Combining Kernelized Autoencoding and Centroid Prediction for Dynamic Multi-objective Optimization (2312.00978v1)

Abstract: Evolutionary algorithms face significant challenges when dealing with dynamic multi-objective optimization because Pareto optimal solutions and/or Pareto optimal fronts change. This paper proposes a unified paradigm, which combines the kernelized autoncoding evolutionary search and the centriod-based prediction (denoted by KAEP), for solving dynamic multi-objective optimization problems (DMOPs). Specifically, whenever a change is detected, KAEP reacts effectively to it by generating two subpopulations. The first subpoulation is generated by a simple centriod-based prediction strategy. For the second initial subpopulation, the kernel autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the historical elite solutions. In this way, an initial population is predicted by the proposed combination strategies with good convergence and diversity, which can be effective for solving DMOPs. The performance of our proposed method is compared with five state-of-the-art algorithms on a number of complex benchmark problems. Empirical results fully demonstrate the superiority of our proposed method on most test instances.

• The paper presents KAEP, a hybrid algorithm that combines kernelized autoencoding with centroid prediction to address dynamic multi-objective challenges.
• It employs a dual subpopulation strategy to forecast Pareto optimal sets, ensuring enhanced convergence and diversity in dynamic environments.
• Empirical evaluations across five benchmarks show KAEP achieving superior performance with improved MIGD, MHV, and MGD metrics.

Overview of "Combining Kernelized Autoencoding and Centroid Prediction for Dynamic Multi-objective Optimization"

The paper "Combining KernelizedAutoencoding and Centroid Prediction for Dynamic Multi-objective Optimization" presents a novel method for tackling the challenges endemic to dynamic multi-objective optimization problems (DMOPs). These challenges arise due to the variability of Pareto optimal solutions (POS) and fronts over time, requiring algorithms that can efficiently track, predict, and adapt to these changes. This work introduces a strategy denoted as KAEP, which merges kernelized autoencoding evolutionary search with centroid-based prediction to address these challenges.

Methodological Insights

The proposed KAEP strategically divides the population into two distinct subpopulations when a change is detected. The first subpopulation leverages a centroid-based prediction strategy, while the second utilizes a kernelized autoencoder to project historical elite solutions and forecast the shifting of the Pareto optimal set. The kernel autoencoder (KAE) employed is capable of capturing more complex, nonlinear relationships within the dynamic environments, overcoming the limitations of linear prediction models such as the linear autoencoding model. This dual-faceted approach allows the prediction of an initial population with enhanced convergence and diversity properties, crucial for effective solutions in dynamic environments.

Empirical Evaluation

The superiority of the KAEP algorithm is empirically validated through comprehensive comparisons with five leading algorithms across a suite of complex benchmark problems. The results emphasize the algorithm's effectiveness, showing favorable performance in terms of convergence and distribution metrics across a majority of test instances. Notably, KAEP was observed to have the best performance according to the metrics of Mean Inverted Generational Distance (MIGD), Mean Hypervolume (MHV), and Mean Generational Distance (MGD) in most scenarios. This indicates a robust capability to maintain solution quality amidst dynamic changes.

Implications and Future Directions

The implications of this research are significant for both practical applications and theoretical advancements in the optimization domain. Practically, the KAEP algorithm can be integrated into existing static multi-objective evolutionary algorithms, transforming them into dynamic ones without substantial overhead. Theoretical contributions include the embedding of KAE within the prediction framework, which enriches the predictive capabilities by effectively managing the balance of diversity and convergence.

For future research, the exploration of different kernel functions and their impacts on the effectiveness of KAEP could provide further insights into optimization strategy enhancements. Additionally, leveraging cutting-edge autoencoding methodologies to deal with random environmental changes could offer novel pathways for optimizing more complex, non-continuous environments.

Conclusion

Overall, the paper provides a substantial contribution to the field of dynamic multi-objective optimization by proposing and validating an innovative strategy that combines kernelized autoencoding with centroid prediction. The thorough empirical evaluations coupled with a detailed ablation paper underscore the potential of KAEP in augmenting current approaches to DMOPs and set the stage for further exploration and development in the domain.