Metaheuristic Search with Inequalities and Target Objectives for Mixed Binary Optimization – Part II

Recent metaheuristics for mixed integer programming have included proposals for introducing inequalities and target objectives to guide this search. These guidance approaches are useful in intensification and diversification strategies related to fixing subsets of variables at particular values. The authors’ preceding Part I study demonstrated how to improve such approaches by new inequalities that dominate those previously proposed. In Part II, the authors review the fundamental concepts underlying weighted pseudo cuts for generating guiding inequalities, including the use of target objective strategies. Building on these foundations, this paper develops a more advanced approach for generating the target objective based on exploiting the mutually reinforcing notions of reaction and resistance. The authors demonstrate how to produce new inequalities by “mining” reference sets of elite solutions to extract characteristics these solutions exhibit in common. Additionally, a model embedded memory is integrated to provide a range of recency and frequency memory structures for achieving goals associated with short term and long term solution strategies. Finally, supplementary linear programming models that exploit the new inequalities for intensification and diversification are proposed.