Multi-Party Multi-Objective Optimization as Consensus Search: Runtime Analysis of Cross-Party Recombination

2026-05-17

AI Summary

This study addresses the challenge of achieving consensus among autonomous decision-makers in multi-party multi-objective optimization by formulating it as a consensus search problem. The authors propose a novel cross-party recombination strategy based on prefix-suffix template assembly and provide the first theoretical proof that it overcomes the gap bottleneck inherent in traditional variation operators. By developing a hierarchical support coverage analysis framework and integrating a CPR-NSGA-II variant with edge-union recombination and uniform repair mechanisms, the approach achieves an expected evaluation complexity of O(n log n) on the MP-JCG benchmark and obtains a (2λ)-common approximate coverage for the BPBOMST problem, along with parameterized bounds on expected runtime.

Abstract

Multi-party multi-objective optimization problems (MPMOPs) require consensus among autonomous decision makers and therefore differ from flattened many-objective formulations. Existing runtime theory for multi-objective evolutionary algorithms is largely tailored to single-party Pareto-front approximation and does not directly explain common-solution search in MPMOPs. We investigate cross-party recombination in two representative settings. On MP-JCG, a pseudo-Boolean benchmark with an explicit gap region, we prove that a payoff-guided mutation baseline faces a gap-crossing bottleneck requiring \(Θ(n^2)\) expected fitness evaluations. In contrast, an analytical CPR-NSGA-II variant discovers both common Pareto-optimal solutions in \(O(n\log n)\) expected evaluations by directly assembling complementary prefix and suffix templates distributed across party populations. Comparing this with the flattened four-objective formulation F-JCG, our full-front coverage analysis illustrates the additional coverage burden introduced by flattening. For BPBOMST, the bi-party, two-objective-per-party specialization of the multi-party multi-objective minimum spanning tree problem, we develop a layered support-cover analysis. For each common Pareto objective vector, the symmetric average projection induces an auxiliary bi-objective MST instance, and suitable support representatives yield a \(2λ\)-common approximation cover with \(λ\in[1,2]\). We further derive an instance-parameterized expected runtime bound for a representative-pool CPR-NSGA-II variant using edge-union recombination and uniform repair. This bound separates the effects of local auxiliary-front filling, cross-party recombination shortcuts, and edge-union repair ambiguity.

Problem

• multi-party multi-objective optimization
• consensus search
• common Pareto-optimal solutions
• runtime analysis
• cross-party recombination

Innovation

• Cross-Party Recombination
• Multi-Party Multi-Objective Optimization
• Runtime Analysis
• Consensus Search
• CPR-NSGA-II