An improved partial enumeration algorithm for integer programming problems

In this paper, we present an improved Partial Enumeration Algorithm for Integer Programming Problems by developing a special algorithm, named PE_SPEEDUP (partial enumeration speedup), to use whatever explicit linear constraints are present to speed up the search for a solution. The method is easy to understand and implement, yet very effective in dealing with many integer programming problems, including knapsack problems, reliability optimization, and spare allocation problems. The algorithm is based on monotonicity properties of the problem functions, and uses function values only; it does not require continuity or differentiability of the problem functions. This allows its use on problems whose functions cannot be expressed in closed algebraic form. The reliability and efficiency of the proposed PE_SPEEDUP algorithm has been demonstrated on some integer optimization problems taken from the literature.