# A study on exponential-size neighborhoods for the bin packing problem with conflicts

## TL;DR

This paper introduces an advanced iterated local search method with large neighborhoods and diversification strategies for the bin packing problem with conflicts, demonstrating high-quality solutions and scalability.

## Contribution

It presents novel large neighborhood structures, efficient evaluation procedures, and diversification techniques for the bin packing with conflicts, enhancing solution quality and scalability.

## Key findings

- The method produces high-quality solutions on benchmark instances.
- 0-cost moves and set covering neighborhoods significantly improve search effectiveness.
- The approach scales well with increasing problem size.

## Abstract

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.