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Double Fuzzy Stopping Rule for a hybrid metaheuristic for the Strip Packing Problem
Double Fuzzy Stopping Rule for a hybrid metaheuristic for the
Strip Packing Problem
Jesu?s David Beltra?n Cano, Jose Eduardo Caldero?n Benito
Ignacio Jose? Garc??a del Amo, Rayco Jorge Cabrera,
Jose? A. Moreno Pe?rez and J. Marcos Moreno-Vega
Departamento de E., I.O. y Computacio?n
Escuela Te?cnica Superior de Ingenier??a Informa?tica,
Universidad de La Laguna. 38271 La Laguna SPAIN.
e-mail: jamoreno@ull.es, jmmoreno@ull.es
Abstract: In this work we propose a double fuzzy stopping rule for an hybrid metaheuristic
approach to solve the Strip Packing Problem (SPP). The hybrid algorithm has two phases, in
the second phase a Variable Neighbourhood Search (VNS) improves the quality of part of the
solutions obtained with a Greedy Randomized Adaptive Search Procedure (GRASP) in the first
phase. The stopping rule is one of the elements of the metaheuristics least studied due to, among
other reasons, the imprecision in the terminology used by experts to formulate good stopping rules.
We formulate in fuzzy terms a double stopping rule for solving the SPP. The double stopping rule
decides when to stop each phase of the hybrid based on different characteristics of the solution
found. The results achieved with the double stopping rule for the hybrid method are compared
with those existing in the literature.
Keywords: GRASP, VNS, Metaheuristics, Fuzzy Stopping Rules, Strip Packing Problem
1 Introduction
The Strip Packing Problem (SPP) consists of packing a finite set of the rectangles, that can be
rotated 90 degrees, in the fixed width strip minimizing the height of the packing. Metaheuristic
searches are general solution procedures for solving problems that must provide high quality
solutions consuming moderate resource (time). A review of the application of metaheuristic
algorithms to the SPP is found in [7]. Two metaheuristics with good performance are Greedy
Randomized Adaptive Search Procedure (GRASP) [5] and Variable Neighborhood Search (VNS)
[6]. In this work we consider a
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