On the effectiveness of genetic algorithms for the multidimensional knapsack problem

In the Multidimensional Knapsack Problem (MKP) there are items easily identifiable as highly (lowly) profitable and likely to be chosen (not chosen) to compose high-quality solutions. For all the other items, the Knapsack Core~(KC), the decision is harder. By focusing the search on the KC effective algorithms have been developed. However, the true KC is not available and most algorithms can only rely on items' efficiencies. Chu & Beasley Genetic Algorithm (CBGA), for example, uses efficiencies in a repair-operator which bias the search towards the KC. This paper shows that, as the search progresses, efficiencies lose their descriptive power and, consequently, CBGA's effectiveness decreases. As a result, CBGA rapidly finds its best solutions and stagnates. In order to circumvent this stagnation, extra information about the KC should be used to implement specific operators. Since there is a correlation between marginal probabilities in a population and efficiencies, we show that KCs can be estimated from the population during the search. By solving the estimated KCs with CPLEX, improvements were possible in many instances, evidencing CBGA's weakness to solve KCs and indicating a promising way to improve GAs for the MKP through the use of KC estimates.