![]() ![]() From a methodological perspective, it is important because many of the techniques embedded in integer programming solvers rely on the availability of both lower and upper bounds. From a practical perspective, finding high-quality solutions and doing so quickly is frequently all that is desired. A straightforward generic implementation in SYMPHONY, an open source solver for mixed-integer programs, is shown to generate high-quality solutions for many MIPLIB instances as well as for large-scale multicommodity fixed-charge network flow instances much more quickly than SYMPHONY itself.Ī highly desirable characteristic of methods for solving 0-1 mixed-integer programs (MIPs) is that they should be capable of producing high-quality solutions in the early stages of the computation. A proof-of-concept computational study demonstrates its potential. This process yields a dynamic search that is likely to find high-quality feasible solutions more quickly than a traditional search and that is also capable of proving optimality. Starting from a restricted 0-1 mixed-integer program, the branch-and-bound algorithm may, at any node of the search tree, selectively relax, or unfix, previously fixed variables, restrict, or fix, additional variables, or unfix and fix variables at the same time using dual or structural information (problem-specific information). ![]() We introduce restrict-and-relax search, a branch-and-bound algorithm that explores the solution space not only by fixing variables (restricting), but also by freeing, or unfixing, previously fixed variables (relaxing). A highly desirable characteristic of methods for solving 0-1 mixed-integer programs is that they should be capable of producing high-quality solutions quickly. ![]()
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