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

TL;DR

Pareto-NRPA is a pioneering Monte-Carlo algorithm that extends NRPA to multi-objective optimization, effectively balancing convergence and diversity in discrete search spaces, and outperforming existing methods on complex benchmarks.

Contribution

This work introduces the first multi-objective adaptation of NRPA, combining policy-based search with Pareto front maintenance for improved multi-objective optimization.

Findings

Achieves competitive results on MO-TSPTW and neural architecture search benchmarks.

Outperforms state-of-the-art evolutionary algorithms on constrained problems.

Demonstrates effective exploration and diversity preservation in multi-objective search.

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.