# Runtime Analysis of Evolutionary Algorithms for Multi-party Multi-objective Optimization

arXiv: https://arxiv.org/abs/2501.16336 · HTML: https://mlsanity.com/paper/2501.16336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [A Survey of Multi-Objective Sequential Decision-Making](https://mlsanity.com/paper/1402.0590/) (2014)
- [Mathematical Runtime Analysis for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)](https://mlsanity.com/paper/2112.08581/) (2021)
- [Runtime Analysis for the NSGA-II: Proving, Quantifying, and Explaining the Inefficiency For Many Objectives](https://mlsanity.com/paper/2211.13084/) (2022)
- [Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees](https://mlsanity.com/paper/2110.09332/) (2021)
- [Runtime Analyses of NSGA-III on Many-Objective Problems](https://mlsanity.com/paper/2404.11433/) (2024)
- [A First Running Time Analysis of the Strength Pareto Evolutionary Algorithm 2 (SPEA2)](https://mlsanity.com/paper/2406.16116/) (2024)
- [Heuristic Search for Multi-Objective Probabilistic Planning](https://mlsanity.com/paper/2303.14363/) (2023)
- [Decision-Making Among Bounded Rational Agents](https://mlsanity.com/paper/2210.08672/) (2022)

## Abstract (arXiv)

In scenarios where multiple decision-makers operate within a common decision space, each focusing on their own multi-objective optimization problem (e.g., bargaining games), the problem can be modeled as a multi-party multi-objective optimization problem (MPMOP). While numerous evolutionary algorithms have been proposed to solve MPMOPs, most results remain empirical. This paper presents the first theoretical analysis of the expected runtime of evolutionary algorithms on bi-party multi-objective optimization problems (BPMOPs). Our findings demonstrate that employing traditional multi-objective 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 multi-party multi-objective optimizers (EMPMO) for pseudo-Boolean optimization and shortest path problems within a multi-party multi-objective context, maintain a common solution set among all parties. Theoretical and experimental results demonstrate that the proposed ( EMPMOrandom ) outperforms previous algorithms in terms of the lower bound on the expected runtime for pseudo-Boolean optimization problems. Additionally, the consensus-based evolutionary multi-party multi-objective optimizer( ( EMPMOconsSP ) ) achieves better efficiency and precision in solving shortest path problems compared to existing algorithms.