Squeaky Wheel Optimization (1105.5454v1)

Abstract: We describe a general approach to optimization which we term Squeaky Wheel' Optimization (SWO). In SWO, a greedy algorithm is used to construct a solution which is then analyzed to find the trouble spots, i.e., those elements, that, if improved, are likely to improve the objective function score. The results of the analysis are used to generate new priorities that determine the order in which the greedy algorithm constructs the next solution. This Construct/Analyze/Prioritize cycle continues until some limit is reached, or an acceptable solution is found. SWO can be viewed as operating on two search spaces: solutions and prioritizations. Successive solutions are only indirectly related, via the re-prioritization that results from analyzing the prior solution. Similarly, successive prioritizations are generated by constructing and analyzing solutions. Thiscoupled search' has some interesting properties, which we discuss. We report encouraging experimental results on two domains, scheduling problems that arise in fiber-optic cable manufacturing, and graph coloring problems. The fact that these domains are very different supports our claim that SWO is a general technique for optimization.

• The paper introduces Squeaky Wheel Optimization (SWO), an iterative method featuring a Construct-Analyze-Prioritize cycle that explores both solution and priority spaces.
• SWO demonstrated strong empirical results, outperforming traditional methods like tabu search and IP in scheduling problems and maintaining competitiveness in graph coloring tasks.
• This approach effectively traverses coupled spaces, offering potential advantages in escaping local optima compared to methods relying solely on local adjustments.

An Expert Overview of Squeaky Wheel Optimization

"Squeaky Wheel Optimization" (SWO), introduced by Joslin and Clements, presents a novel approach to optimization harnessing an iterative cycle characterized by construction, analysis, and prioritization. This method provides an intriguing alternative to conventional local search techniques, carving out its niche by simultaneously exploring solution and priority spaces. The SWO framework is defined by its Construct-Analyze-Prioritize cycle, where solutions are built using a greedy algorithm, analyzed for problematic elements, and then reprioritized to emphasize these elements in subsequent iterations.

Key Features and Methodology

The core mechanics of SWO involve three primary components:

• Constructor: Solutions are assembled by ordering elements based on priority, leveraging a non-backtracking greedy algorithm.
• Analyzer: A quantitative blame factor is assigned to elements contributing to suboptimal performance, illuminating structural weaknesses.
• Prioritizer: It adjusts the sequence of elements, promoting those with higher blame forward in priority, thereby enhancing the focus on problematic regions in the search space.

The iterative nature of SWO facilitates significant solution modifications through the reprioritization process, potentially achieving substantial improvements in objective function scores. This mechanism distinguishes SWO from traditional techniques that may depend on minor local adjustments.

Experimental Domains and Results

Joslin and Clements provide empirical results for two distinct domains—scheduling problems in fiber optic cable manufacturing and graph coloring problems.

1. Scheduling Domain: The authors highlight SWO's adept handling of production line scheduling challenges, successfully outperforming tabu search and integer programming (IP) methods in finding optimal solutions. The use of SWO demonstrated robustness, maintaining efficacy across varying problem sizes and complexities, with the largest problem comprising up to 1,000 tasks on 16 production lines.
2. Graph Coloring Domain: SWO also demonstrated competence in optimizing graph coloring tasks, maintaining competitiveness with specialized algorithms like Impasse and the Iterated Greedy technique. The paper observed that SWO's adaptability allows it to maintain nearly minimal color usage across a wide array of graph configurations.

Contributions and Insights

One insightful contribution of SWO is its ability to traverse coupled solution and priority spaces effectively, enabling large, meaningful search space modifications. This capability can offer advantages in escaping local optima without dependence on domain-specific heuristics. The document specifies that this iterative reassessment and adjustment strategy can transcend the pitfalls of localized search methodologies by leveraging actual solution behavior instead of predetermined heuristic forecasts.

Future Directions and Speculations

The paper suggests various avenues for further exploration, most notably the potential development of an incremental version of SWO. This advancement could mitigate the current limitation of rebuilding solutions from scratch by allowing selective reuse of elements from previous solutions. Additionally, integrating SWO with local search methods could enhance fine-tuning capabilities, providing a hybrid approach that combines the strengths of multi-scale moves across solution spaces.

Conclusion

Joslin and Clements' Squeaky Wheel Optimization introduces a compelling alternative to conventional optimization paradigms. By focusing on coupled optimization problems through iterative prioritization and construction cycles, SWO presents robust potential for both theoretical advancement and practical application. It stands out in its ability to efficiently navigate complex search spaces, an attribute that could influence future AI development and optimization research. With further refinement, particularly in large-scale applicability and incremental solution building, SWO could prove to be a significant addition to the optimization toolkit in diverse, challenging domains.