Research Article: HSTLBO: A hybrid algorithm based on Harmony Search and Teaching-Learning-Based Optimization for complex high-dimensional optimization problems

Date Published: April 12, 2017

Publisher: Public Library of Science

Author(s): Shouheng Tuo, Longquan Yong, Fang’an Deng, Yanhai Li, Yong Lin, Qiuju Lu, Wen-Bo Du.


Harmony Search (HS) and Teaching-Learning-Based Optimization (TLBO) as new swarm intelligent optimization algorithms have received much attention in recent years. Both of them have shown outstanding performance for solving NP-Hard optimization problems. However, they also suffer dramatic performance degradation for some complex high-dimensional optimization problems. Through a lot of experiments, we find that the HS and TLBO have strong complementarity each other. The HS has strong global exploration power but low convergence speed. Reversely, the TLBO has much fast convergence speed but it is easily trapped into local search. In this work, we propose a hybrid search algorithm named HSTLBO that merges the two algorithms together for synergistically solving complex optimization problems using a self-adaptive selection strategy. In the HSTLBO, both HS and TLBO are modified with the aim of balancing the global exploration and exploitation abilities, where the HS aims mainly to explore the unknown regions and the TLBO aims to rapidly exploit high-precision solutions in the known regions. Our experimental results demonstrate better performance and faster speed than five state-of-the-art HS variants and show better exploration power than five good TLBO variants with similar run time, which illustrates that our method is promising in solving complex high-dimensional optimization problems. The experiment on portfolio optimization problems also demonstrate that the HSTLBO is effective in solving complex read-world application.

Partial Text

With the scientific and social progress, new complex problems are more and more encountered in the fields of science and engineering. Especially, many high-dimensional optimization problems in engineering design, production scheduling and scientific calculation need urgently to be solved with high performance and high efficiency, for which there are three challenges: the first one is the very large search space owing to the very high dimensional problems (e.g., >500), which makes the enormous computation burden; the second one is the large number of modals (multi-extremum points), which makes the search algorithm be easily trapped into local search; the third one is the particularity of optimization problem that may be discontinuous, non-differentiable and even have no objective function, for which the traditional mathematical optimization algorithms are powerless due to the requiring of substantial gradient information. Therefore, it is of great challenge to discover the globally optimal solution in an efficient time for solving a complex multimodal optimization problem with more than 1000 dimensions, possibly infinite number of local minima and non-differentiable.

To balance the exploration power and the exploitation power during the searching process, we propose a complementary HSTLBO algorithm.

To investigate the performance of proposed HSTLBO algorithm, numerical simulation experiments on twenty benchmark functions [32–35] are tested. Parameter settings are listed for all compared HS and TLBO variants in Table 1.

To further investigate the performance of HSTLBO algorithm, complex portfolio optimization problem are employed to test the ability of solving real-world application. The portfolio optimization aims to choose the optimal proportions of various assets for obtaining maximum portfolio return with minimum risk. In this work, we apply HSTLBO algorithm to choose the optimal portfolio proportions for Nikkei 225 stock index that maps companies on the Tokyo Stock Exchange (TSE) ( and compare the test results of HSTLBO with four intelligent algorithms (GA, PSO, TS, SA)[38–40]. We employ mean Euclidian distance (MED), variance of returns error (VRE) and mean return error (MRE) as performance indexes that are defined in literatures [39,41].

Both Harmony Search and Teaching-Learning-Based Optimization are new swarm intelligent optimization algorithms, which have got much attention in recent years. In this work, in order to improve the performance of HS and TLBO, a hybrid HSTLBO algorithm is presented.




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