multi-objective local search

This work addresses the limitation in combinatorial optimization where local search neighborhoods typically require manual construction. It proposes, for the first time, a method that automatically generates functional neighborhoods by exploiting symmetries present in constraint specifications. By integrating constraint programming, symmetry analysis, and local search techniques, the approach enables automated neighborhood construction within the IDP system, substantially reducing the need for human intervention. Empirical evaluation across six classical optimization problems demonstrates the effectiveness of the generated neighborhoods, confirming both the feasibility of the method and its capacity to enhance the automation and generality of local search algorithms.

When is local search both effective and efficient for combinatorial optimization? Focusing on fitness landscapes induced by binary constraint satisfaction problems (CSPs), we observe that even on unimodal landscapes—such as semismooth or fully unimodal pseudo-Boolean functions—classical algorithms like steepest ascent may require superpolynomial time, revealing a fundamental efficiency bottleneck. Method: We introduce *conditional smoothness*, a novel landscape class that captures the broadest unimodal structure under which widely used local search algorithms—including randomized ascent, simulated annealing, and Kernighan–Lin—admit polynomial-time convergence. Our analysis integrates partial order modeling, Boolean function theory, local search complexity theory, and structural reasoning over hypercube graphs. Contribution/Results: We prove that all aforementioned algorithms converge in polynomial time on conditionally smooth landscapes, whereas steepest ascent remains superpolynomial. This work provides the first fine-grained theoretical characterization of the precise boundary for efficient local search applicability.

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.

Existing research lacks a unified formal model for stochastic local search (SLS) algorithms, hindering a systematic characterization of their computational power and theoretical limits. This work proposes the first general formal framework that decomposes SLS algorithms into a common structural skeleton and parameterizable components, encompassing representative methods such as genetic algorithms, ant colony optimization, and particle swarm optimization through concrete instantiations. Leveraging this model, we construct an SLS instance capable of simulating any Turing machine, thereby rigorously establishing—for the first time—the Turing completeness of the entire class of SLS algorithms. Consequently, we derive the undecidability of nontrivial properties of these algorithms, revealing fundamental theoretical limitations inherent in their input–output behavior.

Handcrafted heuristic functions in search-based navigation suffer from poor generalization across unseen maps and long-distance paths. Method: This paper proposes a local heuristic learning framework that explicitly defines and end-to-end learns either heuristic bias correction or local cost estimation within a spatial neighborhood—replacing conventional global heuristic modeling. By decomposing complex global prediction into lightweight local regression, the approach significantly reduces learning complexity. Integrated with graph search algorithms (e.g., A*), it operates under supervised learning using local state inputs while preserving bounded suboptimality guarantees. Contribution/Results: Experiments demonstrate 2–20× reduction in node expansions, improved training efficiency, and robust generalization to both unseen maps and long-range trajectories—without compromising solution quality or theoretical guarantees.

This work addresses the limitations of traditional stochastic local search in multi-objective combinatorial optimization, where fixed neighborhood structures often lead to premature convergence and insufficient exploration. To overcome this, the authors propose Variable-Step Stochastic Local Search (VS-RLS), a novel approach that dynamically adjusts step size and neighborhood range throughout the search process. Initially employing large steps to enhance global exploration, VS-RLS progressively reduces step size to enable fine-grained exploitation in later stages, thereby effectively balancing exploration and exploitation. As the first method to incorporate a dynamic variable-step mechanism into local search for multi-objective combinatorial optimization, VS-RLS significantly improves the ability to escape local optima and enhances solution set diversity. Experimental results demonstrate its superior performance over state-of-the-art local search and multi-objective evolutionary algorithms across multiple benchmark problems, highlighting its robustness and generalization capability.

This work proposes E2OC, a novel framework for multi-objective evolutionary algorithms that addresses the challenge of modeling dynamic couplings among multiple neighborhood search operators—a task traditionally reliant on expert-designed heuristics and inadequately handled by existing large language model (LLM)-based approaches. E2OC formulates multi-operator optimization as a Markov decision process, explicitly capturing inter-operator dependencies for the first time. By integrating a co-evolutionary mechanism with an operator rotation strategy, it jointly optimizes both high-level design policies and executable code. Leveraging Monte Carlo tree search for progressive exploration and LLM-driven heuristic generation, E2OC consistently outperforms state-of-the-art methods across varying numbers of objectives and problem scales, demonstrating superior generalization and sustained optimization capability.

This work addresses the challenge of efficiently exploring non-convex Pareto fronts in multi-objective autonomous navigation planning. While traditional weighted-sum approaches fail to capture such non-convex fronts, the Chebyshev scalarization (weighted max) method can recover the full Pareto front but suffers from high computational cost, limiting its practicality. To overcome this limitation, this study introduces Large Neighbourhood Search into the Chebyshev scalarization framework, proposing a novel algorithm for solving discrete multi-objective optimization problems. The proposed method achieves solution quality comparable to existing Chebyshev-based planners while reducing runtime by one to two orders of magnitude. This substantial improvement in computational efficiency enables comprehensive exploration of non-convex Pareto-optimal solutions in real-world autonomous navigation scenarios.

This study investigates the performance limitations of local search for the vertex coloring problem on bipartite graphs, revealing that it can become trapped in arbitrarily poor local optima on certain graph structures. To address this issue, the authors propose a gray-box mutation operator based on color frequency that leverages structural information of the problem to guide the search process. Theoretical analysis demonstrates that on complete bipartite graphs, this operator reduces the expected runtime from exponential to Θ(n log n), enabling efficient discovery of globally optimal colorings. Beyond characterizing the fitness landscape of local search in this context, the work introduces an effective gray-box strategy for combinatorial optimization that exploits problem-specific knowledge to enhance search efficiency.

This work proposes G-LNS, a novel framework that leverages large language models (LLMs) to co-evolve destroy-repair operator pairs within large neighborhood search for combinatorial optimization. Unlike existing LLM-based heuristic design methods constrained by fixed structures and prone to local optima, G-LNS introduces a cooperative evaluation mechanism that captures the interaction logic between operators, enabling effective perturbation and reconstruction of solution structures. This approach transcends the structural limitations of traditional heuristics and substantially enhances global exploration. Evaluated on benchmark problems such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), G-LNS outperforms both state-of-the-art LLM-based heuristic methods and classical solvers, achieving near-optimal solutions with lower computational overhead and demonstrating strong generalization on unseen instances.