Donald Davendra

Scheduling flow shops using differential evolution algorithm

This paper describes a novel optimization method based on a differential evolution (exploration) algorithm and its applications to solving non-linear programming problems containing integer and discrete variables. The techniques for handling discrete variables are described as well as the techniques needed to handle boundary constraints. In particular, the application of differential evolution algorithm to minimization of makespan, flowtime and tardiness in a flow shop manufacturing system is given in order to illustrate the capabilities and the practical use of the method. Experiments were carried out to compare results from the differential evolution algorithm and the genetic algorithm, which has a reputation for being very powerful. The results obtained have proven satisfactory in solution quality when compared with genetic algorithm. The novel method requires few control variables, is relatively easy to implement and use, effective, and efficient, which makes it an attractive and widely applicable approach for solving practical engineering problems. Future directions in terms of research and applications are given.

Differential Evolution: A Handbook for Global Permutation-Based Combinatorial Optimization

This is the first book devoted entirely to Differential Evolution (DE) for global permutative-based combinatorial optimization. Since its original development, DE has mainly been applied to solving problems characterized by continuous parameters. This means that only a subset of real-world problems could be solved by the original, classical DE algorithm. This book presents in detail the various permutative-based combinatorial DE formulations by their initiators in an easy-to-follow manner, through extensive illustrations and computer code. It is a valuable resource for professionals and students interested in DE in order to have full potentials of DE at their disposal as a proven optimizer. All source programs in C and Mathematica programming languages are downloadable from the website of Springer.

Chaos driven evolutionary algorithms for the task of PID control

Chaos driven Differential Evolution algorithm and Self-Organizing Migrating Algorithm are presented in this paper for the task of PID (Proportional-Integral-Derivative) controller optimization. The dissipative chaotic Lozi map is embedded as a number generator inside DE and SOMA in order to avoid local optima stagnation and embed a superior search strategy. Three unique PID controller problems are presented and successfully resolved using these new approaches. The obtained results compare favorably with published results.

On the behavior and performance of chaos driven PSO algorithm with inertia weight

In this paper, the utilization of chaos pseudorandom number generators based on three different chaotic maps to alter the behavior and overall performance of PSO algorithm is proposed. This paper presents results of testing the performance and behavior of the proposed algorithm on typical benchmark functions that represent unimodal and multimodal problems. The promising results are analyzed and discussed.

Analytical Programming - a Novel Approach for Evolutionary Synthesis of Symbolic Structures

This chapter discusses an alternative approach for symbolic structures and solutions synthesis and demonstrates a comparison with other methods, for example Genetic Programming (GP) or Grammatical Evolution (GE). Generally, there are two well known methods, which can be used for symbolic structures synthesis by means of computers. The first one is called GP and the other is GE. Another interesting research was carried out by Artificial Immune Systems (AIS) or/and systems, which do not use tree structures like linear GP and other similar algorithm like Multi Expression Programming (MEP), etc. In this chapter, a different method called Analytic Programming (AP), is presented. AP is a grammar free algorithmic superstructure, which can be used by any programming language and also by any arbitrary Evolutionary Algorithm (EA) or another class of numerical optimization method. This chapter describes not only theoretical principles of AP, but also its comparative study with selected well known case examples from GP as well as applications on synthesis of: controller, systems of deterministic chaos, electronics circuits, etc. For simulation purposes, AP has been co-joined with EA’s like Differential Evolution (DE), Self-Organising Migrating Algorithm (SOMA), Genetic Algorithms (GA) and Simulated Annealing (SA). All case studies has been carefully prepared and repeated in order to get valid statistical data for proper conclusions. The term symbolic regression represents a process during which measured data sets are fitted, thereby a corresponding mathematical formula is obtained in an analytical way. An output

Utilization of SOMA and differential evolution for robust stabilization of chaotic Logistic equation

This paper deals with the utilization of two evolutionary algorithms Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE) for the optimization of the control of chaos. This paper is aimed at an explanation on how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing fast, precise and mainly robust stabilization of selected chaotic system on a desired state for any initial conditions. The role of EA here is as a powerful tool for an optimal tuning of control technique input parameters. As a model of deterministic chaotic system, the one-dimensional discrete Logistic equation was used. The four canonical strategies of SOMA and six canonical strategies of DE were utilized. For each EA strategy, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF securing robust solution. Satisfactory results obtained by both heuristic and the two proposed cost functions are compared with previous research, given by different cost function designs.

Chaos PSO algorithm driven alternately by two different chaotic maps - An initial study

In this paper, a new approach for chaos driven PSO algorithm is proposed. Two different chaotic maps are alternately used as pseudorandom number generators and switched over during the run of chaos driven PSO algorithm. The motivation for this research came from the previous successful experiments with PSO algorithm driven by different chaotic maps. Promising results of this innovative approach are presented in the results section and briefly analyzed.

Discrete Self-Organising Migrating Algorithm for flow-shop scheduling with no-wait makespan

Abstract This paper introduces a novel Discrete Self-Organising Migrating Algorithm for the task of flow-shop scheduling with no-wait makespan. The new algorithm is tested with the small and medium Taillard benchmark problems and the obtained results are competitive with the best performing heuristics in the literature.

Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming

Abstract This research deals with the utilization of analytic programming for a synthesis of control law for three selected discrete chaotic systems. The novelty of the approach is that a tool for symbolic regression–analytic programming–is used for such kinds of difficult problems. The paper consists of the descriptions of analytic programming as well as chaotic systems and used cost functions. For simulations, evolutionary algorithm SOMA (Self-Organizing Migrating Algorithm) and analytic programming were used. For each case study, repeated simulations were conducted to outline the effectiveness and robustness of used methods. All repeated simulations have given satisfactory results.

Complex network analysis of differential evolution algorithm applied to flowshop with no-wait problem

This paper analyses the attributes of population dynamics of Differential Evolution algorithm using Complex Network Analysis tools. The population is visualised as an evolving complex network, which exhibits non-trivial features. Complex network attributes such as adjacency graph gives interconnectivity, centralities give the overview of convergence and stagnation, whereas cliques outlines the depth of interconnection and subgraphs within the population. The community graph plot gives an overview of the hierarchical grouping of the individuals in the population. These attributes give a clear description of the population during evaluation and can be utilised for adaptive population and parameter control.