bonsaiG - Algorithms & Design

This report describes the implementation of bonsaiG, a program for mixed-integer linear programming (MILP). bonsaiG is a research code, designed to explore the utility and power of arc consistency as a general technique for solving MILP problems, and to provide a foundation for exploring other techniques. It strives to provide maximum flexibility, control, and robustness, while retaining a reasonable level of efificiency. It implements a LP-based branch-and-bound algorithm and supports binary, general integer, and continuous variables. The underlying LP is an implementation of a dynamic LP algorithm. The tree exploration strategy is depth-first with best-first backtracking. Selection of the next active subproblem is based on a function which can incorporate the objective function and the integer infeasibility of a subproblem. The branching algorithm allows the specification of priorities for selecting branching variables, and the specification of groups of integer variables which are expanded and fixed simultaneously. General integer variables are treated by default with a 4-way branch. The evaluation of each subproblem incorporates LP, up/down penalties, and arc consistency, applied iteratively in an integrated variable forcing loop. The partial arc consistency algorithm is used to enforce integrality constraints and dynamically tighten bounds on variables. Arc consistency and up/down penalties provide complementary techniques for forcing integer variables to integral values. All data structures supporting the constraint system and search tree are dynamically allocated, so that there is no a priori limit on the size of problems which bonsaiG can attempt. bonsaiG has been tested on the MIPLIB 3.0 test suite, and performs adequately well compared to other MILP codes. As bonsaiG is the successor of bonsai, this report is the successor of [4], modified to incorporate the changes entailed in supporting general integer variables and replacement of the underlying LP code and constraint system data structure.