Random is Faster than Systematic in Multi-Objective Local Search

2026-01-09

arXiv.org

AI Summary

This study investigates the efficiency of neighborhood exploration strategies in multi-objective local search, with a focus on the performance gap between systematic traversal and random sampling. Through empirical analysis across diverse multi-objective optimization problems and supporting probabilistic modeling, the work provides the first theoretical and experimental evidence that random sampling consistently outperforms systematic exploration—including both best-improvement and first-improvement strategies. This advantage stems from the observation that high-quality neighboring solutions are sparsely and approximately uniformly distributed in the solution space, enabling random sampling to discover non-dominated solutions more efficiently at lower computational cost. These findings establish a new paradigm for designing multi-objective local search algorithms.

Technology Category

• Search and Optimization: Sampling/Simulation-based 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Local search is a fundamental method in operations research and combinatorial optimisation. It has been widely applied to a variety of challenging problems, including multi-objective optimisation where multiple, often conflicting, objectives need to be simultaneously considered. In multi-objective local search algorithms, a common practice is to maintain an archive of all non-dominated solutions found so far, from which the algorithm iteratively samples a solution to explore its neighbourhood. A central issue in this process is how to explore the neighbourhood of a selected solution. In general, there are two main approaches: 1) systematic exploration and 2) random sampling. The former systematically explores the solution's neighbours until a stopping condition is met -- for example, when the neighbourhood is exhausted (i.e., the best improvement strategy) or once a better solution is found (i.e., first improvement). In contrast, the latter randomly selects and evaluates only one neighbour of the solution. One may think systematic exploration may be more efficient, as it prevents from revisiting the same neighbours multiple times. In this paper, however, we show that this may not be the case. We first empirically demonstrate that the random sampling method is consistently faster than the systematic exploration method across a range of multi-objective problems. We then give an intuitive explanation for this phenomenon using toy examples, showing that the superior performance of the random sampling method relies on the distribution of ``good neighbours''. Next, we show that the number of such neighbours follows a certain probability distribution during the search. Lastly, building on this distribution, we provide a theoretical insight for why random sampling is more efficient than systematic exploration, regardless of whether the best improvement or first improvement strategy is used.

Problem

• multi-objective local search
• neighborhood exploration
• random sampling
• systematic exploration
• search efficiency

Innovation

• multi-objective local search
• random sampling
• systematic exploration
• neighborhood distribution
• stochastic efficiency