Finding and Exploring Promising Search Space for the 0-1 Multidimensional Knapsack Problem
Jitao Xu, Hongbo Li, Minghao Yin
TL;DR
This work introduces FEPSS, a hybrid framework that blends Evolutionary Computation with an exact Integer Programming solver to tackle the 0-1 Multidimensional Knapsack Problem. It leverages a population to extract high-potential partial assignments and uses a customized Large Neighbourhood Search to guide a focused IP exploration of the resulting subspaces, updating the population with a novel scoring function that balances solution quality, diversity, and resource use. Comprehensive experiments on OR-Library and MK_GK benchmarks demonstrate superior solution quality and competitiveness on large, hard instances, including new lower bounds on several problems. The approach advances practical capabilities for large-scale MKP by effectively combining population-driven insight with exact search in a structured, tunable framework.
Abstract
The 0-1 Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0-1 MKP. It maintains a set of solutions and utilizes the information from the population to extract good partial assignments. To find high-quality solutions, an exact algorithm is applied to explore the promising search space specified by the good partial assignments. The new solutions are used to update the population. Thus, the good partial assignments evolve towards a better direction with the improvement of the population. Extensive experimentation with commonly used benchmark sets shows that our algorithm outperforms the state-of-the-art heuristic algorithms, TPTEA and DQPSO, as well as the commercial solver CPlex. It finds better solutions than the existing algorithms and provides new lower bounds for 10 large and hard instances.