Constraint Handling in Genetic Algorithms: The Set Partitioning Problem

Authors:
P. C. Chu;J. E. Beasley
Affiliations:
The Management School, Imperial College, London SW7 2AZ, England. p.chu@ic.ac.uk URL: http://mscmga.ms.ic.ac.uk/pchu/pchu.html;The Management School, Imperial College, London SW7 2AZ, England. j.beasley@ic.ac.uk URL: http://mscmga.ms.ic.ac.uk/jeb/jeb.html
Venue:
Journal of Heuristics
Year:
1998

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Abstract

In this paper we present a genetic algorithm-based heuristic forsolving the set partitioning problem (SPP). The SPP is animportant combinatorial optimisation problem used by manyairlines as a mathematical model for flight crew scheduling.A key feature of the SPP is that it is a highly constrainedproblem, all constraints being equalities. New genetic algorithm(GA) components: separate fitness and unfitness scores, adaptivemutation, matching selection and ranking replacement, areintroduced to enable a GA to effectively handle suchconstraints. These components are generalisable to any GA forconstrained problems.We present a steady-state GA in conjunction with a specialisedheuristic improvement operator for solving the SPP. Theperformance of our algorithm is evaluated on a large set ofreal-world problems. Computational results show that thegenetic algorithm-based heuristic is capable of producinghigh-quality solutions.