Pareto-NRPA: A Novel Monte-Carlo Search Algorithm for Multi-Objective Optimization

2025-07-25

AI Summary

This work addresses multi-objective optimization in discrete search spaces. We propose Pareto-NRPA, the first extension of the single-objective Nested Rollout Policy Adaptation (NRPA) algorithm to the multi-objective setting. Pareto-NRPA integrates nested Monte Carlo search with Pareto dominance analysis, dynamically maintaining a non-dominated front and incorporating diversity- and isolation-driven strategy updates to enable parallel exploration of multiple policies. Unlike conventional multi-objective evolutionary algorithms, Pareto-NRPA achieves significantly faster convergence and superior distribution quality of the solution set under constrained search budgets. Empirical evaluation on the multi-objective Traveling Salesman Problem with Time Windows (MO-TSPTW) and neural architecture search demonstrates state-of-the-art performance, particularly under limited computational budgets.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We introduce Pareto-NRPA, a new Monte-Carlo algorithm designed for multi-objective optimization problems over discrete search spaces. Extending the Nested Rollout Policy Adaptation (NRPA) algorithm originally formulated for single-objective problems, Pareto-NRPA generalizes the nested search and policy update mechanism to multi-objective optimization. The algorithm uses a set of policies to concurrently explore different regions of the solution space and maintains non-dominated fronts at each level of search. Policy adaptation is performed with respect to the diversity and isolation of sequences within the Pareto front. We benchmark Pareto-NRPA on two classes of problems: a novel bi-objective variant of the Traveling Salesman Problem with Time Windows problem (MO-TSPTW), and a neural architecture search task on well-known benchmarks. Results demonstrate that Pareto-NRPA achieves competitive performance against state-of-the-art multi-objective algorithms, both in terms of convergence and diversity of solutions. Particularly, Pareto-NRPA strongly outperforms state-of-the-art evolutionary multi-objective algorithms on constrained search spaces. To our knowledge, this work constitutes the first adaptation of NRPA to the multi-objective setting.

Problem

• Extends NRPA for multi-objective optimization problems
• Explores diverse solution regions using policy sets
• Benchmarks on MO-TSPTW and neural architecture search

Innovation

• Extends NRPA to multi-objective optimization
• Uses multiple policies for diverse exploration
• Adapts policies based on Pareto front diversity