Inequalities and Target Objectives for Metaheuristic Search - Part I: Mixed Binary Optimization

Recent adaptive memory and evolutionary metaheuristics for mixed integer programming have included proposals for introducing inequalities and target objectives to guide the search. These guidance approaches are useful in intensification and diversification strategies related to fixing subsets of variables at particular values, and in strategies that use linear programming to generate trial solutions whose variables are induced to receive integer values. We show how to improve such approaches by new inequalities that dominate those previously proposed and by associated target objectives that underlie the creation of both inequalities and trial solutions. We also propose supplementary linear programming models that exploit the new inequalities for intensification and diversification, and introduce additional inequalities from sets of elite solutions that enlarge the scope of these models. Part I (the present paper) focuses on 0-1 mixed integer programming, and Part II covers the extension to more general mixed integer programming problems. Our methods can also be used for problems that lack convenient mixed integer programming formulations, by generating associated linear programs that encode part of the solution space in mixed binary or general integer variables