On the Heuristics of Discrete Optimization

The importance of developing optimization techniques capable of tackling realistic engineering problems cannot be underestimated. In this study, a modification to the usual Branch and Bound algorithm is presented. This modification deals with the high dimensionality of linear integer problems in three steps. The first step, statistical design of experiments is used to detect the most and least important variables. The least important variables are assigned the maximum or minimum value according to the nature of original problem. The second step, the remaining variables are assigned to an orthogonal array of proper size. The complexity of our algorithm becomes n (m – o) instead of the usual n (m). Results encouraged the extension of the developed algorithm to include continuous nonlinear problems. The nonlinear continuous problem uses the integer linear optimum solution resulted from the two stages as input for the third stage. The third stage assigns increments for the variables in a suitably chosen orthogonal array. This array is used to enumerate the optimum solution with the variations. These modifications enrich the subject of optimization through combination of search techniques and orthogonal statistical design of experiments and accommodate the problem of size. Several test cases are used to verify the performance of these modifications and conclusions are drawn.