Dynamic Multi-Objective Optimization with Changing Objectives
Dynamic Multi-Objectives Optimization (DMO) has posed significant challenges due to the presence of time-dependent objective functions and constraints. While the majority of research efforts in this domain have concentrated on such aspects, the scenario involving a dynamically changing number of objectives has remained relatively unexplored. The paper "Dynamic Multi-Objectives Optimization with a Changing Number of Objectives" addresses this gap by providing a systematic approach to solving the dynamic multi-objective optimization problem (DMOP) when the number of objectives varies over time.
Summary of Methodology
The paper introduces a dynamic two-archive evolutionary algorithm (DTAEA) designed to tackle the aforementioned challenge. The algorithm maintains two co-evolving populations or archives: the convergence archive (CA) and the diversity archive (DA). Each population is sorted based on different criteria to maintain their complementarity. The CA focuses on pressure toward the Pareto-optimal front (PF), ensuring convergence, while the DA focuses on maintaining a promising diversity of solutions.
Specific reconstruction mechanisms are employed to adapt these populations to changes in the environment, such as an increase or decrease in the number of objectives—a process that leads to the expansion or contraction of the PF. For instance, increasing the number of objectives necessitates maintaining the optimal solutions within the convergence archive and generating random solutions for the diversity archive to ensure it remains well-spread across the solution space. Conversely, decreasing the number of objectives involves re-evaluating solutions to maintain continuity in both convergence and diversity archives.
The algorithm leverages interaction between the CA and DA during the mating selection process, adapting strategies depending on the population’s distribution diversity. Offspring reproduction utilizes simulated binary crossover and polynomial mutation, facilitated by a restricted mating selection mechanism that favors mate choices from either the CA or DA depending on specific criteria.
Results and Performance
Comprehensive experiments illustrate the effectiveness of DTAEA across a set of dynamic benchmark problems. These include problems where only the number of objectives changes and scenarios where both the number of objectives and position of the solution set vary over time. The algorithm outperforms both stationary and other dynamic evolutionary algorithms like DNSGA-II and MOEA/D-KF, as demonstrated by superior performance metrics such as Mean Inverted Generational Distance (MIGD) and Mean Hypervolume (MHV).
DTAEA’s structure successfully navigates the inherent dynamics of the optimization landscape, offering robustness to rapid changes and scalability across various objective dimensionalities. In particular, its capacity to balance convergence and diversity effectively propels solutions toward the expanded or contracted PF as dictated by environmental changes.
Implications and Future Work
The implications of this work are significant for fields where dynamic optimization is crucial. DTAEA’s design allows adaptation to environments where objectives shift due to changes in requirements, resource availability, or external constraints—a common scenario in real-world applications like software development, project scheduling, and cloud computing.
Future research directions may explore handling dynamic constraints, integrating adaptive reproduction operations, and developing even more complex dynamic problem suites. Moreover, efforts should be made to develop new performance metrics which could offer deeper insights into the effectiveness of dynamic evolutionary strategies.
In conclusion, this paper advances the domain of dynamic multi-objective optimization by systematically addressing the less-studied aspect of dynamically changing objectives. The proposed DTAEA demonstrates significant promise and invokes further interest in developing more sophisticated algorithmic approaches for dynamic environments.