Multimodal Function Optimization Problems Research Articles

OPTIMISASI FUNGSI RASTRIGIN MENGGUNAKAN FLOWER POLLINATION ALGORITHM

The Rastrigin function is a multimodal function. It is difficult to find a global minimum of the function because it has many local minimums. So, we need an effective and efficient algorithm to find a solution to the global minimum of the function without being trapped by the local minimum. The flower pollination algorithm is a metaheuristic algorithm, it is expected to be capable of solving multimodal function optimization problems. In this study flower pollination algorithm is used to find the global minimum of the Rastrigin function of two variables with MATLAB. The Rastrigin function of two variables is used as objective function for the flower pollination algorithm. The parameters are divided into three configurations based on the difference amount of pollen gamets, the probability switch, and the search domain, with two different iterations 300 and 1500. In order, to get the best results each configuration is running for 10 times. The best results from the flower pollination algorithm are obtained from the first configuration and 1500 iterations

A Metaheuristic Algorithm for Coverage Enhancement of Wireless Sensor Networks

When wireless sensors are randomly deployed in natural environments such as ecological monitoring, military monitoring, and disaster monitoring, the initial position of sensors is generally formed through deployment methods such as air-drop, and then, the second deployment is carried out through the existing optimization methods, but these methods will still lead to serious coverage holes. In order to solve this problem, this paper proposes an algorithm to improve the coverage rate for wireless sensor networks based on an improved metaheuristic algorithm. The sensor deployment coverage model was firstly established, and the sensor network coverage problem was transformed into a high-dimensional multimodal function optimization problem. Secondly, the global searching ability and searching range of the algorithm are enhanced by the reverse expansion of the initial populations. Finally, the firefly principle is introduced to reduce the local binding force of sparrows and avoid the local optimization problem of the population in the search process. The experimental results showed that compared with ALO, GWO, BES, RK, and SSA algorithms, the EFSSA algorithm is better than other algorithms in benchmark function tests, especially in the test of high-dimensional multimodal function. In the tests of different monitoring ranges and number of nodes, the coverage of EFSSA algorithm is higher than other algorithms. The result can tell that EFSSA algorithm can effectively enhance the coverage of sensor deployment.

Performance evaluation of the particle swarm optimization for clustering based on different parameter selection

Particle Swamp Optimization (PSO) is an effective method for solving a wide range of problems. However, the most existing PSO algorithms easily trap into local optima when solving complex multimodal function optimization problems. In this paper, we explain the importance of PSO algorithm’s general purposes to optimize strategy which has various parameters that decide its conduct and viability in advancing a given issue. This study gives a rundown of the best selections of parameters for different advancement situations which should enable the specialist to accomplish better outcomes with less exertion. In this paper, we define an important in the PSO algorithm, the parameters and how to apply this algorithm to different type of datasets online and offline. Repeat Consumption Matrices Dataset has been tested with PSO algorithm to define the number of clusters using selection of parameters. The results are then having been compared with the Genetic Algorithm (GA) where the algorithms have been tested based on the number of cluster and DB index for each of the data. Based on the results, it is shown that the PSO algorithm gives good and efficient results compared to GA algorithm. The output of the research is a PSO-based clustering algorithm that can be used in data mining by providing accurate and robust results in clustering, which can be realized in web search engines and automatic doc-ument organization.

Research and implementation of parallel artificial bee colony algorithm based on ternary optical computer

The artificial bee colony (ABC) algorithm is a widely used algorithm in the field of function optimization problems. The traditional ABC algorithm has long search time, slow convergence speed and easy to fall into local optimum at the end of the search. In this paper, the design scheme and method of implementing parallel ABC algorithm are studied, which makes use of the characteristics of many data bits and easy expansion of data bits of the ternary optical computer (TOC). First, by analysing the traditional ABC algorithm, we can find the parallel parts and parallel design. Then the detailed algorithm implementation flow is given and the clock cycle of the algorithm is analysed. Finally, the correctness of the parallel scheme is verified by experiments. Compared with the ABC algorithm and parallel ABC algorithms based on computer (PABC), the ABC algorithm based on TOC (TOC-PABC) effectively shortens the search time, improves the optimization performance of complex multimodal function optimization problems and obtains a higher speedup.

Kinematic calibration method for a two-segment hydraulic leg based on an improved whale swarm algorithm

Abstract Legged robots have become a hot topic in robotics owing to their superior mobility. In this study, a two-segment hydraulic robotic leg with the kinematic model is first presented. In this leg, the tracking accuracy of the joint angle depends on the kinematic model precision. However, this model is highly nonlinear and it is very difficult to obtain accurate parameters by means of traditional techniques. To overcome this problem, it is converted into a constrained multimodal function optimization problem; thereafter, a novel kinematic calibration method based on an improved whale swarm algorithm (IWSA) is proposed. Several modification strategies are implemented to improve the searching ability and robustness of the IWSA. Moreover, an effective constraint-handling mechanism is designed for the IWSA. To evaluate the IWSA performance, we compare the IWSA with the WSA and other algorithms on several benchmark functions and calibration experiments. The results indicate the superiority of the IWSA over its competitors. The further case study shows that the tracking accuracy is significantly improved after calibration, which confirms the application effectiveness of the proposed IWSA-based calibration method.

Clinical and genetic determinants of serum brain-derived neurotrophic factor (BDNF) levels in psychotic patients: A longitudinal prospective study

Legged robots have become a hot topic in robotics owing to their superior mobility. In this study, a two-segment hydraulic robotic leg with the kinematic model is first presented. In this leg, the tracking accuracy of the joint angle depends on the kinematic model precision. However, this model is highly nonlinear and it is very difficult to obtain accurate parameters by means of traditional techniques. To overcome this problem, it is converted into a constrained multimodal function optimization problem; thereafter, a novel kinematic calibration method based on an improved whale swarm algorithm (IWSA) is proposed. Several modification strategies are implemented to improve the searching ability and robustness of the IWSA. Moreover, an effective constraint-handling mechanism is designed for the IWSA. To evaluate the IWSA performance, we compare the IWSA with the WSA and other algorithms on several benchmark functions and calibration experiments. The results indicate the superiority of the IWSA over its competitors. The further case study shows that the tracking accuracy is significantly improved after calibration, which confirms the application effectiveness of the proposed IWSA-based calibration method.

PSO-based stability analysis of unreinforced and reinforced soil slopes using non-circular slip surface

Slope stability analysis is one of the most intricate problems of geotechnical engineering because it is mathematically difficult to search the critical slip surface of earth slopes with complex strata owing to the involved multimodal function optimization problem. At present, a minimum factor of safety for a non-circular slip surface in a uniform and unreinforced earth slope can be calculated using several methods; however, for a reinforced soil slope, it cannot be easily calculated because of the additional effect of the reinforcement. One efficient method to search the critical slip surface is particle swarm optimization (PSO). PSO can solve complex non-differentiable problems, and its increasing ease of use has facilitated its application to multimodal function optimization problems in a variety of fields. However, the recommended PSO parameters to calculate the safety factors of unreinforced and reinforced soil slopes, namely the inertia and local and global best solution weighting coefficients, have not been sufficiently investigated. Moreover, the computational efficiency of PSO for safety factor calculation, including computational accuracy and time, has not been clarified. To calculate the unreinforced and reinforced soil slope safety factors, this study considers force and moment equilibriums, including the tensile force of the reinforcement. Firstly, the computational efficiency of the calculation process by PSO was shown to increase the maximum number of slip surface nodes in the calculation of the safety factor. Then, an analysis was carried out to investigate the safety factor sensitivity to the PSO parameters. Based on this analysis, appropriate PSO parameters for the safety factor calculation of unreinforced and reinforced soil slopes were proposed.

Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization.

This paper presents a variant of multiscale quantum harmonic oscillator algorithm for multimodal optimization named MQHOA-MMO. MQHOA-MMO has only two main iterative processes: quantum harmonic oscillator process and multiscale process. In the two iterations, MQHOA-MMO only does one thing: sampling according to the wave function at different scales. A set of benchmark test functions including some challenging functions are used to test the performance of MQHOA-MMO. Experimental results demonstrate good performance of MQHOA-MMO in solving multimodal function optimization problems. For the 12 test functions, all of the global peaks can be found without being trapped in a local optimum, and MQHOA-MMO converges within 10 iterations.

Multimodal function optimizations with multiple maximums and multiple minimums using an improved PSO algorithm

In this paper, a multimodal function optimization problem consisting of multiple maximums and multiple minimums is solved using an improved particle swarm optimization (PSO) algorithm. In the proposed scheme, the original population needs to be randomly divided into two main groups in the first stage. One group is to tackle the maximum optimization of the multimodal function and the other then focuses on the function minimum optimization. In the second stage, each group is split up into several subgroups in order to seek for function optimums simultaneously. There is no relation among subgroups and each subgroup can individually seek for one of function optimums. To achieve that, it is necessary to enroll the best particle information of each subgroup. It means that the proposed structure contains a number of best particles, not a single global best particle. The third stage is to modify the velocity updating formula of the algorithm where the global best particle is simply replaced by the best particle of each subgroup. Under the proposed scheme, multiple maxima and minima of the multimodal function can probably be solved separately and synchronously. Finally, many different kinds of multimodal function problems are illustrated to certify the applicability of the presented method, including one maximum and one minimum, two maximums and two minimums, multiple maximums and multiple minimums, and a complex engineering optimization problem with inequality conditions.

Multimodal optimization problem in contamination source determination of water supply networks

Abstract It makes great economic losses and bad social influence for our country about some accidental drinking water contamination and vicious attacks to water distribution networks. In terms of solving the problems of drinking water contamination caused by accidental contaminant event in water supply network, used the techniques just like sensor network which could determinate the source location to isolate the contaminated area and minimized its hazards. Previous studies have shown that the contamination source determination problem model can be utilized to convert the contamination source determination problem to an unimodal function optimization problem. However, we notice that it is a multimodal function optimization problem in essence and the number of its solution has non-uniqueness feature. In this paper, we first modified the problem model with formulate the threshold value based on the previous works and proposed the niching genetic algorithm calculate multiple contamination sources, and provide the possibility for screening the true contamination source. Furthermore, this paper applies different distribution networks verify the validity after the threshold formulation as well as the effectiveness of algorithm from various aspects.

Application of Self-adaptive Immune Differential Algorithm in Multimodal Function Optimization Problem

Application of Self-adaptive Immune Differential Algorithm in Multimodal Function Optimization Problem

A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems

In this paper, a modified particle swarm optimization (PSO) algorithm is developed for solving multimodal function optimization problems. The difference between the proposed method and the general PSO is to split up the original single population into several subpopulations according to the order of particles. The best particle within each subpopulation is recorded and then applied into the velocity updating formula to replace the original global best particle in the whole population. To update all particles in each subpopulation, the modified velocity formula is utilized. Based on the idea of multiple subpopulations, for the multimodal function optimization the several optima including the global and local solutions may probably be found by these best particles separately. To show the efficiency of the proposed method, two kinds of function optimizations are provided, including a single modal function optimization and a complex multimodal function optimization. Simulation results will demonstrate the convergence behavior of particles by the number of iterations, and the global and local system solutions are solved by these best particles of subpopulations.

Seismic stability and displacement analyses of earth slopes using non-circular slip surface

The seismic stability and deformability of earth slopes are conventionally evaluated by simple, practical methods. Because a multimodal function optimization problem makes it mathematically difficult to search large critical slip surface of earth slopes with complex strata, stability analysis is one of the classical problems of geotechnical engineering. One option is to evaluate the seismic deformability of earth slopes using permanent seismic displacements via Newmark׳s sliding block analysis in the current seismic design. The advantage of this method is that it is useful in practice and is less time consuming in terms of calculations. However, the calculations require that the critical slip is assumed either linear or circular. This paper proposes two methods for computing safety factors and permanent seismic displacements of earth slopes using an efficient non-circular slip surface search algorithm based on the force equilibrium given by the Spencer method. The validity of these proposed methods is verified by applying them to models with a known safety factor or theoretically calculated permanent seismic displacement and the results obtained compared. Comparative analyses are also conducted in order to demonstrate their efficacy in terms of computation precision and convergence performance. Further, they are utilized to calculate the permanent seismic displacement of a practical earth slope model subjected to seismic motions in both the horizontal and vertical directions. The results obtained indicate that they can calculate the safety factor of earth slopes using a smaller number of simulations than conventional methods and that they can also be applied to calculate the permanent seismic displacement of earth slopes. The results also indicate that the permanent seismic displacement calculated is an important index that can be used to quantitatively evaluate the seismic performance of earth slopes.

Improved ant colony algorithm for parameter estimation on the BISQ model

In this paper, based on the Biot/Squirt model including the Biot-flow and squirt-flow mechanism simultaneously, we estimated reservoir parameters using the improved ant colony algorithm, that is, the niche ant colony algorithm (NACA) based on fitness sharing principle. We used the improved ACA in a multi-modal function optimization problem and verified the effectiveness of the NACA. We then estimated reservoir parameters, such as porosity and permeability using the improved ACA based on the unsaturated porous media Biot/Squirt model. The numerical results indicate that the relative error of the inversion of a single parameter can be maintained at less than 0.08%, similar to that of the inversion of two parameters (porosity and saturation). In addition, the effect of the inversion of three parameters (porosity, solid density and fluid density) was found to be slightly weak, but the relative error can still be maintained at less than 4%. Moreover, we compared the inversion results with those obtained using the niche genetic algorithm. The comparison shows that the former has higher precision over the latter. The results of the numerical simulation demonstrate that the proposed approach is an effective convergent optimization method.

An Improved Particle Swarm Optimization Based on Biological Chemotaxis

Standard particle swarm algorithm for function optimization prone to local optimal and premature convergence, and thus the biological chemotaxis principle introduction to particle swarm optimization algorithm, this paper proposed an improved algorithm to maintain the diversity of the populationand the choice of key parameters. Simulation results show that, compared with the traditional particle swarm optimization algorithm, an improved particle swarm algorithm for dealing with complex multimodal function optimization problem can be significantly improved algorithm for global optimization.

An adaptive particle swarm optimization method based on clustering

Particle swarm optimization (PSO) is an effective method for solving a wide range of problems. However, the most existing PSO algorithms easily trap into local optima when solving complex multimodal function optimization problems. This paper presents a variation, called adaptive PSO based on clustering (APSO-C), by considering the population topology and individual behavior control together to balance local and global search in an optimization process. APSO-C has two steps. First, via a K-means clustering operation, it divides the swarm dynamically in the whole process to construct variable subpopulation clusters and after that adopts a ring neighborhood topology for information sharing among these clusters. Then, an adaption mechanism is proposed to adjust the inertia weight of all individuals based on the evaluation results of the states of clusters and the swarm, thereby giving the individual suitable search power. The experimental results of fourteen benchmark functions show that APSO-C has better performance in the terms of convergence speed, solution accuracy and algorithm reliability than several other PSO algorithms.

Artificial fish swarm parallel algorithm based on multi-core cluster

Concerning the problems of low accuracy,limitations of stagnation and slow convergence speed in the later evolution process of Artificial Fish Swarm Algorithm(AFSA),a Parallel Dynamic weigh Niches Artificial Fish Swarm(PDNAFS) algorithm based on multi-core cluster was proposed. Firstly,the advantages and disadvantages of AFSA were analyzed,and dynamic weighting factor strategy and niche mechanism were adopted,hence a new Dynamic weigh Niches Artificial Fish Swarm(DN-AFS) algorithm was put forward. Then parallel design and analysis of DN-AFS algorithm based on parallel programming model(MPI + OpenMP) were introduced. Finally,the simulation experiments on multi-core cluster environment were given. The experimental results show that PDN-AFS can effectively improve the convergence speed and optimization performance of the complex multimodal function optimization problem,and achieve high speed ratio.

A Review of Niching Genetic Algorithms for Multimodal Function Optimization

In this paper, a comprehensive review of approaches to solve multimodal function optimization problems via genetic niching algorithms is provided. These algorithms are presented according to their space---time classification. Methods based on fitness sharing and crowding methods are described in detail as they are the most frequently used.

Multi-model function optimization based on immune clonal optimization with self-adaptive population size

In order to balance the impact of population size on the efficiency and effectiveness of the search algorithm,an immune clonal algorithm with self-adaptive population size for multi-modal function optimization problem was proposed.The change rules,magnitude and the detailed realization of population size were given.The change of self-adaptive population size with the evolutionary process was achieved.In addition,in terms of multi-modal function optimization characteristics,Baldwin learning was used as a local search strategy to enhance the search ability for the optimal solution.The experimental results show that the algorithm has better optimization ability,faster convergence and is more stable than existing algorithms.

Glowworm Swarm Optimization (GSO) Algorithm for Optimization Problems: A State-of-the-Art Review

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.