Multi-modal optimization is often encountered in engineering problems,
especially when different and alternative solutions are sought. Evolutionary
algorithms can efficiently tackle multi-modal optimization thanks to their
features such as the concept of population, exploration/exploitation, and being
suitable for parallel computation.
This paper introduces a multi-modal optimization version of the Big Bang-Big
Crunch algorithm based on clustering, namely, k-BBBC. This algorithm guarantees
a complete convergence of the entire population, retrieving on average the 99%
of local optima for a specific problem. Additionally, we introduce two
post-processing methods to (i) identify the local optima in a set of retrieved
solutions (i.e., a population), and (ii) quantify the number of correctly
retrieved optima against the expected ones (i.e., success rate).
Our results show that k-BBBC performs well even with problems having a large
number of optima (tested on 379 optima) and high dimensionality (tested on 32
decision variables). When compared to other multi-modal optimization methods,
it outperforms them in terms of accuracy (in both search and objective space)
and success rate (number of correctly retrieved optima) — especially when
elitism is applied. Lastly, we validated our proposed post-processing methods
by comparing their success rate to the actual one. Results suggest that these
methods can be used to evaluate the performance of a multi-modal optimization
algorithm by correctly identifying optima and providing an indication of
success — without the need to know where the optima are located in the search
space.
Multi-modal optimization is a complex problem that is frequently encountered in engineering. It involves finding multiple alternative solutions to a problem, rather than just a single optimal solution. Evolutionary algorithms, with their ability to explore and exploit the search space, are well-suited for tackling multi-modal optimization.
Introducing k-BBBC Algorithm
In this paper, the authors introduce a multi-modal optimization version of the Big Bang-Big Crunch algorithm, called k-BBBC. This algorithm relies on clustering to ensure complete convergence of the entire population and achieve high retrieval rates of local optima. In their experiments, the authors found that k-BBBC was able to retrieve 99% of local optima for the problems tested.
Post-processing Methods
The paper also presents two post-processing methods that enhance the analysis of the results. The first method is used to identify local optima within a set of retrieved solutions, while the second method quantifies the success rate by comparing the number of correctly retrieved optima against the expected ones. These post-processing methods provide valuable insights into the algorithm’s performance without the need for prior knowledge of the optima locations in the search space.
K-BBBC Performance
The experimental results demonstrate that k-BBBC performs well even in challenging scenarios with a large number of optima and high dimensionality. It outperforms other multi-modal optimization methods in terms of accuracy, both in search space and objective space, as well as success rate. Notably, when elitism is applied, k-BBBC shows particularly impressive results.
Validation of Post-processing Methods
To validate the proposed post-processing methods, the authors compare their success rate to the actual success rate. The results indicate that these methods are effective in correctly identifying optima and providing a reliable indication of success. This validation is crucial for evaluating the performance of a multi-modal optimization algorithm.
The Multi-disciplinary Nature of the Concepts
This research combines concepts from various disciplines, such as optimization, clustering, and evolutionary algorithms. The utilization of clustering enhances the Big Bang-Big Crunch algorithm to handle multi-modal optimization effectively. Moreover, the post-processing methods contribute to the field of algorithm evaluation by providing a comprehensive analysis of the algorithm’s performance without requiring prior knowledge of the problem’s solution space.
In conclusion, the k-BBBC algorithm presented in this paper demonstrates excellent performance in multi-modal optimization. The incorporation of clustering and the use of post-processing methods further enhance its capabilities. This research contributes to the growing field of multi-modal optimization and offers valuable insights for practitioners working on complex engineering problems.