Proximity search for 0-1 mixed-integer convex programming

In this paper we investigate the effects of replacing the objective function of a 0-1 Mixed-Integer Convex Program (MIP) with a “proximity” one, with the aim of enhancing the heuristic behavior of a black-box solver. The relationship of this approach with primal integer methods is also addressed. Promising computational results on different proof-of-concept implementations are presented, suggesting that proximity search can be very effective in quickly improving the incumbent in the early part of the search. This is particularly true when a sequence of similar MIPs has to be solved as, e.g., in a column-