Techniques for Highly Multiobjective Optimisation: Some Nondominated Points are Better than Others (0908.3025v1)

Abstract: The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly when problems have many (e.g. five or more) objectives. One of the chief reasons for this is believed to be that, in many-objective EMO search, populations are likely to be largely composed of nondominated solutions. In turn, this means that the commonly-used algorithms cannot distinguish between these for selective purposes. However, there are methods that can be used validly to rank points in a nondominated set, and may therefore usefully underpin selection in EMO search. Here we discuss and compare several such methods. Our main finding is that simple variants of the often-overlooked Average Ranking strategy usually outperform other methods tested, covering problems with 5-20 objectives and differing amounts of inter-objective correlation.

• The paper demonstrates that the Average Ranking method outperforms alternative strategies in efficiently ordering nondominated solutions in high-dimensional objective spaces.
• It rigorously compares ranking techniques using experimental analyses on complex problems like multi-objective TSP and job-shop scheduling.
• The study highlights the computational efficiency and robustness of the ARF method, promoting its use in tackling many-objective optimisation challenges.

Overview of "Techniques for Highly Multiobjective Optimisation: Some Nondominated Points are Better than Others"

This paper presents a rigorous investigation into the challenges and methodologies associated with many-objective optimization within the field of evolutionary multiobjective optimization (EMO). As the number of objectives increases, traditional EMO algorithms face significant scaling issues, as evidenced by the performance degradation when dealing with problems involving five or more objectives. This research seeks to address the limitations of distinguishing solutions when faced with numerous nondominated points—a common scenario in many-objective problems.

Key Contributions

The paper evaluates several methodologies for ranking nondominated points, proposing the utility of a preference ordering system that operates without specific domain preferences. The main findings revolve around several ranking strategies, notably the underappreciated 'Average Ranking' method, which generally outperforms other methods tested in diverse scenarios involving five to 20 objectives.

1. Challenge of Many Objectives:
   • High dimensional objective spaces tend to diminish the effectiveness of existing multiobjective evolutionary algorithms (MOEAs), such as MOGA, NSGA, and SPEA, whose selection mechanisms are impeded by large sets of nondominated solutions.
   • The paper underscores reasons for poor scaling: reliance on non-scalable data structures, prevalence of nondominated solutions, and the phenomenon of fitness deterioration.
2. Ranking Strategies:
   • Average Ranking (AR): Demonstrated superior performance through empirical analysis. Simple yet effective, it offered high selective pressure by providing clear preference orderings within a nondominated set.
   • Sum of Ratios (SR) and Its Derivatives: While providing alternative ordering mechanisms, these were less effective compared to AR under test conditions.
   • Favour Relation and k-Optimality: Examined for their ability to impose partial orderings on nondominated sets, albeit with limitations in handling many-objective scenarios efficiently.
   • Winning Score and Its Equivalence to AR: Showed comparable rank induction, reinforcing AR's robustness through theoretical equivalence.
3. Experimental Analysis:
   • Comprehensive comparative experiments across multiobjective traveling salesperson problems (MOTSPs) and multiobjective single-machine job-shop problems (SMJSPs) highlighted the consistent performance of the ARF method.
   • The ARF method emerged as notably effective, especially as the number of objectives and degree of correlation between objectives increased.

Implications and Future Directions

The findings suggest that the ARF method is a strong candidate for use in highly multiobjective contexts due to its simplicity and computational efficiency. This holds potential for further exploration in both theoretical and practical applications involving many-objective optimization. The results advocate for revisiting such methods even in standard scenarios with fewer objectives, given their promising performance.

Considering the ongoing advancements in optimization and computational power, the exploration of ranking methods like k-optimality and the introduction of dimension reduction strategies may open new pathways for research. Future work could focus on enhancing the EF-quality of rankings, exploring dynamic settings of the ranking parameters, and integrating these strategies into broader AI systems to advance autonomous decision-making processes in complex environments.

Overall, the paper makes a significant contribution to the field of evolutionary computation, offering insights into effectively navigating the complexities introduced by many-objective problems and providing a foundation for future research in this essential area of paper.