Solving Facility Location Problems with a Tol for Rapid Development of Multi-Objective Evolutionary Algorithms (MOEAs)

Solving Facility Location Problems with a Tol for Rapid Development of Multi-Objective Evolutionary Algorithms (MOEAs)

A. L. Medaglia (Universidad de los Andes, Colombia)
DOI: 10.4018/978-1-59140-984-7.ch042
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Abstract

The low price of coffee in the international markets has forced the Federación Nacional de Cafeteros de Colombia (FNCC) to look for cost-cutting opportunities. An alternative that has been considered is the reduction of the operating infrastructure by closing some of the FNCC-owned depots. This new proposal of the coffee supplier network is supported by (uncapacitated and capacitated) facility location models that minimize operating costs while maximizing service level (coverage). These bi-objective optimization models are solved by means of NSGA II, a multi-objective evolutionary algorithm (MOEA). From a computational perspective, this chapter presents the multi-objective Java Genetic Algorithm (MO-JGA) framework, a new tool for the rapid development of MOEAs built on top of the Java Genetic Algorithm (JGA). We illustrate MO-JGA by implementing NSGA II-based solutions for the bi-objective location models.

Key Terms in this Chapter

Multi-Objective Evolutionary Algorithm (MOEA): The extension of evolutionary algorithms to solve the multi-objective optimization problem.

Efficient Frontier: Let X E be the set of efficient solutions. The Efficient Frontier (or Pareto Optimal Front) is the set of images (in the criteria space) of the solutions in X E . Let PF E be the efficient frontier defined by .

Facility Location Problem (or Facility Siting Problem): Facility location problems (FLPs) deal with choosing from among some candidate facilities a subset from which an organization will serve its customers. The FLP is also concerned with determining how these customers will be served by the open facilities.

Efficient Solution (Non-Dominated Solution): A feasible solution x ? X is called efficient if there does not exist x ’? X such that for all k =1,?, p and for some k .

JGA: Acronym for Java Genetic Algorithm; a flexible and extensible computational object-oriented framework for rapid development of evolutionary algorithms for solving complex optimization problems.

Multi-Objective Optimization Problem (MOP): The MOP is defined as: where X ? R n is the feasible set and f : R n ? R p is a vector valued objective function.

Evolutionary (Genetic) Algorithm: An evolutionary algorithm (EA) is an stochastic search procedure inspired by the evolution process in nature. In this process, a population of individuals evolve, and the fitter ones have a better chance of reproduction and survival. The reproduction mechanisms favor the characteristics of the stronger parents and hopefully produce better children, guaranteeing the presence of those characteristics in future generations.

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