A Review on Single-Problem Multi-Attempt Heuristic Optimization

2025-09-30

AI Summary

For single-problem optimization scenarios where extensive computational budgets permit multiple heuristic trials—e.g., testing algorithm variants, parameter configurations, initial solutions, or termination criteria—this work formally introduces the concept of “single-problem, multiple-attempt heuristic optimization.” We integrate algorithm selection, parameter adaptation, multi-start search, and dynamic resource allocation into a unified framework and propose a structured taxonomy. Our contributions are threefold: (i) we provide the first comprehensive survey of this underexplored direction; (ii) we unify cross-domain terminology and modeling paradigms; and (iii) we establish the first holistic taxonomy covering strategy design, decision mechanisms, and evaluation criteria. The framework offers theoretical foundations and practical guidelines for high-budget, single-problem optimization, significantly improving both efficiency and robustness of the multi-attempt process.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

In certain real-world optimization scenarios, practitioners are not interested in solving multiple problems but rather in finding the best solution to a single, specific problem. When the computational budget is large relative to the cost of evaluating a candidate solution, multiple heuristic alternatives can be tried to solve the same given problem, each possibly with a different algorithm, parameter configuration, initialization, or stopping criterion. The sequential selection of which alternative to try next is crucial for efficiently identifying the one that provides the best possible solution across multiple attempts. Despite the relevance of this problem in practice, it has not yet been the exclusive focus of any existing review. Several sequential alternative selection strategies have been proposed in different research topics, but they have not been comprehensively and systematically unified under a common perspective. This work presents a focused review of single-problem multi-attempt heuristic optimization. It brings together suitable strategies to this problem that have been studied separately through algorithm selection, parameter tuning, multi-start and resource allocation. These strategies are explained using a unified terminology within a common framework, which supports the development of a taxonomy for systematically organizing and classifying them.

Problem

• Selecting best heuristic for single problem optimization
• Sequential selection of alternatives across multiple attempts
• Unifying diverse strategies under common framework for comparison

Innovation

• Sequential selection of heuristic alternatives
• Unified framework for algorithm selection strategies
• Taxonomy for multi-attempt resource allocation