Informatica

Derivative-free DIRECT-type global optimization algorithms are increasingly favoured for their simplicity and effectiveness in addressing real-world optimization challenges. This review examines their practical applications through a systematic analysis of scientific journals and computational studies. In particular, significant challenges in reproducibility have been identified with practical problems. To address this, we conducted an experimental study using practical problems from reputable CEC libraries, comparing DIRECT-type techniques against their state-of-the-art counterparts. Therefore, this study sheds light on current gaps, opportunities, and future prospects for advanced research in this domain, laying the foundation for replicating and expanding the research findings presented herein.

Multidimensional scaling with city-block distances is considered in this paper. The technique requires optimization of an objective function which has many local minima and can be non-differentiable at minimum points. This study is aimed at developing a fast and effective global optimization algorithm spanning the whole search domain and providing good solutions. A multimodal evolutionary algorithm is used for global optimization to prevent stagnation at bad local optima. Piecewise quadratic structure of the least squares objective function with city-block distances has been exploited for local improvement. The proposed algorithm has been compared with other algorithms described in literature. Through a comprehensive computational study, it is shown that the proposed algorithm provides the best results. The algorithm with fine-tuned parameters finds the global minimum with a high probability.