Multidimensional Knapsack Problem: The Influence of Representation

Fitness landscape analysis techniques are used to better understand the influence of genetic representations and associated variation operators when solving a combinatorial optimization problem. Five representations are investigated for the Multidimensional Knapsack problem. Common mutation operators (like bit-flip mutation) and classic 1-point and uniform crossover are employed to generate fitness landscapes. Measures such as fitness distance correlation and autocorrelation are applied to examine the landscapes associated with the tested genetic encodings. Furthermore, additional experiments are made to observe the effects of adding heuristics and local optimization to the representations. The goal of this work is to study the influence of representations on the design of efficient evolutionary algorithms. A comprehensive set of experiments is performed to accomplish this task. Results show that the selection of a suitable representation is crucial when solving combinatorial optimization problems. Encodings with a strong heuristic bias are more efficient and the addition of local optimization techniques further enhance its performance. Finally, results show that, for the Multidimensional Knapsack problem, the choice of a representation influences the selection of mutation.