Brain storm optimization with adaptive search radius for optimization

In this work Amplified Brain Storm Optimization (ABS) algorithm and Quantum based Brain Storm (QBS) Optimization Algorithm is used for solving optimal reactive power problem. In the projected amplified Brain storm optimization algorithm Hamiltonian cycle has been applied to improve the search abilities and also to avoid of trap in local optimal solution. A node is arbitrarily chosen from the graph as the preliminary point to form a Hamiltonian cycle. At generation t and t+1, L<sub>t</sub> and L<sub>t</sub><sub>+1</sub> are the length of Hamiltonian cycle correspondingly. In the QBS algorithm a Quantum state of an idea is illustrated by a wave function as an alternative of the position modernized only in Brain storm optimization algorithm. Monte Carlo simulation method<em> </em>is used, to measure the position for each idea from the<em> </em>quantum state to the traditional one. Proposed Amplified Brain Storm Optimization (ABS) algorithm and Quantum based Brain Storm (QBS) Optimization Algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithms reduced the real power loss effectively.

Recently, inspired by the human brainstorming process, a new kind of metaheuristic algorithm, called brain storm optimization (BSO) algorithm was proposed for global optimization. Experimental results have shown its excellent performance when solving optimization problems. In order to further improve the search ability of the BSO, this paper proposes an improved BSO (IBSO) algorithm by introducing graph theory into it. In IBSO, new individuals will be generated to replace some old individuals when the BSO algorithm is in a poor status. Whether a BSO algorithm is in a poor status is determined by the length of Hamiltonian cycle, which can be obtained by transferring all the individuals into an undirected weight graph. A Hamiltonian cycle and its length will be computed according to a modified cycle algorithm. The proposed IBSO algorithm is tested on twelve benchmarks, and the experimental results illustrate its effectiveness.

In this chapter, the human brainstorming process is modeled, based on which two versions of a Brain Storm Optimization (BSO) algorithm are introduced. Simulation results show that both BSO algorithms perform reasonably well on ten benchmark functions, which validates the effectiveness and usefulness of the proposed BSO algorithms. Simulation results also show that one of the BSO algorithms, BSO-II, performs better than the other BSO algorithm, BSO-I, in general. Furthermore, average inter-cluster distance Dc and inter-cluster diversity De are defined, which can be used to measure and monitor the distribution of cluster centroids and information entropy of the population over iterations. Simulation results illustrate that further improvement could be achieved by taking advantage of information revealed by Dc, which points at one direction for future research on BSO algorithms.

Using swarm intelligence to obtain multiple optima in a single run simultaneously proved efficient for solving multimodal optimization problems (MOPs). However, the existing studies fail to resolve the contradiction between the required solution accuracy and the number of solutions. In this paper, an improved brain storm optimization (BSO) algorithm based on knowledge learning (KLBSO) is proposed as a solution to the problem. The properties of the improved algorithm and the domain knowledge of the problem are combined during the search process. Two factors need to be taken into account to solve a MOP: the accuracy and the diversity of the solution set. In the proposed algorithm, there are two learning approaches. Firstly, improving the learning method by replacing the perturbation operator of the random solution with the inter-solution learning of the worst solutions, improves the optimization ability of the algorithm. Secondly, by analyzing the MOPs, adding an archive set guarantees the solution’s diversity. To assess the efficiency of KLBSO, eight benchmark functions with various sizes and complexities were used. Comparing the results of KLBSO with those of state-of-the-art methods which are brain storm optimization algorithm (BSO), brain storm optimization algorithm in objective space (BSOOS), two kinds of pigeon-inspired optimization algorithms (PIO, PIOr), the comparison results show that the KLBSO is able to solve the contradiction between required solution accuracy and the number of solutions, and improves the outcomes where BSO is ranked first followed by the test algorithms.

Alternate search pattern-based brain storm optimization

This chapter explains the mathematical formulation of brain storm optimization (BSO), conduct a comprehensive literature survey for the last 3 years, detail how BSO is applied to one real-world application, finally highlight promising future research directions. Since its introduction in 2011, different researchers have studied BSO behavior, proposed improvements to BSO, hybridized BSO with other techniques, developed cooperative BSO frameworks, applied BSO to real-world applications. Experimental results showed that simplex-BSO provided a better performance than BSO and Nelder-Mead simplex as well as being the best algorithm at any given computational cost. The term population-based metaheuristics refers to one large class of algorithms that has been successfully applied to solve continuous and discrete optimization problems. Reliability of the power supply is defined as the ability of a power system to supply customers in acceptable degree of adequacy and security. The work concluded that in lower dimensions, BSO produced good results as the population interaction of BSO follows a power law distribution.

Brain Storm Optimization (BSO) algorithm is a swarm intelligence algorithm inspired by human being’s behavior of brainstorming. The performance of BSO is maintained by the creating process of ideas, but when it cannot find a better solution for some successive iterations, the result will be so inefficient that the population might be trapped into local optima. In this paper, we propose an improved BSO algorithm with differential evolution strategy and new step size method. Firstly, differential evolution strategy is incorporated into the creating operator of ideas to allow BSO jump out of stagnation, owing to its strong searching ability. Secondly, we introduce a new step size control method that can better balance exploration and exploitation at different searching generations. Finally, the proposed algorithm is first tested on 14 benchmark functions of CEC 2005 and then is applied to train artificial neural networks. Comparative experimental results illustrate that the proposed algorithm performs significantly better than the original BSO.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O(n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U-12,12 mutation operator are approximately twice those of BSOs with the U(-1,1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.

Brain storm optimization is a new swarm intelligence, which mimics the human brainstorming process. In this paper, a modified brain storm optimization is proposed based on uncertainty information. It adopts affinity propagation clustering instead of k-means clustering. Meanwhile, a creating operator combining the information of multiple clusters is introduced by borrowing the idea of cloud drops algorithm. The proposed brain storm optimization is characterized by mining and utilizing the uncertain information of candidate solutions with no need for the number of clusters. Finally, the modified brain storm optimization is applied to numerical optimization. The simulation results show that the proposed algorithm has better optimization results and higher rate of success than the original version.

In this paper, a hybrid approach which combines brain storm optimization algorithm (BSO) with sine-cosine search mechanism is proposed. BSO is a newly proposed meta-heuristic algorithm which takes inspiration from the brainstorming behavior. It can obtain good results in solving some optimization problems. However, its performance is still raw, especially in dealing with complex and multi-modal problems. Thus, in this paper, we introduce a powerful search mechanism taken from sine cosine algorithm (SCA) which has considerable capacity to enhance the search ability of BSO. The proposed algorithm is tested by CEC’17 benchmark functions and the result indicates that this hybridization has considerable merit.

Brain Storm Optimization (BSO), which is an effective swarm intelligence method inspired by the human brainstorming process, has shown promising results in solving static optimization problems. However, The search spaces of many real-world problems change over time, in which the original BSO and its variants are not able to cope with. This paper extends BSO as an adaptive multi-population based algorithm, i.e., mBSO, to solve dynamic optimization problems (DOPs). Firstly, a modified BSO, which uses new update mechanisms independent from the maximum number of iterations and objective space grouping method, is proposed. Then, the modified BSO is embedded in a multi-population framework. Several mechanisms such as convergence detection, exclusion, and re-diversification are employed to address the challenging issues of DOPs. The moving peaks benchmark (MPB) is used to evaluate the performance of mBSO along with comparison with other state-of-the-art methods. The outcome indicates the efficiency of the proposed mBSO in locating optima and tracking them after environmental changes.

A reinforcement learning brain storm optimization algorithm (BSO) with learning mechanism

With the development of computational intelligence, many intelligence algorithms have attracted the attention of the scientific community, and a great deal of work on optimizing these algorithms is in full swing. One of the optimization techniques that we focus on is the hybridization of algorithms. Brain storm optimization algorithm (BSO), belonging to the swarm intelligence algorithms, is proposed by taking inspiration of human brain storming behavior. Meanwhile, the covariance matrix adaptive evolutionary strategy algorithm (CMA-ES) which belongs to the field of evolutionary strategy is also concerned. The purpose of this paper is to combine the search capability of BSO with the search efficiency of CMA-ES to achieve a relatively balanced and effective solution.

This paper proposes total optimization of energy networks in a smart city (SC) by cooperative coevolution using global-best brain storm optimization (CCGBSO). The smart city problem is one of mixed integer nonlinear programming (MINLP) problems. Therefore, various evolutionary computation methods such as differential evolutionary particle swarm optimization (DEEPSO), Brain Storm Optimization (BSO), Modified BSO (MBSO), Global-best BSO (GBSO) have been applied to the problem. However, quality of solution is still required to be improved. Cooperative Cooperation has a possibility to improve solution quality of large scale optimization problems such as the SC problem and this paper proposes a new cooperative coevolution algorithm, CCGBSO. The results of the proposed CCGBSO based method are verified to be the most improved comparing with those of the conventional DEEPSO, BSO, MBSO, and GBSO based methods.

Scheduling is to determine when and who to process the task in order to minimize the makespan, the cost, and the tardiness/earliness of jobs, etc. Evolutionary algorithms (EAs) are very promising approaches for the scheduling problems due to its dynamic characteristics, multiple contradicting objectives and highly nonlinear constraints. Brain storm optimization (BSO) algorithm and its variations are new emerging evolutionary algorithms. In this chapter, our focus will be on BSOs for the flexible job shop scheduling problems (FJSP). First, FJSP will be formulated as a combinatorial optimization problem. Second, approaches for FJSP will be summarized briefly. Third, BSOs will be introduced and the key issues in the application of BSOs for FJSP will be emphasized. Fourth, four BSOs will be developed to solve FJSP and the details designed for FJSP will be illustrated. Their strength and weakness will be discussed as well. Finally, a group of experiments will be conducted to compare the four BSO algorithms. The results will be analyzed statistically. Finally, a conclusion will be summarized.