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The group teaching optimization algorithm (GTOA) is a meta heuristic optimization algorithm simulating the group teaching mechanism. The inspiration of GTOA comes from the group teaching mechanism. Each student will learn the knowledge obtained in the teacher phase, but each student's autonomy is weak. This paper considers that each student has different learning motivations. Elite students have strong self-learning ability, while ordinary students have general self-learning motivation. To solve this problem, this paper proposes a learning motivation strategy and adds random opposition-based learning and restart strategy to enhance the global performance of the optimization algorithm (MGTOA). In order to verify the optimization effect of MGTOA, 23 standard benchmark functions and 30 test functions of IEEE Evolutionary Computation 2014 (CEC2014) are adopted to verify the performance of the proposed MGTOA. In addition, MGTOA is also applied to six engineering problems for practical testing and achieved good results. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid gradient simulated annealing algorithm is guided to solve the constrained optimization problem. In trying to solve constrained optimization problems using deterministic, stochastic optimization methods or hybridization between them, penalty function methods are the most popular approach due to their simplicity and ease of implementation. There are many approaches to handling the existence of the constraints in the constrained problem. The simulated-annealing algorithm (SA) is one of the most successful meta-heuristic strategies. On the other hand, the gradient method is the most inexpensive method among the deterministic methods. In previous literature, the hybrid gradient simulated annealing algorithm (GLMSA) has demonstrated efficiency and effectiveness to solve unconstrained optimization problems. In this paper, therefore, the GLMSA algorithm is generalized to solve the constrained optimization problems. Hence, a new approach penalty function is proposed to handle the existence of the constraints. The proposed approach penalty function is used to guide the hybrid gradient simulated annealing algorithm (GLMSA) to obtain a new algorithm (GHMSA) that finds the constrained optimization problem. The performance of the proposed algorithm is tested on several benchmark optimization test problems and some well-known engineering design problems with varying dimensions. Comprehensive comparisons against other methods in the literature are also presented. The results indicate that the proposed method is promising and competitive. The comparison results between the GHMSA and the other four state-Meta-heuristic algorithms indicate that the proposed GHMSA algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final result. [ABSTRACT FROM AUTHOR]

The Competitive Swarm Optimizer (CSO) has emerged as a prominent technique for solving intricate optimization problems by updating only half of the population in each iteration. Despite its effectiveness, the CSO algorithm often exhibits a slow convergence rate and a tendency to become trapped in local optimal solutions, as is common among metaheuristic algorithms. To address these challenges, this paper proposes a hybrid approach combining the CSO with the Salp Swarm algorithm (SSA), CL-SSA, to increase the convergence rate and enhance search space exploration. The proposed approach involves a two-step process. In the first step, a pairwise competition mechanism is introduced to segregate the solutions into winners and losers. The winning population is updated through strong exploitation using the SSA algorithm. In the second step, non-winning solutions learn from the winners, achieving a balance between exploration and exploitation. The performance of the CL-SSA is evaluated on various benchmark functions, including the CEC2017 benchmark with dimensions 50 and 100, the CEC2008lsgo benchmark with dimensions 200, 500 and 1000, as well as a set of seven well-known constrained design challenges in various engineering domains defined in the CEC2020 conference. The CL-SSA is compared to other metaheuristics and advanced algorithms, and its results are analyzed through statistical tests such as the Friedman and Wilcoxon rank-sum tests. The statistical analysis demonstrates that the CL-SSA algorithm exhibits improved exploitation, exploration, and convergence patterns compared to other algorithms, including SSA and CSO, as well as popular algorithms. Furthermore, the proposed hybrid approach performs better in solving most test functions. [ABSTRACT FROM AUTHOR]

The artificial Gorilla Troop Optimization (GTO) algorithm (GTO) is a metaheuristic optimization algorithm that simulates the social life of gorillas. This paper proposes three innovative strategies considering the GTO algorithm's insufficient convergence accuracy and low convergence speed. First, a shrinkage control factor fusion strategy is proposed to expand the search space and reduce search blindness by strengthening the communication between silverback gorillas and other gorillas to improve global optimization performance. Second, a sine cosine interaction fusion strategy based on closeness is proposed to stabilize the performance of silverback gorillas and other gorilla individuals and improve the convergence ability and speed of the algorithm. Finally, a gorilla individual difference identification strategy is proposed to reduce the difference between gorilla and silverback gorillas to improve the quality of the optimal solution. In order to verify the optimization effect of the modified artificial gorilla troop optimization (MGTO) algorithm, we used 23 classic benchmark functions, 30 CEC2014 benchmark functions, and 10 CEC2020 benchmark functions to test the performance of the proposed MGTO algorithm. In this study, we used a total of 63 functions for algorithm comparison. At the same time, we carried out the exploitation and exploration balance experiment of 30 CEC2014 and 10 CEC2020 functions for the MGTO algorithm. In addition, the MGTO algorithm was also applied to test seven practical engineering problems, and it achieved good results. [ABSTRACT FROM AUTHOR]

Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality constraints are relaxed, a series of linear relaxation subproblems with auxiliary variables and bound constraints are generated, which can determine the effective lower bound of the global optimal value of QCQP. To enhance the compactness of sub-rectangles and improve the ability to remove sub-rectangles, two rectangle-reduction strategies are employed. Besides, two ϵ -subproblem deletion rules are introduced to improve the convergence speed of the algorithm. Therefore, a relaxation and bound algorithm based on auxiliary variables are proposed to solve QCQP. Numerical experiments show that this algorithm is effective and feasible. [ABSTRACT FROM AUTHOR]

This paper proposes a new meta-heuristic called Jumping Spider Optimization Algorithm (JSOA), inspired by Arachnida Salticidae hunting habits. The proposed algorithm mimics the behavior of spiders in nature and mathematically models its hunting strategies: search, persecution, and jumping skills to get the prey. These strategies provide a fine balance between exploitation and exploration over the solution search space and solve global optimization problems. JSOA is tested with 20 well-known testbench mathematical problems taken from the literature. Further studies include the tuning of a Proportional-Integral-Derivative (PID) controller, the Selective harmonic elimination problem, and a few real-world single objective bound-constrained numerical optimization problems taken from CEC 2020. Additionally, the JSOA's performance is tested against several well-known bio-inspired algorithms taken from the literature. The statistical results show that the proposed algorithm outperforms recent literature algorithms and is capable to solve challenging real-world problems with unknown search space. [ABSTRACT FROM AUTHOR]

This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach. [ABSTRACT FROM AUTHOR]

Firefly-Algorithm (FA) is an eminent nature-inspired swarm-based technique for solving numerous real world global optimization problems. This paper presents an overview of the constraint handling techniques. It also includes a hybrid algorithm, namely the Stochastic Ranking with Improved Firefly Algorithm (SRIFA) for solving constrained real-world engineering optimization problems. The stochastic ranking approach is broadly used to maintain balance between penalty and fitness functions. FA is extensively used due to its faster convergence than other metaheuristic algorithms. The basic FA is modified by incorporating opposite-based learning and random-scale factor to improve the diversity and performance. Furthermore, SRIFA uses feasibility based rules to maintain balance between penalty and objective functions. SRIFA is experimented to optimize 24 CEC 2006 standard functions and five well-known engineering constrained-optimization design problems from the literature to evaluate and analyze the effectiveness of SRIFA. It can be seen that the overall computational results of SRIFA are better than those of the basic FA. Statistical outcomes of the SRIFA are significantly superior compared to the other evolutionary algorithms and engineering design problems in its performance, quality and efficiency. [ABSTRACT FROM AUTHOR]