Enabling Population-Based Architectures for Neural Combinatorial Optimization

TL;DR

This paper introduces a population-based approach to neural combinatorial optimization, enabling neural networks to manage and evolve sets of solutions, which improves robustness and performance in combinatorial problems.

Contribution

It proposes a taxonomy of population awareness levels and develops methods for neural networks to represent and evolve populations, bridging NCO with classical population-based search.

Findings

Population-aware methods outperform single-solution approaches.

Shared information across populations improves solution quality.

Balancing exploration and exploitation enhances optimization results.

Abstract

Neural Combinatorial Optimization (NCO) has mostly focused on learning policies, typically neural networks, that operate on a single candidate solution at a time, either by constructing one from scratch or iteratively improving it. In contrast, decades of work in metaheuristics have shown that maintaining and evolving populations of solutions improves robustness and exploration, and often leads to stronger performance. To close this gap, we study how to make NCO explicitly population-based by learning policies that act on sets of candidate solutions. We first propose a simple taxonomy of population awareness levels and use it to highlight two key design challenges: (i) how to represent a whole population inside a neural network, and (ii) how to learn population dynamics that balance intensification (generating good solutions) and diversification (maintaining variety). We make these ideas concrete with two complementary tools: one that improves existing solutions using information shared across the whole population, and the other generates new candidate solutions that explicitly balance being high-quality with diversity. Experimental results on Maximum Cut and Maximum Independent Set indicate that incorporating population structure is advantageous for learned optimization methods and opens new connections between NCO and classical population-based search.