Abstract
We implemented a parallel mixed-integer linear programming system and evaluated performance on a parallel computer with shared memory. Mixed-integer programming systems are implemented by branch-and-bound (B&B) and simplex algorithms in commercial systems. The system can solve problems including both integers and real variables in linear equations. Problems are solved by generating linear programming (LP) relaxation problems in the B&B algorithm and applying them to simplex algorithms. The parallel mixed-integer linear programming system is written in about 4,000 lines of C. In the initial problem solving stage, the system searches a tree using a depth-first strategy to find an incumbent solution as soon as possible. After the system finds an initial solution, it carries out branch cut processing using a breadth-first strategy. If the queue list managing the subproblem executed by simplex algorithm is empty, the incumbent is the optimal solution. We applied parallel programming to the search using a bread...
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