Applied & Interdisciplinary
Babak Masoudi
Abstract
Relational graph structures add a layer of complexity to multi-objective combinatorial optimization (MOCO) that often renders large-scale NP-hard instances computationally prohibitive. While traditional metaheuristics like NSGA-II remain the industry standard, their reactive nature prevents them from ...
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Relational graph structures add a layer of complexity to multi-objective combinatorial optimization (MOCO) that often renders large-scale NP-hard instances computationally prohibitive. While traditional metaheuristics like NSGA-II remain the industry standard, their reactive nature prevents them from learning policies that generalize to unseen tasks. To address this, an end-to-end Deep Reinforcement Learning (DRL) framework is introduced, integrated with a Graph Convolutional Network (GCN) specifically for the Multi-Objective Project Portfolio Selection Problem (PPSP). By mapping the structural interdependencies of projects, the GCN provides critical cues that allow a Proximal Policy Optimization (PPO) agent to construct high-quality portfolios. Training stability is ensured through a reward normalization strategy derived from weighted-sum Pareto scalarization theory. Benchmarks on Barab\'{a}si-Albert and fully-connected graph instances reveal that the proposed DRL agent achieves a Hypervolume indicator 2.4 times higher than NSGA-II on 50-project tasks. Notably, interpretability analysis shows the model learns to prioritize high-degree "hub" projects with strategic synergies. Regarding scalability, the agent maintained over 90% of its Hypervolume performance when transitioned from 50 to 200 projects in a zero-shot manner, requiring no further training. This efficiency is mirrored in its computational speed; an average inference time of 12.69 ms represents a 300-fold acceleration compared to the metaheuristic baseline. Such results underscore the potential of GNN-driven structural exploitation as a robust alternative for high-speed, multi-objective optimization.
