A Bayesian Optimisation Approach for Multidimensional Knapsack Problem

This paper considers the application of Bayesian optimisation to well-known multidimensional knapsack problem which is strongly NP-hard. For with a large number items and constraints, two-level formulation presented take advantage global capability approach, efficiency integer programming solvers on small problems. The first level makes decisions about optimal allocation capacities different item groups, while second solves reduced size for each group. To accelerate guided search process, various techniques are proposed including variable domain tightening, initialisation by Genetic Algorithm, landscape smoothing local search. Computational experiments carried out widely used benchmark instances up 100 30 constraints. preliminary results demonstrate effectiveness solution approach.