Abstract. A new scheme of approximate lexicographic search is proposed for the solution of the multidimensional boolean knapsack problem. The main idea of the algorithm is gradual definition of lexicographic order (ordering of variables) in which “qualitative” solutions of the problem belong to a direct two-sided lexicographic constraint whose upper bound is the lexicographic maximum of the set of feasible solutions of the problem in this order. Since the search for “qualitative” solutions in each order is carried out on a bounded lexicographic interval, the proposed algorithm is called a bounded lexicographic search. The quality of the approximate method of bounded lexicographic search is investigated by solving test problems from the well-known Beasley and Glover–Kochenberger sets.

Keywords: lexicographic order, lexicographic maximum, multidimensional boolean knapsack problem, lexicographic search algorithm.