Iterated two-phase local search for the Set-Union Knapsack Problem
  The Set-union Knapsack Problem (SUKP) is a generalization of the popular 0-1
knapsack problem. Given a set of weighted elements and a set of items with
profits where each item is composed of a subset of elements, the SUKP involves
packing a subset of items in a capacity-constrained knapsack such that the
total profit of the selected items is maximized while their weights do not
exceed the knapsack capacity. In this work, we present an effective iterated
two-phase local search algorithm for this NP-hard combinatorial optimization
problem. The proposed algorithm iterates through two search phases: a local
optima exploration phase that alternates between a variable neighborhood
descent search and a tabu search to explore local optimal solutions, and a
local optima escaping phase to drive the search to unexplored regions. We show
the competitiveness of the algorithm compared to the state-of-the-art methods
in the literature. Specifically, the algorithm discovers 18 improved best
results (new lower bounds) for the 30 benchmark instances and matches the
best-known results for the 12 remaining instances. We also report the first
computational results with the general CPLEX solver, including 6 proven optimal
solutions. Finally, we investigate the effectiveness of the key ingredients of
the algorithm on its performance.
