An order based memetic evolutionary algorithm for set partitioning problems

Abstract

Metaheuristic algorithms, such as simulated annealing, tabu search and evolutionary algorithms, are popular techniques for solving optimization problems when exact methods are not practical. For example, the run times required to obtain exact solutions to many common combinatorial problems grow exponentially (or worse) with the problem size, and as a result, solving even a relatively modest sized problem of this type may require many centuries of computation time, even on the fastest computer of the day. Such problems are known collectively as NP-Hard, and include the travelling salesman problem (TSP), which is probably the best known problem in the class. The present study will concentrate on a type of NP-Hard combinatorial problem known as the set partitioning problem. If we have n objects to partition into m sets, in such a way that each object must be assigned to exactly one set, it follows that there are m n different ways that the n objects can be assigned to the m sets, for a straightforward unconstrained problem. It is instructive to note that every time the problem size of the set partitioning problem is increased by one object, the corresponding run time for an exhaustive search algorithm will increase by a factor of m, and thus the run time grows exponentially as the number of objects - n - increases. While it is true that much better exact methods than exhaustive search have been developed for most NP-Hard problems, the 'growth factor' remains exponential for the run time, and no one in history has so far managed to change that. © 2008 Springer-Verlag Berlin Heidelberg.