Abstract
An indirect genetic algorithm for the non-unicost set covering problem is presented. The algorithm is a two-stage meta-heuristic, which in the past was successfully applied to similar multiple-choice optimisation problems. The two stages of the algorithm are an ‘indirect’ genetic algorithm and a decoder routine. First, the solutions to the problem are encoded as permutations of the rows to be covered, which are subsequently ordered by the genetic algorithm. Fitness assignment is handled by the decoder, which transforms the permutations into actual solutions to the set covering problem. This is done by exploiting both problem structure and problem specific information. However, flexibility is retained by a self-adjusting element within the decoder, which allows adjustments to both the data and to stages within the search process. Computational results are presented.
Highlights
Aim: Develop a Genetic Algorithm to solve SetCovering Problems
The solutions to the problem are encoded as permutations of the rows to be covered, which are subsequently ordered by the genetic algorithm
Fitness assignment is handled by the decoder, which transforms the permutations into actual solutions to the set covering problem
Summary
The problem of covering the rows of an m-row, ncolumn, zero-one matrix aij by a subset of the columns at minimal cost. Defining xj = 1 if column j with cost cj is in the solution and xj = 0 otherwise. Idea: If the order of rows is right, a (relatively) simple heuristic can solve the problem. New Solutions inherit good parts from old solutions. Fitness: The fitter a solution, the more likely it will contribute to new solutions. (Here: The cost of the columns to cover the rows.). Selection: Individuals (solutions) are ranked according to fitness. Crossover: Combining parts of parent individuals (cut and paste) to create new solutions: ‘Building Block Hypotheses’. Replacement: ‘Elitist’ Strategy, i.e. the best 20% of the old solutions are kept.
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