Branch and Bound Combined Design of Experiment Algorithm: A Data Analytics Approach

The chapter introduces a novel hybrid approach that integrates orthogonal arrays and strong branching rules to solve Mixed Integer Problems using the branch-and-bound technique. For low to medium size problems, full orthogonal arrays are employed without the need to apply the strong branching rule because full-size arrays yield optimum solution consistently. For higher size problems, which return large number of continuous variables, the user uses fractional orthogonal arrays to simplify the solution process of the problem. Fractional arrays result in low number of function evaluations and produce incumbent solutions. Strong branching rule, a widely recognized variable selection rule, is employed and integrated with orthogonal arrays mainly in order to improve the quality of the obtained results from fractional arrays and to minimize the time consumed in solving the problem. The hybrid algorithm has been empirically shown to generate considerably smaller branch-and-bound trees compared to other known rules and the method's effectiveness is validated through several model solutions.