An Effective Integrated Metaheuristic Algorithm For Solving Engineering Problems Adis Alihodzic University of Sarajevo, BiH Department of Mathematics ul. Zmaja od Bosne, 33-35, Sarajevo Email: adis.alihodzic@pmf.unsa.ba Sead Delalic University of Sarajevo, BiH Department of Mathematics ul. Zmaja od Bosne, 33-35, Sarajevo Email: delalic.sead@pmf.unsa.ba Dzenan Gusic University of Sarajevo, BiH Department of Mathematics ul. Zmaja od Bosne, 33-35, Sarajevo Email: dzenang@pmf.unsa.ba Abstract—To tackle a specific class of engineering problems, in this paper, we propose an effectively integrated bat algorithm with simulated annealing for solving constrained optimization problems. Our proposed method (I-BASA) involves simulated an- nealing, Gaussian distribution, and a new mutation operator into the simple Bat algorithm to accelerate the search performance as well as to additionally improve the diversification of the whole space. The proposed method performs balancing between the grave exploitation of the Bat algorithm and global exploration of the Simulated annealing. The standard engineering benchmark problems from the literature were considered in the competition between our integrated method and the latest swarm intelligence algorithms in the area of design optimization. The simulations results show that I-BASA produces high-quality solutions as well as a low number of function evaluations. I. I NTRODUCTION I N THE last fifteen years, it was shown that most de- sign nonlinear constrained optimization problems are an essential class of issues in real-world applications, and almost all are characterized as NP-hard problems. For such design optimization problems, the finding of the best solution may require centuries, even with a supercomputer. These highly nonlinear and multimodal optimization problems are based on the optimization of objective functions with complex con- straints which usually involve thousands of or even millions of elements, and they were written in the form of simple bounds or more often as nonlinear inequalities. Nonlinearly constrained optimization problems contain continuous and discrete design variables, nonlinear objective functions, and constraints, some of which may be active at the global optima. Due to the complex nature of an objective function, as well as the constraints that need to be met, it is challenging how to ef- fectively and robustly explore overall search space. Therefore, practically solving engineering problems are come down to some efficient methods which are problem-specific [1]. Since optimization methods can not escape falling in into some of the local optima, metaheuristics as very modern and efficient global techniques are considered to overcome these type of problems [2]. Besides, those are capable of generating quality solutions in a reasonable amount of time. The creating of quality solutions is related to the establishment of the right bal- ance between exploration and exploitation. [3]. Since a magic formula does not exist, which works for all types of problems [4], in this paper, several swarm intelligence algorithms [5] have been adopted for solving nonlinear engineering problems. Some of the most popular swarm intelligence optimization techniques are artificial bee colony(ABC) [6][7][8][9], firefly algorithm (FA) [10][1][11][12], cuckoo search (CS) [13][14], bat algorithm (BA) [15][16][17][18][19], flower pollination algorithm [20], and etc. In this article, we have combined the bat algorithm as a representative of swarm intelligent multi- agent algorithm with one agent simulated annealing method to produce as much as possible suboptimal solutions. The Bat meta-heuristic algorithm (BA) has proposed by Xin-She Yang 2010 [15]. The primary mechanism of this swarm intelligence technique propagates echolocation of bats as agents. The agents seek for prey and avoid obstacles by using echolocation. In the paper [19], it has been shown that the BA very well performs local search, but at times it deviated into some local optima, and it can not reach the optimal solution while solving a hard problem. The original version of bat algorithm, as well as the other metaheuristic algorithms, were designed to address unconstrained problems. To tackle the constrained problems, bat algorithm (BA) uses a penalty approach as a constraint handling technique [16]. From the experiments presented in [16], it can be seen that the BA is almost always superior to other metaheuristics. To promote the results obtained by the simple bat algorithm, in this article, we propose an integrated I-BASA approach to take on engineering problems. Unlike the original bat algorithm which is not capable to found satisfying balance between diversification and intensification, the proposed I- BASA approach based on simulated annealing (SA) [21], a new mutation operator, and Gaussian distribution achieves a right balance and raises overall search performance. The integrated I-BASA method was tested on the eight well-chosen benchmark problems, and the simulation results report that our approach almost always wins the state-of-the-art algorithms regarding the convergence and accuracy. In this paper, we have decided to exploit Deb’s rules as a constraint handling process instead of a standard penalty method. Throughout the simulation results, it can be seen that introduced rules significantly improve the quality of the solutions. The basic structure of the article looks like this. The basic definitions related to constrained optimization are described in Proceedings of the Federated Conference on Computer Science and Information Systems pp. 207–214 DOI: 10.15439/2020F81 ISSN 2300-5963 ACSIS, Vol. 21 IEEE Catalog Number: CFP2085N-ART ©2020, PTI 207