Easily searched encodings for number partitioning

Can stochastic search algorithms outperform existing deterministic heuristics for the NP-hard problemNumber Partitioning if given a sufficient, but practically realizable amount of time? In a thorough empirical investigation using a straightforward implementation of one such algorithm, simulated annealing, Johnson et al. (Ref. 1) concluded tentatively that the answer is negative. In this paper, we show that the answer can be positive if attention is devoted to the issue of problem representation (encoding). We present results from empirical tests of several encodings ofNumber Partitioning with problem instances consisting of multiple-precision integers drawn from a uniform probability distribution. With these instances and with an appropriate choice of representation, stochastic and deterministic searches can—routinely and in a practical amount of time—find solutions several orders of magnitude better than those constructed by the best heuristic known (Ref. 2), which does not employ searching.