This chapter explores the application of the Bees Algorithm to multi-solution problems, where the goal is to find multiple optimal or near-optimal solutions with diverse characteristics. It starts with a preliminary gearbox design problem to illustrate the concept and challenges of multi-solution optimisation. The chapter then introduces the concept of diversification of search, which is essential for finding diverse solutions. The chapter presents a modified Bees Algorithm, LORRE-BA (Local Optimum Region Radius Estimator Bees Algorithm), designed to enhance diversity in continuous optimisation problems. LORRE-BA incorporates mechanisms to estimate the radius of local optimum regions, derate the fitness of solutions within these regions, and prune similar solutions to maintain diversity. The performance of LORRE-BA is evaluated using benchmark functions and compared to other algorithms, demonstrating its effectiveness in finding diverse solutions. The chapter concludes by discussing the importance and challenges of multi-solution optimisation, highlighting its relevance in real-world applications where multiple design alternatives are desired.

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Case Study—Preliminary Design and Multi-solution Problems

  • Duc Truong Pham,
  • Marco Castellani,
  • Luca Baronti

摘要

This chapter explores the application of the Bees Algorithm to multi-solution problems, where the goal is to find multiple optimal or near-optimal solutions with diverse characteristics. It starts with a preliminary gearbox design problem to illustrate the concept and challenges of multi-solution optimisation. The chapter then introduces the concept of diversification of search, which is essential for finding diverse solutions. The chapter presents a modified Bees Algorithm, LORRE-BA (Local Optimum Region Radius Estimator Bees Algorithm), designed to enhance diversity in continuous optimisation problems. LORRE-BA incorporates mechanisms to estimate the radius of local optimum regions, derate the fitness of solutions within these regions, and prune similar solutions to maintain diversity. The performance of LORRE-BA is evaluated using benchmark functions and compared to other algorithms, demonstrating its effectiveness in finding diverse solutions. The chapter concludes by discussing the importance and challenges of multi-solution optimisation, highlighting its relevance in real-world applications where multiple design alternatives are desired.