A Very Fast Heuristic for Combinatorial Optimization With Specific Application to Priority Rule Sequencing in Operations Management: Fuzzy Greedy Search

A Very Fast Heuristic for Combinatorial Optimization With Specific Application to Priority Rule Sequencing in Operations Management: Fuzzy Greedy Search

Kaveh Sheibani (ORLab Analytics, Vancouver, Canada)
DOI: 10.4018/IJORIS.2018070104

Abstract

This article presents mathematics of a generic polynomial-time heuristic which can be integrated into approaches for hard combinatorial optimization problems. The proposed method evaluates objects in a way that combines fuzzy reasoning with a greedy mechanism, thereby exploiting a fuzzy solution space using greedy methods. The effectiveness and efficiency of the proposed method are demonstrated on job-shop scheduling as one of the most challenging classical sequencing problems in the area of combinatorial optimization.
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Fuzzy Sets

In many real-world problems fuzzy sets allow us to represent vague concepts expressed in natural language. The membership function of a fuzzy set A can be denoted by µA: X → [0,1]. Each fuzzy set should be uniquely defined by one particular membership function. Consider a fuzzy set where membership function is defined in Equation (1). This is one of the general formulae of a parameterized family of membership functions described in Klir and Yuan (1995):

IJORIS.2018070104.m01
(1)

This fuzzy set expresses, in a particular form, the general concept of a class of real numbers that are close to r. When the non-negative parameter ρ increases, the graph of µA(x) becomes narrower. The function has the following properties: µA(r) = 1 and µA(x) < 1 for all xr. For a complete discussion of fuzzy sets we refer to (Klir and Yuan, 1995; Zimmermann, 2001; Wang & Klir, 2013).

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