Exact and Evolutionary Algorithms for Sequential Multi-Objective Transmission Topology Planning

Large-scale multi-objective optimization problems (LSMOPs) remain challenging due to the high-dimensional decision spaces, complex variable interactions, and limited function evaluation budgets, which make it difficult to balance the convergence, diversity, and stability. Existing two-archive evolutionary algorithms can alleviate the conflict between convergence and diversity, but they often underuse archive reliability and problem-structure information, leading to inefficient search, incomplete front coverage, and late-stage archive drift. To address these issues, this paper proposes TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm. Archive trustworthiness is defined by integrating evolutionary progress with convergence-archive maturity, and is used to coordinate variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. TRUST-TAEA is evaluated on the LSMOP benchmark suite with 500--5000 decision variables and 2, 3-objectives. Experimental results show that TRUST-TAEA achieves superior and highly competitive performance in terms of convergence, diversity, and stability. A three-objective day-ahead scheduling case of a grid-connected microgrid further demonstrates its practical applicability, where TRUST-TAEA obtains the best IGD$^+$ value and generates a feasible dispatch strategy balancing cost, emissions, and grid-power fluctuation.

Networked systems, from power grids to traffic networks and cloud clusters, carry loads across nodes with limited capacity. A node whose load exceeds its capacity fails and sheds its load onto its neighbors, which can trigger a system-wide cascade. We study how to allocate a fixed capacity budget across nodes to resist these cascades under local load redistribution. The problem is difficult because no optimal allocation is known, and the fail-or-survive objective is non-differentiable and piecewise constant, so exact and gradient-based optimization methods do not directly apply. We introduce TANGCO (Topology-Aware Neural Graph-Guided Capacity Optimization), which uses a graph neural network policy trained through the cascade simulator with policy-gradient learning and a heuristic anchor. We evaluate TANGCO on five synthetic graph families and five real networks spanning power, road, air, and Internet topologies. The learned policy improves on the best of four hand-designed heuristics in all 450 synthetic instances and in 40 of 45 real-network conditions, with robustness gains ranging from 1.6% to 246%. The learned policies transfer to unseen graphs within a family and partially across related topologies, and TANGCO$^{pre}$, pre-trained on synthetic graphs, matches per-network training on unseen real networks. Training scales near-linearly with graph size, and TANGCO$^{pre}$ allocates on a new network with no per-target training, matching the deployment cost of a hand-designed heuristic. Free-vector variants without the GNN, stay close to the heuristics, so the graph representation carries the gain beyond numerical search. Finally, analysis of the learned allocations identifies when local risk is sufficient, leads to an improved closed-form heuristic, and reveals the regimes where a topology-aware learned policy remains necessary.

Evolutionary algorithms have been used for a wide range of multi-objective combinatorial optimization problems. Despite practical success, theoretical results on the runtime of evolutionary algorithms for multi-objective combinatorial problems are rather limited. One classical problem that has been investigated is the multi-objective minimum spanning tree problem for which runtime bounds have been obtained to compute all extremal corner points of the Pareto front. With this paper, we provide some more detailed insights into the structure of the Pareto front when the edge weights take on a small number of distinct values. Based on these insights, we derive new runtime results for evolutionary multi-objective algorithms and complement our theoretical results with experimental investigations.