An Exact Optimization Algorithm for Linear Decomposition of Index Generation Functions

This paper proposes an exact optimization algorithm based on a branch and bound method for linear decomposition of index generation functions. The proposed algorithm efficiently finds the optimum linear decomposition of an index generation function by pruning non-optimum solutions using effective branch and bound strategies. The branch strategy is based on our previous heuristic [2] using a balanced decision tree, and the bound is based on a lower bound on the number of variables needed for linear decomposition. Experimental results using a benchmark index generation function show its optimum linear decompositions and effectiveness of the strategies.