Learnable Evolutionary Multi-Objective Combinatorial Optimization via Sequence-to-Sequence Model
Jiaxiang Huang, Licheng Jiao
TL;DR
This work targets permutation-based multi-objective combinatorial optimization (MOCO), a domain challenged by discrete search spaces. It introduces SeqMO, a learnable evolutionary MOCO framework that couples a sequence-to-sequence model with evolutionary algorithms to exploit historical solution trajectories. Training data are constructed by dividing each generation into elite and poor solutions and forming one-to-one mappings that minimize the angle between objective vectors, computed as $\angle(f(p),f(e))=\arccos\left(\frac{f(p)\cdot f(e)}{\|f(p)\|\|f(e)\|}\right)$, with matching solvable by greedy or Hungarian methods; a Pointer Network is trained to predict promising solution trajectories. The trained network generates new candidate permutations to guide population updates, preserving diversity while steering solutions toward the Pareto front. Empirical results on MOTSP and MOQAP show SeqMO-enhanced variants outperform strong baselines in Pareto-front coverage (Hypervolume HV) and convergence, and code is provided for reproducibility.
Abstract
Recent advances in learnable evolutionary algorithms have demonstrated the importance of leveraging population distribution information and historical evolutionary trajectories. While significant progress has been made in continuous optimization domains, combinatorial optimization problems remain challenging due to their discrete nature and complex solution spaces. To address this gap, we propose SeqMO, a novel learnable multi-objective combinatorial optimization method that integrates sequence-to-sequence models with evolutionary algorithms. Our approach divides approximate Pareto solution sets based on their objective values' distance to the Pareto front, and establishes mapping relationships between solutions by minimizing objective vector angles in the target space. This mapping creates structured training data for pointer networks, which learns to predict promising solution trajectories in the discrete search space. The trained model then guides the evolutionary process by generating new candidate solutions while maintaining population diversity. Experiments on the multi-objective travel salesman problem and the multi-objective quadratic assignment problem verify the effectiveness of the algorithm. Our code is available at: \href{https://github.com/jiaxianghuang/SeqMO}{https://github.com/jiaxianghuang/SeqMO}.