Improved Canonical Dual Algorithms for the Maxcut Problem

TL;DR

This paper introduces improved algorithms for the maxcut problem using quadratic perturbation and duality techniques, transforming the problem into a more tractable form and employing reduction and compensation methods for robustness.

Contribution

It proposes novel canonical dual algorithms with quadratic perturbation, enhancing solution feasibility and robustness for the maxcut problem.

Findings

Algorithms outperform existing methods in experiments.

Quadratic perturbation improves problem tractability.

Reduction and compensation techniques enhance solution robustness.

Abstract

By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be solved easily by the well-developed optimization methods. Considering that there may exist no critical points in the dual feasible domain, a reduction technique is used gradually to guarantee the feasibility of the reduced solution, and a compensation technique is utilized to strengthen the robustness of the solution. The similar strategy is also applied to the maxcut problem with linear perturbation and its hybrid with quadratic perturbation. Experimental results demonstrate the effectiveness of the proposed algorithms when compared with other approaches.