Cooperating Memetic and Branch-and-Cut Algorithms for Solving the Multidimensional Knapsack Problem

Recent work in combinatorial optimization indicates the high potential of combining metaheuristics with integer linear programming (ILP) techniques. We study here a hybrid system in which a memetic algorithm (MA) and a general purpose ILP solver based on branch-and-cut (B&C) are executed in parallel and continuously exchange information in a bidirectional, asynchronous way. As target problem, we consider the multidimensional knapsack problem (MKP). The memetic algorithm uses a direct binary encoding of candidate solutions and repair and local improvement strategies that are steered by pseudo-utility ratios. As B&C framework we use the general purpose commercial ILP-solver CPLEX. The information exchanged between the two heterogenous algorithms are so-far best primal solutions and promising dual variable values of solutions to certain linear programming (LP) relaxations. These dual variable values are used in the MA to update the pseudo-utility ratios of local improvement and repair.