The quadratic multiple knapsack problem and three heuristic approaches to it

The quadratic multiple knapsack problem extends the quadratic knapsack problem with K knapsacks, each with its own capacity Ck. A greedy heuristic fills the knapsacks one at a time with objects whose contributions are likely to be large relative to their weights. A hill-climber and a genetic algorithm encode candidate solutions as strings over {0, 1, . . . , K} with length equal to the number of objects. The hill-climber's neighbor operator is also the GA's mutation. In tests on 60 problem instances, the GA performed better than the greedy heuristic on the smaller instances, but it fell behind as the numbers of objects and knapsacks grew. The hill-climber always outperformed the greedy heuristic, and on the larger instances, also the GA. Categories and Subject Descriptors G.2.1 [Mathematics of Computing]: Discrete Mathematics--Combinatorics; I.2.8 [Problem Solving, Control Methods, and Search]: Heuristic Methods General Terms Algorithms Keywords Knapsack problems, quadratic ...

• Type: Conference
• Year: 2006
• Where: GECCO
• Authors: Amanda Hiley, Bryant A. Julstrom
• Keywords: GECCO 2006, Greedy Heuristic, Knapsack Problem, Multiple Knapsack Problem, Optimization