Responsive strategic oscillation for solving the disjunctively constrained knapsack problem.

•The disjunctively constrained knapsack problem is a general model for a number of applications.•We propose an effective heuristic algorithm for solving this computationally challenging problem.•The algorithm relies on an original combination of feasible search and infeasible search.•The algorithm shows excellent results on 6361 benchmark instances of the literature.•The algorithm discovers 39 improved best results (new lower bounds).