. Copyright 1996 Elsevier Science Ltd.

Unified particle swarm optimization for solving constrained engineering optimization problems

We investigate the performance of the recently proposed Unified Particle Swarm Optimization method on constrained engineering optimization problems. For this purpose, a penalty function approach is employed and the algorithm is modified to preserve feasibility of the encountered solutions. The algorithm is illustrated on four well–known engineering problems with promising results. Comparisons with the standard local and global variant of Particle Swarm Optimization are reported and discussed.

Memetic particle swarm optimization

Abstract We propose a new Memetic Particle Swarm Optimization scheme that incorporates local search techniques in the standard Particle Swarm Optimization algorithm, resulting in an efficient and effective optimization method, which is analyzed theoretically. The proposed algorithm is applied to different unconstrained, constrained, minimax and integer programming problems and the obtained results are compared to that of the global and local variants of Particle Swarm Optimization, justifying the superiority of the memetic approach.