Enhancing an algorithm for set covering problems

Article Abstract:

Improvements on a previously proposed algorithm for the optimal solution of set covering problems are presented. The improvements involve applications of aLagrangean heuristic, feasible solution exclusion constraints, Gomory f-cuts and an improved branching strategy. Computational results from applications in FORTRAN run on a Cray X-MP/28 using the CFT compiler with maximum optimization show that the improved algorithm yields better solutions than the original algorithm for problems involving up to 400 rows and 4,000 columns.

Usage, Lagrangian functions, Branching processes

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A tree search algorithm for the crew scheduling problem

Article Abstract:

A tree search procedure for solving a crew scheduling problem (CSP) with a total working period constraint is introduced. It requires the problem to be expressed as a zero-one integer linear program that, after being subjected to Lagrangean relaxation, provides a lower bound for the CSP. The lower bound, which is refined via subgradient optimization, is embedded into the algorithm to obtain optimal solutions even for large problems.

Operations research, Research, Management science, Linear programming, Case studies, Scheduling (Management), Search theory

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A heuristic for Euclidean and rectilinear Steiner problems

Article Abstract:

A heuristic for Euclidean and rectilinear Steiner problems is presented.The model finds optimal Steiner solutions for connected subgraphs of the minimal spanning tree of the entire vertex set. While existing models can solveproblems with up to 10 vertices, computational results for randomly generated problems show the model's effectivity for up to 10,000 vertices.

Block designs, Trees (Graph theory)

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