BRANCH AND BOUND EXPERIMENTS IN NONLINEAR INTEGER PROGRAMMING

OMPRAKASH KALYANPRASAD GUPTA, Purdue University

Abstract

The branch and bound principle has been established as an effective computational tool for solving linear integer programming problems. In the present dissertation the feasibility of branch and bound procedures in solving nonlinear integer programming problems is investigated. Since the implementation of the branch and bound requires solving of a number of nonlinear continuous problems, the algorithms available for solving nonlinear continuous problems and their corresponding computer codes are first investigated and an efficient code (OPT--based on generalized reduced gradient method) is selected. The efficiency of the branch and bound technique generally depends on the various selection parameters such as selection of branching variables, and branching nodes. Among others, the concepts of 'pseudo-costs' and 'estimations' are implemented in selecting the branching variables and the branching nodes. The efficiency of the algorithm also depends on the availibility of a quick upper bound on the objective minimum. Therefore, heuristics are developed which would first locate an integer feasible solution and thus provide an upper bound on the objective. The different rules for selecting the branching variables, nodes and heuristics form a total of 27 branch and bound strategies. A computer code capable of invoking each of these 27 strategies is developed. Since the generation of subproblems requires storing of a number of nodes, an effective computer storage scheme is developed for the Intermediate storage purpose. Each of the 27 strategies is tested on a set of 22 test problems. The numerical results are provided, and a statistical analysis is performed to evaluate and compare the overall effectiveness of these strategies. Additional experiments are also carried out to evaluate the effect due to the problem parameters such as number of integer variables and constraints.

Degree

Ph.D.

Subject Area

Industrial engineering|Computer science

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