A Genetic Algorithm for the Multiple-Choice Integer Program

Abstract

We present a genetic algorithm for the multiple-choice integer program that finds an optimal solution with probability one (though it is typically used as a heuristic). General constraints are relaxed by a nonlinear penalty function for which the corresponding dual problem has weak and strong duality. The relaxed problem is attacked by a genetic algorithm with solution representation special to the multiple-choice structure. Nontraditional reproduction, crossover and mutation operations are employed. Extensive computational tests for dual degenerate problem instances show that suboptimal solutions can be obtained with the genetic algorithm within running times that are shorter than those of the OSL optimization routine.

Exploiting Problem Structure in a Genetic Algorithm Approach to a Nurse Rostering Problem

“…Here we use an encoding that follows directly from the IP formulation in Section 2 and is equivalent to that used by Hadj-Alouane and Bean [10] for general mult iple -choice integer programs. Each individual represents a full one-week schedule, i.e.…”

“…The former problem is addressed by Hadj-Alouane and Bean [10] , who consider a GA approach to a multiple -choice integer program occurring in facility location model. They point out that in problems where there are many optimal solutions, the lower bound obtained by relaxing constraints (3) in Lagrangian fashion is frequently slack.…”

“…This implie s that even if a different penalty is associated with each violated constraint there is no combination of linear penalties that gives a relaxation equivalent to the original problem. In view of [10] we considered both linear and quadratic penalties for our problem. However, as there appeared to be no advantage in the use of quadratic penalties the remainder of the paper is based on the use of the linear form.…”

Constrained Optimization with Evolutionary Algorithms: A Comprehensive Review

“…Various methods have been developed to overcome the above-mentioned burdens. Penalty based approaches can be classified as static (we consider death penalty approaches under static penalty methods) (Hoffmeister & Sprave, 1996), (Homaifar, Qi, & Lai, 1994), dynamic (C. , and adaptive (Hamida & Schoenauer, 2002), (Hadj-Alouane & Bean, 1997), (Hinterding, 2001) penalty function methods. Penalty function method introduced in (Smith & Tate, 1993) is improved and embedded by Tasgetiren and Suganthan (2006) into a multi-populated DE where they introduced near feasibility threshold (NFT) mechanism in which the NFT region is considered a promising search region beyond the feasible region.…”

Optimización estructural y topológica de estructuras morfológicamente no definidas mediante algoritmos genéticos

“…La primera aproximación a este tipo de penalización la realizaron Bean y Ben Hadj-Alouane [36,39]. En ella la función de penalización se retroalimenta según la fórmula:…”