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Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics.
Energetic reasoning is one of the most powerful propagation algorithms in cumulative scheduling. In practice, however, it is not commonly used because it has a high running time and its success highly depends on the tightness of the variable bounds. In order to speed up energetic reasoning, we provide an easy-to-check necessary condition for energetic reasoning to detect infeasibilities. We present an implementation of energetic reasoning that employs this condition and that can be parametrically adjusted to handle the trade-off between solving time and propagation overhead. Computational results on instances from the PSPLIB are provided. These results show that using this condition decreases the running time by more than a half, although more search nodes need to be explored.
Primal heuristics are an important component of state-of-the-art codes for mixed integer programming. In this paper, we focus on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation). We give an overview of eight different approaches. To assess the impact of these primal heuristics on the ability to find feasible solutions, in particular early during search, we introduce a new performance measure, the primal integral. Computational experiments evaluate this and other measures on MIPLIB~2010 benchmark instances.
Primal heuristics are an important component of state-of-the-art codes for mixed integer nonlinear programming (MINLP). In this article we give a compact overview of primal heuristics for MINLP that have been suggested in the literature of recent years. We sketch the fundamental concepts of different classes of heuristics and discuss specific implementations. A brief computational experiment shows that primal heuristics play a key role in achieving feasibility and finding good primal bounds within a global MINLP solver.