A study of bi-space search for solving the one-dimensional bin packing problem

Abstract

Traditionally search techniques explore a single space to solve the problem at hand. This paper investigates performing search across more than one space which we refer to as bi-space search. As a proof of concept we illustrate this using the solution and heuristic spaces. In previous work two approaches for combining search across the heuristic and solution spaces have been studied. The first approach, the sequential approach, firstly explores the heuristic space to obtain complete solutions and then applies local search to explore the solution space created by these solutions. The second approach, the interleaving approach, alternates search in the heuristic and solution space on partial solutions until complete solutions are produced. This paper provides an alternative to these two approaches, namely, the concurrent approach, which searches the heuristic and solution spaces simultaneously. This is achieved by implementing a genetic algorithm selection hyper-heuristic that evolves a combination of low-level construction heuristics and local search move operators that explore the space of solutions (both partial and complete). The performance of the three approaches are compared, to one another as well as with a standard selection construction hyper-heuristic, using the one dimensional bin packing problem. The study revealed that the concurrent approach is more effective than the other two approaches, with the interleaving approach outperforming the sequential approach. All 3 approaches outperformed the standard hyper-heuristic. Given the potential of searching more than one space and the effectiveness of the concurrent approach, future work will examine additional spaces such as the design space and the program space, as well as extending the bi-space search to a multi-space search.