Runtime Analysis of Evolutionary Algorithms for Multiparty Multiobjective Optimization

Abstract

In scenarios where multiple decision-makers operate within a common decision space, each focusing on their own multiobjective optimization problem (e.g., bargaining games), the problem can be modeled as a multiparty MOP (MPMOP). While numerous evolutionary algorithms have been proposed to solve MPMOPs, most results remain empirical. This article presents the first theoretical analysis of the expected runtime of evolutionary algorithms on bi-party MOPs (BPMOPs). Our findings demonstrate that employing traditional multiobjective optimization algorithms to solve MPMOPs is both time-consuming and inefficient, as the resulting population contains many solutions that fail to achieve consensus among decision-makers. An alternative approach involves decision-makers individually solving their respective optimization problems and seeking consensus only in the final stage. While feasible for pseudo-Boolean optimization problems, this method may fail to guarantee approximate performance for one party in NP-hard problems. Finally, we propose evolutionary multiparty multiobjective optimizers (EMPMO) for pseudo-Boolean optimization and shortest path (SP) problems within a multiparty multiobjective context, maintain a common solution set among all parties. Theoretical and experimental results demonstrate that the proposed $ \text {EMPMO}_{\text {random}} $ outperforms previous algorithms in terms of the lower bound on the expected runtime for pseudo-Boolean optimization problems. Additionally, the consensus-based evolutionary multiparty multiobjective optimizer( $ \text {EMPMO}_{\text {cons}}^{\text {SP}} $ ) achieves better efficiency and precision in solving SP problems compared to existing algorithms.