A Fuzzy Simulated Evolution Algorithm for Hard Problems

A Fuzzy Simulated Evolution Algorithm for Hard Problems

Michael Mutingi (University of Johannesburg, South Africa & University of Botswana, Botswana)
DOI: 10.4018/978-1-4666-4450-2.ch029
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Abstract

As problem complexity continues to increase in industry, developing efficient solution methods for solving hard problems, such as heterogeneous vehicle routing and integrated cell formation problems, is imperative. The focus of this chapter is to develop from the classical simulated evolution algorithm, a Fuzzy Simulated Evolution Algorithm (FSEA) that incorporates the concepts of fuzzy set theory, evolution, and constructive perturbation. The aim is to improve the search efficiency of the algorithm by enhancing the major phases of the algorithm through initialization, evaluation, selection, and reconstruction. Illustrative examples are provided to demonstrate the candidate application areas and to show the strength of the algorithm. Computational experiments are conducted based on benchmark problems in the literature. Results from the computational experiments demonstrate the strength of the algorithm. It is anticipated that the application of the FSEA metaheuristic can be extended to other hard large scale problems.
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Introduction

Intelligent soft computing algorithms, particularly biologically inspired evolutionary algorithms, have attracted the attention of many researchers and practitioners in a wide range of disciplines, including logistics engineering, business, economics, operations management, manufacturing systems design, production planning, and scheduling (Dostal, 2013; Senvar et al., 2013). Intelligent soft computing, unlike conventional (hard) computing, is known to be tolerant of imprecision, uncertainty, partial truth, and approximation. As such, this approach mimics the human mind and other natural phenomena when addressing real-world complex problems (Holland, 1992, 1997; Dostal, 2013). Some of the most popular algorithms are genetic algorithms, neural networks, simulated annealing, particle swarm intelligence, ant colony algorithms, and evolutionary algorithms. Oftentimes, these algorithms incorporate fuzzy set theory, fuzzy logic, and chaos theory, and other knowledge-based techniques. In order to enhance their operational efficiency and effectiveness. (Zadeh, 1978; Sugeno, 1985; Hererra & Lozano, 1996; Zimmerman, 1993; FLT, 2012; Vasant, 2013). In developing these algorithms, researchers seek to come up with enhanced heuristics for robust global optimization of real-world problems that cannot be solved by conventional approaches in polynomial time.

Most real-world problems have complex characteristics: 1.) they are combinatorial and computationally hard in nature, 2.) they are highly constrained or restricted, and 3.) they are fuzzy due to the presence of imprecise data, or 4.) they have numerous local optima. These inherent complex characteristics continue to pose serious challenges to decision makers in various disciplines across the globe. Although many heuristic and meta-heuristic algorithms have been developed, more and more complexities continue to arise in various research disciplines due to a combination of factors (Senvar et al., 2013). Consequently, the need for global soft computing and optimization algorithms continues to increase in industry. Therefore, the development of more enhanced and robust algorithms is imperative.

Key Terms in this Chapter

Evolutionary Algorithm: A metaheuristic algorithm based on the theories of evolution and natural selection.

Metaheuristic: An iterative computational algorithm that optimizes a hard problem from a single or population of candidate solutions.

Crisp Set: A conventional set for which an element is either a member of the set or not.

Membership Function: An indicator function representing the degree of truth as an extension of valuation.

Linguistic Variables: Natural language non-numeric variables to facilitate the expression of rules and facts.

Fuzzy Logic: A form of many-valued logic that deals with approximate rather fixed or exact reasoning.

Vehicle Routing: The design and assignment of routes to specific vehicles according to a defined objective function.

Fuzzy Set: A set whose elements have degrees of membership, rather than crisp membership or non-membership in classical sets.

Cell Formation: An application of group technology to clustering machines (and parts) into efficient groups for efficient manufacturing process.

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