Tight oscillations tabu search for multidimensional knapsack problems with generalized upper bound constraints

In a recent paper, the author and Curry solved the multidimensional knapsack problem with generalized upper bound constraints by a critical-event tabu-search method which navigates both sides of the feasibility boundary with varied depth of oscillations. Efforts were made to explore the solution space near the feasibility boundary by using local swaps according to the objective function values (the resulting solutions are referred to as simple trial solutions). In this paper, a specialized tight-oscillation process is launched to intensify the search when the previous method finds good solutions or simple trial solutions near the feasibility boundary. Both feasibility changes and objective-function value changes are incorporated into the choice of moves process. This paper demonstrates the merits of using different choice rules at different stages of the heuristic. The balance of intensification and diversification is achieved by using two levels of strategic oscillation approaches together with tabu memory at the main heuristic stage and the trial solution stage. With the tight oscillation method, the heuristic is able to find high-quality solutions very efficiently.