Computer simulation-based optimisation: hybrid branch and bound and orthogonal array-based enumeration algorithm

Branch and Bound method. This method is based on integration of orthogonal arrays and enumeration based techniques. Several observations are given supplemented with simple model solutions to verify our assumptions. The modified algorithm is valid for higher dimensional problems. The algorithm employs several 2-levels orthogonal arrays and the complexity of solutions is always of the order n 2. For low to medium size problems, full factorial orthogonal arrays are employed. For higher size problems, the user uses fractional orthogonal arrays and the complexity of solution is always of the order , k n 2 −. n k ≤ Results show that full size arrays yield optimum solution consistently. When fractional arrays are used, the solution is always incumbent. The number of function evaluations is always low. We show that this conclusion, though true, is rare as the number of continuous solutions resulting from relaxations is always tractable with full size arrays. This method utilizes the fact that the number of continuous solutions from relaxations is lesser than the original problem size. Numerical results show that the proposed hybrid algorithm is able to save 20% ~ 96% of the original computations. Fractional arrays allow fractionation and consequent deviation from the best solution.