A Scalable MapReduce-enabled Glowworm Swarm Optimization Approach for High Dimensional Multimodal Functions

Glowworm Swarm Optimization (GSO) algorithm is a derivative-free, meta-heuristic algorithm and mimicking the glow behavior of glowworms which can efficiently capture all the maximum multimodal function. Nevertheless, there are several weaknesses to locate the global optimum solution for instance low calculation accuracy, simply falling into the local optimum, convergence rate of success and slow speed to converge. This paper reviews the exposition of a new method of swarm intelligence in solving optimization problems using GSO. Recently the GSO algorithm was used simultaneously to find solutions of multimodal function optimization problem in various fields in today industry such as science, engineering, network and robotic. From the paper review, we could conclude that the basic GSO algorithm, GSO with modification or improvement and GSO with hybridization are considered by previous researchers in order to solve the optimization problem. However, based on the literature review, many researchers applied basic GSO algorithm in their research rather than others.

This chapter will deal with the problem of searching higher dimensional spaces using glowworm swarm optimization (GSO), a novel swarm intelligence algorithm, which was recently proposed for simultaneous capture of multiple optima of multimodal functions. Tests are performed on a set of three benchmark functions and the average peak-capture fraction is used as an index to analyze GSO’s performance as a function of dimension number. Results reported from tests conducted up to a maximum of eight dimensions show the efficacy of GSO in capturing multiple peaks in high dimensions. With an ability to search for local peaks of a function (which is the measure of fitness) in high dimensions, GSO can be applied to identification of multiple data clusters, satisfying some measure of fitness defined on the data, in high dimensional databases.

The glowworm swarm optimisation (GSO) algorithm is a novel algorithm with the simultaneous computation of multiple optima of multimodal functions. Data-clustering techniques are classification algorithms that have a wide range of applications. Since K-means algorithm is easy to fall into the local optimum by the selection of initial clustering centre, GSO algorithm is used for the telecom customers clustering. The customer consumption data is extracted by means of the recency frequency monetary (RFM) model and the standardised data is clustered automatically using the GSO algorithm's synchronous optimisation ability. In the clustering optimisation algorithm, adaptive step size is used instead of the original fixed step size to avoid local optimisation of the algorithm and obtain higher accuracy. Compared with K-means clustering algorithm, GSO approach can automatically generate the number of clusters and use RFM model to reduce effectively the size of the data processing. The results of the experiments demonstrate that the GSO-based clustering technique is a promising technique for the data clustering problems.

Concerning the low accuracy and convergence of Glowworm Swarm Optimization(GSO) algorithm when resolving high-dimensional functions,an Improved GSO(IGSO) algorithm with mutation operator and foraging behavior was proposed.Using mutation operator to guide the evolution of glow worms which cannot find their peers in the visible range,the proposed algorithm could enhance the utilization of outliers and improve the overall efficiency.The operator with foraging behavior substantially increased the accuracy and convergence speed by searching accurately in the global optimal field captured by the algorithm.In the meantime,the operator could effectively avoid local optimum and enlarge the global search range of the algorithm in the late stage.The experimental results indicate that IGSO has better ability of global optimization and higher success ratio than GSO according to the tests of eight Benchmarks.

Under local shading conditions outdoors, the output P-V curve of photovoltaic arrays exhibits multiple peaks, which makes the traditional maximum power point algorithms fail to track its global peak. Even though the published swarm intelligence maximum power point tracking algorithms can get the global peak, which removes the drawbacks of the traditional algorithms, the shortages of long optimization time, easily local peak capture, as well as large steady oscillation, restrict their application. For this reason, an MPPT algorithm named as glowworm swarm optimization and variable-step perturbation & observation(GSO-VP&O) is proposed. The proposed algorithm is realized with two stages of searching known as global searching and local searching. In the global searching, the adaptive adjustment ability of glowworm swarm optimization(GSO) and the excellent global convergence of the multimodal function can mitigate the risk of local optima. In the local searching, the variable-step perturbation & observation is employed to quickly arrive at the global maximum power point and reduce the ripple of steady output. To validate the proposal, the platforms for the algorithms are constructed and simulated. Simulation results show that compared with the other swarm intelligent algorithms, the proposed GSO-VP&O can get a shorter optimization time and faster tracking speed as well as the minimum ripple in a steady state.

The hyperspherical acceleration effect particle swarm optimizer

This study presents an improved version of the Driving Training-Based Optimization (DTBO) algorithm, the Improved Driving Training-Based Optimization (IDTBO). The work addresses fundamental issues in selecting drivers and learners for the conventional DTBO, which substantially impact the algorithm's accuracy and convergence speed. Two significant improvements are proposed: including the crowding distance technique for more diverse driver and learner selection and incorporating the Levy Flight distribution for better exploration and local optima avoidance. The IDTBO's performance is evaluated using twelve benchmark functions, including unimodal and high-dimensional multimodal optimization functions. The results indicate that IDTBO performs exceptionally well, with more extraordinary exploitation ability on unimodal functions and consistent achievement of the global optima. The proposed IDTBO demonstrated exceptional exploration capabilities on high-dimensional multimodal functions and performed competitively with other algorithms in the literature. From six functions, the IDTBO obtained zero optimal values. Again, the rate of convergence analysis demonstrates that IDTBO finds optimal solutions in fewer iterations, demonstrating its capacity to balance exploration and exploitation. To assess the strength of the IDTBO in solving real-world problems, the improved DTBO is further tested on two practical benchmark engineering problems. The IDTBO again produced a competitive performance against other algorithms in the literature. The study shows that IDTBO is a valuable metaheuristic algorithm that can tackle various real-world optimization problems.

A novel genetic algorithm (GA) using minimal representation size cluster (MRSC) analysis is designed and implemented for solving multimodal function optimization problems. The problem of multimodal function optimization is framed within a hypothesize-and-test paradigm using minimal representation size (minimal complexity) for species formation and a GA. A multiple-population GA is developed to identify different species. The number of populations, thus the number of different species, is determined by the minimal representation size criterion. Therefore, the proposed algorithm reveals the unknown structure of the multimodal function when a priori knowledge about the function is unknown. The effectiveness of the algorithm is demonstrated on a number of multimodal test functions. The proposed scheme results in a highly parallel algorithm for finding multiple local minima. In this paper, a path-planning algorithm is also developed based on the MRSC_GA algorithm. The algorithm utilizes MRSC_GA for planning paths for mobile robots, piano-mover problems, and N-link manipulators. The MRSC_GA is used for generating multipaths to provide alternative solutions to the path-planning problem. The generation of alternative solutions is especially important for planning paths in dynamic environments. A novel iterative multiresolution path representation is used as a basis for the GA coding. The effectiveness of the algorithm is demonstrated on a number of two-dimensional path-planning problems.

Particle Swarm Optimization (PSO) algorithm has recently gained more attention in the global optimization research due to its simplicity and global search ability. This paper proposes a hybrid of PSO and Generalized Generation Gap model with Parent- Centric Recombination operator (G3PCX) [25], a well-known real-coded genetic algorithm. The proposed hybrid algorithm, namely PSPG, combines fast convergence and rotational invariance of G3PCX as well as global search ability of PSO. The performance of PSPG algorithm is evaluated using 8 widely-used nonlinear benchmark functions of 30 and 200 decision variables having different properties. The experiments study the effects of its new probability parameter Px and swarm size for optimizing those functions. The results are analyzed and compared with those from the Standard PSO [14] and G3PCX algorithms. The proposed PSPG with Px = 0.10 and 0.15 can outperform both algorithms with a statistical significance for most functions. In addition, the PSPG is not much sensitive to its swarm size as most PSO algorithms are. The best swarm sizes are 40 and 50 for unimodal and multimodal functions, respectively, of 30 decision variables.

This article’s innovation and novelty are introducing a new metaheuristic method called mother optimization algorithm (MOA) that mimics the human interaction between a mother and her children. The real inspiration of MOA is to simulate the mother’s care of children in three phases education, advice, and upbringing. The mathematical model of MOA used in the search process and exploration is presented. The performance of MOA is assessed on a set of 52 benchmark functions, including unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, and the CEC 2017 test suite. The findings of optimizing unimodal functions indicate MOA’s high ability in local search and exploitation. The findings of optimization of high-dimensional multimodal functions indicate the high ability of MOA in global search and exploration. The findings of optimization of fixed-dimension multi-model functions and the CEC 2017 test suite show that MOA with a high ability to balance exploration and exploitation effectively supports the search process and can generate appropriate solutions for optimization problems. The outcomes quality obtained from MOA has been compared with the performance of 12 often-used metaheuristic algorithms. Upon analysis and comparison of the simulation results, it was found that the proposed MOA outperforms competing algorithms with superior and significantly more competitive performance. Precisely, the proposed MOA delivers better results in most objective functions. Furthermore, the application of MOA on four engineering design problems demonstrates the efficacy of the proposed approach in solving real-world optimization problems. The findings of the statistical analysis from the Wilcoxon signed-rank test show that MOA has a significant statistical superiority compared to the twelve well-known metaheuristic algorithms in managing the optimization problems studied in this paper.

In order to overcome the basic glowworm swarm optimization (GSO) algorithm in the high dimension space function optimization effect is poor defects. This paper, we introduce the idea of the traditional complex method, with the complex method the worst part of the glowworm guidance for reflection be good glowworm swarm, so as to continuously make the worst glowworm swarm become the better glowworm swarm. Finally, an improved artificial glowworm algorithm solves high dimension space of function optimization effect improvement. And through the and basic glowworm swarm algorithm, artificial fish algorithm (AFSA) and particle swarm optimization (PSO) to eight test function optimization results are compared. The show that the efficiency of the method.

Features of several well-known global and local optimization methods were discussed and their robustness and efficiency were tested on several artificial test functions in Matlab environment. The tested local methods were the interior-point, the quasi-Newton method, Nelder–Mead simplex, the pattern search, the NEWUOA and the BOBYQA methods. The global methods were the genetic algorithm (GA), the simulated annealing (SA), the particle swarm optimization (PSO), and the covariance matrix adaptation evolutionary strategy (CMA-ES) methods (see subsections 2.2 and 2.3 for their details). Furthermore, a novel global optimization method, called FOCusing robusT Optimization with Uncertainty-based Sampling (FOCTOPUS), which proved to be very efficient in the optimization of constrained and highly correlated parameters of combustion kinetic models, was also tested. The test functions were selected in such a way that they had a variety of features: uni-modal and multi-modal, differentiable and non-differentiable, separable and non-separable, low dimensional and high dimensional. The following test functions were used: the 20D Alpine function, the 4D Ackley function, the Cross-in-tray 2D function, the Hartmann-6D function, the Holder table 2D function, the 5D Rastrigin function, the 5D Rosenbrock function, the 4D modified Rosenbrock function, the 20D Zakharov function and a typical 2D multi-modal function. The general conclusion here is that, the global methods performed well on the multi-modal and high-dimensional test functions while the local methods were superior in the case of low-dimensional and uni-modal test functions. For the highly multi-modal test functions, the GA was better than all the other methods. The FOCTOPUS method proved to be inferior to GA for most of the test functions, thus its application cannot be generally recommended.

This contribution deals with a new idea of how to create evolutionary algorithms by means of symbolic regression and Analytic Programming. The motivation was not only to tune some existing algorithms to their better performance, but also to find a new robust evolutionary algorithm. In this study operators of Differential Evolution (DE), SelfOrganizing Migrating Algortithm (SOMA), Hill Climbing (HC) and Simulated Annealing (SA) were used during a process of Analytic Programming. The results showed that AP was able to find successful as well as the original DE or SOMA. The cost function includes not only success in unimodal and multimodal benchmark function but also rules concerned to cost function evaluations. Results were tested on 16 benchmark functions in 2D, 20 D and 100 dimensional versions, i.e. 192 test, each was 100 times repeated and each of 100 repetitions has around 200 000 cost function evaluations. The results are presented in tabelar and graphic form.

This paper presents a new bio-inspired metaheuristic algorithm called Red Panda Optimization (RPO) that imitates the natural behaviors of red pandas in nature. The main design idea of RPO is derived from two characteristic natural behaviors of red pandas: (i) foraging strategy, and (ii) climbing trees to rest. The proposed RPO approach is mathematically modeled in two phases of exploration based on the simulation of red pandas’ foraging strategy and exploitation based on the simulation of red pandas’ movement in climbing trees. The main advantage of the proposed approach is that there is no control parameter in its mathematical modeling, and for this reason, it does not need a parameter adjustment process. The performance of RPO is evaluated on fifty-two standard benchmark functions including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types as well as CEC 2017 test suite. The optimization results obtained by the proposed RPO approach are compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that RPO, by maintaining the balance between exploration and exploitation, is effective in solving optimization problems and its performance is superior over competitor algorithms. Based on the analysis of the optimization results, RPO has provided more successful performance compared to the competitor algorithms in 100% of unimodal functions, 100% of high-dimensional multimodal functions, 100% of fixed-dimensional multimodal functions, and 86.2% of CEC 2017 test suite benchmark functions. Also, the statistical analysis of the Wilcoxon rank sum test shows that the superiority of RPO in the competition with the compared algorithms is significant from a statistical point of view. In addition, the results of implementing RPO on four engineering design problems confirms the ability of the proposed approach to handle real-world optimization applications.

The laws of gravity and mass interactions inspire the gravitational search algorithm (GSA), which nds optimal regions of complex search spaces through the interaction of individuals in a population of particles. Although GSA has proven effective in both science and engineering, it is still easy to suffer from premature convergence especially facing complex problems. In this paper, we pro- posed a new hybrid algorithm by integrating genetic algorithm (GA) and GSA (GA-GSA) to avoid premature convergence and to improve the search ability of GSA. In GA-GSA, crossover and mutation operators are introduced from GA to GSA for jumping out of the local optima. To demonstrate the search ability of the proposed GA-GSA, 23 complex benchmark test functions were employed, including unimodal and multimodal high-dimensional test functions as well as multimodal test functions with xed dimensions. Wilcoxon signed-rank tests were also utilized to execute statistical analysis of the results obtained by PSO, GSA, and GA-GSA. Experimental results demonstrated that the proposed algorithm is both efficient and effective.