Weight-Codings in a Genetic Algorithm for the Multiconstraint Knapsack Problem

This paper presents different variants of weight-coding in a genetic algorithm (GA) for solving the multiconstraint knapsack problem (MKP). In this coding, a chromosome is a vector of weights associated with the items of the MKP. The phenotype is obtained by using the weights to generate a modified version of the original problem and applying a decoding heuristic to it. Four techniques of biasing the original problem with weights are discussed. Two well working decoding heuristics, one based on the surrogate relaxation and the other one based on the Lagrangian relaxation, are introduced. The different weight-coding variants are experimentally compared to each other using a steady-state GA. Furthermore, the influence of the biasing strength, a strategy parameter of the codings, is investigated. In general, the GA found solutions being substantially better than those obtained by applying heuristics to the MKP directly.