Cascading-heuristics for the solution of staircase linear programs

Abstract

A heuristic solution cascading scheme is applied to the decomposition-solution of Staircase Linear Programs (SLPs). The scheme works as if the intermediate solutions cascade through the different combinations or levels of subproblems, improving the quality of the solution at each stage. The complete problem is solved in the final step of the cascade. We address a number of heuristics to generate alternative cascading schemes. On a set of test problems drawn from a variety of applications, some heuristics have resulted in computation time savings of up to 70%. Three features of the approach make it particularly attractive. First, it is a meta-algorithm; that is, it can be embedded with any selected LP solver, to obtain a relative reduction in the solution times. Second, the computational gains from this procedure may be expected to increase with larger problems. Third, the procedure lends itself easily to parallel processing.