arXiv:2411.17999v1 Announce Type: new Abstract: As the interest in multi- and many-objective optimization algorithms grows, the performance comparison of these algorithms becomes increasingly important. A large number of performance indicators for multi-objective optimization algorithms have been introduced, each of which evaluates these algorithms based on a certain aspect. Therefore, assessing the quality of multi-objective results using multiple indicators is essential to guarantee that the evaluation considers all quality perspectives. This paper proposes a novel multi-metric comparison method to rank the performance of multi-/ many-objective optimization algorithms based on a set of performance indicators. We utilize the Pareto optimality concept (i.e., non-dominated sorting algorithm) to create the rank levels of algorithms by simultaneously considering multiple performance indicators as criteria/objectives. As a result, four different techniques are proposed to rank algorithms based on their contribution at each Pareto level. This method allows researchers to utilize a set of existing/newly developed performance metrics to adequately assess/rank multi-/many-objective algorithms. The proposed methods are scalable and can accommodate in its comprehensive scheme any newly introduced metric. The method was applied to rank 10 competing algorithms in the 2018 CEC competition solving 15 many-objective test problems. The Pareto-optimal ranking was conducted based on 10 well-known multi-objective performance indicators and the results were compared to the final ranks reported by the competition, which were based on the inverted generational distance (IGD) and hypervolume indicator (HV) measures. The techniques suggested in this paper have broad applications in science and engineering, particularly in areas where multiple metrics are used for comparisons. Examples include machine learning and data mining.
The article “A Novel Multi-Metric Comparison Method for Ranking Multi-/Many-Objective Optimization Algorithms” addresses the growing interest in multi- and many-objective optimization algorithms and the need for performance comparison. With numerous performance indicators available, it is crucial to assess the quality of results using multiple metrics to ensure a comprehensive evaluation. The paper proposes a new method that utilizes the Pareto optimality concept to rank algorithms based on multiple performance indicators. This approach allows researchers to effectively assess and rank multi-/many-objective algorithms using a set of existing or newly developed metrics. The method was applied to rank 10 competing algorithms in the 2018 CEC competition, demonstrating its scalability and applicability. The techniques presented in this paper have broad applications in science and engineering, particularly in areas such as machine learning and data mining, where multiple metrics are used for comparisons.
Ranking Multi-Objective Optimization Algorithms: A Novel Approach
Multi- and many-objective optimization algorithms have gained increasing interest in various fields of science and engineering. With the growing number of available algorithms, it becomes crucial to compare their performance effectively. While numerous performance indicators have been introduced, evaluating algorithms based on a single aspect might not provide a comprehensive assessment.
This paper introduces a novel multi-metric comparison method that ranks the performance of multi-/ many-objective optimization algorithms using a set of performance indicators. By employing the Pareto optimality concept, we create rank levels of algorithms, simultaneously considering multiple performance indicators as criteria/objectives. As a result, we propose four different techniques to rank algorithms based on their contribution at each Pareto level.
The proposed method allows researchers to utilize a combination of existing and newly developed performance metrics to assess and rank multi-/many-objective algorithms effectively. With its scalable and flexible nature, the method can easily accommodate any newly introduced metric.
To evaluate the effectiveness of our approach, we applied it to rank 10 competing algorithms in the 2018 CEC competition, solving 15 many-objective test problems. The Pareto-optimal ranking was conducted based on 10 well-known multi-objective performance indicators. We compared the results to the final ranks reported by the competition, which were based on the inverted generational distance (IGD) and hypervolume indicator (HV) measures.
The techniques suggested in this paper have broad applications in various fields of science and engineering, particularly in areas where multiple metrics are used for comparisons. For instance, in machine learning and data mining, comparing algorithms based on a single performance indicator might not provide an accurate understanding of their strengths and weaknesses. By adopting our multi-metric comparison method, researchers can gain deeper insights into the performance of these algorithms.
In conclusion, our novel multi-metric comparison method provides a comprehensive and flexible approach to rank multi-/many-objective optimization algorithms. By considering multiple performance indicators, researchers can ensure a more nuanced evaluation. We believe that our proposed techniques will contribute to the advancement of multi-objective optimization algorithms and their applications in various fields.
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The paper discusses the importance of comparing the performance of multi- and many-objective optimization algorithms and proposes a novel multi-metric comparison method to rank these algorithms based on a set of performance indicators. This is a significant contribution to the field as it addresses the need for a comprehensive evaluation framework that considers multiple quality perspectives.
The authors utilize the concept of Pareto optimality, specifically the non-dominated sorting algorithm, to create rank levels for the algorithms. This approach allows for the simultaneous consideration of multiple performance indicators as criteria or objectives. By ranking algorithms based on their contribution at each Pareto level, the proposed method provides a more holistic assessment of their performance.
One of the key strengths of the proposed method is its scalability and flexibility. It can accommodate any existing or newly introduced performance metric, making it adaptable to future developments in the field. This is particularly important as new metrics are constantly being proposed to evaluate the quality of multi-objective optimization algorithms.
To validate the effectiveness of the proposed method, the authors applied it to rank 10 competing algorithms in the 2018 CEC competition. They compared the results obtained using their multi-metric approach with the final ranks reported by the competition, which were based on the inverted generational distance (IGD) and hypervolume indicator (HV) measures. This comparison demonstrates that the proposed method is capable of producing rankings that align with those obtained using established metrics.
The implications of this research extend beyond the field of optimization algorithms. The proposed method has broad applications in science and engineering, particularly in areas where multiple metrics are used for comparisons. For example, in machine learning and data mining, where the evaluation of different models often involves considering multiple performance indicators, the proposed method can provide a more comprehensive and accurate assessment.
In conclusion, the paper presents a novel multi-metric comparison method for ranking multi- and many-objective optimization algorithms. The use of Pareto optimality and the consideration of multiple performance indicators as criteria make this method a valuable contribution to the field. Its scalability and applicability to various domains make it a promising tool for researchers in science and engineering.
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