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Our research deals with the optimization version of the set partitionproblem, where the objective is to minimize the absolute difference between thesums of the two disjoint partitions. Although this problem is known to beNP-hard and requires exponential time to solve, we propose a less demandingversion of this problem where the goal is to find a locally optimal solution.In our approach, we consider the local optimality in respect to any movement ofat most two elements. To accomplish this, we developed an algorithm that cangenerate a locally optimal solution in at most $O(N^2)$ time and $O(N)$ space.Our algorithm can handle arbitrary input precisions and does not requirepositive or integer inputs. Hence, it can be applied in various problemscenarios with ease.

A 2-opt Algorithm for Locally Optimal Set Partition Optimization