Correlated Mutations for Integer Programming
This paper addresses the lack of evolutionary algorithms theoretically grounded in discrete structures for integer programming (IP). We propose Integer Evolution Strategies (IES), a novel framework designed specifically for IP. Its core contributions are threefold: (i) the first use of the ℓ₁-norm—rather than the conventional ℓ₂-norm—as the distance metric in integer search space; (ii) a correlated mutation mechanism for unbounded integer variables, based on a bigeometric distribution, with theoretical proof of superiority over truncated normal distributions; and (iii) a quantification method for correlation on discrete lattices, coupled with entropy-driven mutation analysis. Experiments on nonseparable quadratic integer programs demonstrate that IES significantly outperforms state-of-the-art heuristic methods, empirically validating the critical role of the ℓ₁-norm and bigeometric distribution in enhancing the efficiency of discrete stochastic optimization.