Chupov S.V.
An approximate algorithm for lexicographic search in multiple orders for the solution of the multidimensional boolean knapsack problem

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 to gradually define the 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 tasks from the well-known Beasley and Glover–Kochenberger sets. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: lexicographic maximum, lexicographic order, lexicographic search algorithm, multidimensional Boolean knapsack problem, Computer science, Cybernetics, Approximate algorithms, Approximate methods, Feasible solution, Knapsack problems, lexicographic maximum, Lexicographic order, Order of variables, Search Algorithms, Combinatorial optimization

Cite:
Chupov S.V. (2018). An approximate algorithm for lexicographic search in multiple orders for the solution of the multidimensional boolean knapsack problem. Cybernetics and Systems Analysis, 54 (4), 56-69. doi: https://doi.org/10.1007/s10559-018-0057-5 http://jnas.nbuv.gov.ua/article/UJRN-0000889045 [In Ukrainian].