High-dimensional Global Optimization Problems Research Articles

An enhanced sparrow search swarm optimizer via multi-strategies for high-dimensional optimization problems

With the development of science and technology, high-dimensional global optimization problems have become increasingly prevalent for scientific research and engineering, such as gene recognition, vehicle routing, job scheduling, and network topology. These problems are typically characterized by enormous and complex search spaces and numerous local minima, making it challenging to find the global optimal solution with limited computing resources. This paper introduces an enhanced sparrow search swarm optimizer (ESSSO) based on a bio-mimetic method. The ESSSO employs an adaptive sinusoidal walk strategy based on the von Mises distribution, a learning strategy utilizing roulette wheel selection, a two-stage evolution strategy, and a selection mutation strategy to address these issues. The proposed sinusoidal walk strategy, grounded in the von Mises distribution, supports a balanced evolutionary search. This mechanism disperses the individuals in a swarm in various directions based on a circular normal distribution. It then leads the search and adaptively adjusts their step sizes according to the size of the search domain during each generation of evolution. The learning strategy, based on roulette wheel selection, enhances the diversity of the population and improves the global search capability of the algorithm during the initial iterations. The two-stage evolution strategy involves a sine-learning mechanism based on the von Mises distribution and an adaptive mutation mechanism. The former is designed to boost the convergence speed of ESSSO, while the latter prevents ESSSO from getting trapped in a local optimum. Additionally, the selection mutation strategy further enhances convergence speed while maintaining population diversity. These strategies promote exploration in the early stages of evolution and exploitation in the later stages, enabling a well-balanced search for optimal solutions. We conducted comprehensive experiments two standard benchmark sets (i.e., CEC2010 and CEC2013), antenna array optimization, feature selection, and four engineering design problems. The results indicate that ESSSO outperforms ten comparison algorithms, especially in scenarios with smaller population sizes. This confirms its effectiveness in high-dimensional global optimization tasks and demonstrates that it can achieve better results with less computational resource consumption.

Hybrid Sine Cosine and Particle Swarm Optimization Algorithm for High-Dimensional Global Optimization Problem and Its Application

Particle Swarm Optimization (PSO) is facing more challenges in solving high-dimensional global optimization problems. In order to overcome this difficulty, this paper proposes a novel PSO variant of the hybrid Sine Cosine Algorithm (SCA) strategy, named Velocity Four Sine Cosine Particle Swarm Optimization (VFSCPSO). The introduction of the SCA strategy in the velocity formulation ensures that the global optimal solution is found accurately. It increases the flexibility of PSO. A series of experiments are conducted on the CEC2005 test suite with compositional algorithms, algorithmic variants, and good intelligent algorithms. The experimental results show that the algorithm effectively improves the overall performance of compositional algorithms; the Friedman test proves that the algorithm has good competitiveness. The algorithm also performs better in PID parameter tuning. Therefore, the VFSCPSO is able to solve the high-dimensional global optimization problems in a better way.

An efficient manta ray foraging optimization algorithm with individual information interaction and fractional derivative mutation for solving complex function extremum and engineering design problems

The manta ray foraging optimization algorithm (MRFO) is a recently proposed meta-heuristic algorithm that mimics the foraging process of manta rays. It has yielded good outcomes in solving some optimization problems because its mechanism is clear, no additional parameters need to be set, and the balance between global and local search is good. Nonetheless, while dealing with high-dimensional global optimization and complex engineering optimization problems, there are also issues such as premature convergence, low optimization-seeking accuracy, or unstable solutions. To this end, this article proposes an efficient manta ray foraging optimization algorithm (NIFMRFO) by incorporating individual information interaction and fractional derivative mutation. First, to prevent premature convergence of the algorithm, a nonlinear cosine adjustment parameter is presented, which is intended to make the demand relationship between global exploration and local development more reasonable. Then, an information interaction strategy among random individuals is employed to expedite the rate at which the algorithm converges. Finally, a fractional derivative mutation strategy is utilized to continually enhance individuals’ quality in each iteration, which not only increases the population diversity but also helps to improve the precision and stability of the search results. Theoretical analysis indicates that the improved NIFMRFO algorithm and basic MRFO algorithm have the same time complexity. In simulation experiments, the CEC2017 suite is used to conduct comparison tests with six superior-performance representative comparison algorithms in several dimensions. In terms of the optimization-seeking accuracy, convergence curve, violin plot, and Friedman average ranking, the analysis of these graphs and data shows that the NIFMRFO algorithm’s ameliorated strategy improves superiority-seeking power, convergence speed, and steadiness. Meanwhile, the Wilcoxon rank-sum test result illustrates significant differences between NIFMRFO and other compared algorithms. Finally, these algorithms are utilized to tackle seven realistic engineering design optimization problems. The result makes it clear that NIFMRFO is distinctly superior to the other six algorithms, showing that its solving ability is superior and has broad application prospects.

Enhanced crow search algorithm with multi-stage search integration for global optimization problems.

Crow search algorithm (CSA), as a new swarm intelligence algorithm that simulates the crows' behaviors of hiding and tracking food in nature, performs well in solving many optimization problems. However, while handling complex and high-dimensional global optimization problems, CSA is apt to fall into evolutionary stagnation and has slow convergence speed, low accuracy, and weak robustness. This is mainly because it only utilizes a single search stage, where position updating relies on random following among individuals or arbitrary flight of individuals. To address these deficiencies, a CSA with multi-stage search integration (MSCSA) is presented. Chaos and multiple opposition-based learning techniques are first introduced to improve original population quality and ergodicity. The free foraging stage based on normal random distribution and Lévy flight is designed to conduct local search for enhancing the solution accuracy. And the following stage using mixed guiding individuals is presented to perform global search for expanding the search space through tracing each other among individuals. Finally, the large-scale migration stage based on the best individual and mixed guiding individuals concentrates on increasing the population diversity and helping the population jump out of local optima by moving the population to a promising area. All of these strategies form multi-level and multi-granularity balances between global exploration and local exploitation throughout the evolution. The proposed MSCSA is compared with a range of other algorithms, including original CSA, three outstanding variants of CSA, two classical meta-heuristics, and six state-of-the-art meta-heuristics covering different categories. The experiments are conducted based on the complex and high-dimensional benchmark functions CEC 2017 and CEC 2010, respectively. The experimental and statistical results demonstrate that MSCSA is competitive for tackling large-scale complicated problems, and is significantly superior to the competitors.

Opposition-based learning equilibrium optimizer with Levy flight and evolutionary population dynamics for high-dimensional global optimization problems

The equilibrium optimizer (EO) is a recently proposed physics-based metaheuristic algorithm inspired by the dynamic mass balance on a control volume. However, EO may encounter local convergence and low accuracy when solving high-dimensional optimization problems. In this work, we propose the opposition-based learning EO algorithm with the Levy flight and the evolutionary population dynamics for high-dimensional global optimization problems, called EOOBLE. Firstly, the opposition-based learning strategy is embedded into the initialization and updating process of EO. Then, the Levy flight strategy is used to improve the exploration ability of EO in the updating mechanism. Moreover, the strategy of evolutionary population dynamics is used in the proposed algorithm to avoid falling into the local optimum. The performance of the proposed algorithm is tested by 25 benchmark functions with dimensions from 100 to 5000, and is compared with 8 state-of-the-art metaheuristic algorithms. The statistical results indicate that the proposed algorithm has better convergence capacity than the compared algorithms. Besides, the proposed algorithm is also compared with different variants of EO, which outperforms the original EO and variants of EO with one or two operators. Therefore, the EOOBLE is a competitive algorithm in solving high-dimensional global optimization problems. Finally, a high-dimensional engineering design problem demonstrates the effectiveness of the EOOBLE.

A water cycle algorithm based on quadratic interpolation for high-dimensional global optimization problems

A water cycle algorithm based on quadratic interpolation for high-dimensional global optimization problems

A Dual Biogeography-Based Optimization Algorithm for Solving High-Dimensional Global Optimization Problems and Engineering Design Problems

Biogeography-based optimization (BBO) cannot effectively solve high-dimensional global optimization problems due to its single migration mechanism and random mutation operator. To overcome these limitations, this paper propose a dual BBO based on sine cosine algorithm (SCA) and dynamic hybrid mutation, named SCBBO. Firstly, the Latin hypercube sampling method is innovatively used to improve the initial population ergodicity. Secondly, a nonlinear transformation parameter and a inertia weight adjustment factor are designed into the position update formula of SCA to make SCBBO suitable for high dimensional environments. Then, a dynamic hybrid mutation operator is designed by combining Laplacian and Gaussian mutation, which helps the algorithm to escape from local optima and balance the exploration and exploitation. Finally, the dual learning strategy is integrated, so the convergence accuracy is further improved by generating dual individuals. Meanwhile, A sequence convergence model is established to prove the algorithm can converge to the global optimal solution with probability 1. Compared with other state-of-the-art evolutionary algorithms, SCBBO effectively improves the optimization accuracy and convergence speed for high-dimensional optimization problems. To further show the superiority of SCBBO, the performance is compared on 1000, 2000, 5000 and 10000 dimensions, respectively. The comparsions show that SCBBO’s optimization results on these dimensions are basically the same. SCBBO also applied to engineering design problems, and the simulation results demonstrate that the proposed method is also effective on constrained optimization problems.

Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems

This paper proposes a new meta-heuristic algorithm inspired by horses’ herding behavior for high-dimensional optimization problems. This method, called the Horse herd Optimization Algorithm (HOA), imitates the social performances of horses at different ages using six important features: grazing, hierarchy, sociability, imitation, defense mechanism and roam. The HOA algorithm is created based on these behaviors, which has not existed in the history of studies so far. A sensitivity analysis is also performed to obtain the best values of coefficients used in the algorithm. HOA has a very good performance in solving complex problems in high dimensions, due to the large number of control parameters based on the behavior of horses at different ages. The proposed algorithm is compared with popular nature-inspired optimization algorithms, including grasshopper optimization algorithm (GOA), sine cosine algorithm (SCA), multi-verse optimizer (MVO), moth–flame optimizer (MFO), dragonfly algorithm (DA), and grey​ wolf optimizer (GWO). Solving several high-dimensional benchmark functions (up to 10,000 dimensions) shows that the proposed algorithm is highly efficient for high-dimensional global optimization problems. The HOA algorithm also outperforms the mentioned popular optimization algorithms for the case of accuracy and efficiency with lowest computational cost and complexity.

A new improved whale optimization algorithm with joint search mechanisms for high-dimensional global optimization problems

Similar to other swarm-based algorithms, the recently developed whale optimization algorithm (WOA) has the problems of low accuracy and slow convergence. It is also easy to fall into local optimum. Moreover, WOA and its variants cannot perform well enough in solving high-dimensional optimization problems. This paper puts forward a new improved WOA with joint search mechanisms called JSWOA for solving the above disadvantages. First, the improved algorithm uses tent chaotic map to maintain the diversity of the initial population for global search. Second, a new adaptive inertia weight is given to improve the convergence accuracy and speed, together with jump out from local optimum. Finally, to enhance the quality and diversity of the whale population, as well as increase the probability of obtaining global optimal solution, opposition-based learning mechanism is used to update the individuals of the whale population continuously during each iteration process. The performance of the proposed JSWOA is tested by twenty-three benchmark functions of various types and dimensions. Then, the results are compared with the basic WOA, several variants of WOA and other swarm-based intelligent algorithms. The experimental results show that the proposed JSWOA algorithm with multi-mechanisms is superior to WOA and the other state-of-the-art algorithms in the competition, exhibiting remarkable advantages in the solution accuracy and convergence speed. It is also suitable for dealing with high-dimensional global optimization problems.

A whale optimization algorithm based on quadratic interpolation for high-dimensional global optimization problems

Whale Optimization Algorithm (WOA), as a new population-based optimization algorithm, performs well in solving optimization problems. However, when tackling high-dimensional global optimization problems, WOA tends to fall into local optimal solutions and has slow convergence rate and low solution accuracy. To address these problems, a whale optimization algorithm based on quadratic interpolation (QIWOA) is presented. On the one hand, a modified exploration process by introducing a new parameter is proposed to efficiently search the regions and deal with the premature convergence problem. On the other hand, quadratic interpolation around the best search agent helps QIWOA to improve the exploitation ability and the solution accuracy. Moreover, the algorithm tries to make a balance between exploitation and exploration. QIWOA is compared with several state-of-the-art algorithms on 30 high-dimensional benchmark functions with dimensions ranging from 100 to 2000. The experimental results show that QIWOA has faster convergence rate and higher solution accuracy than both WOA and other population-based algorithms. For functions with a flat or sharp bottom, QIWOA is difficult to find the global optimum, but it still performs best compared with other algorithms.

Controlled showering optimization algorithm: an intelligent tool for decision making in global optimization

In this study a novel population based meta-heuristic, called controlled showering optimization (CSO) algorithm, for global optimization of unconstrained problems is presented. Modern irrigation systems are equipped with smart tools manufactured and controlled by human intelligence. The proposed CSO algorithm is inspired from the functioning of water distribution tools to model search agents for carrying out the optimization process. CSO imitates the mechanism of projection of water units by sprinklers and the movements of their platforms to the desired locations for scheming optimum searching procedures. The proposed method has been tested using a number of diverse natured benchmark functions with low and high dimensions. Statistical analysis of the empirical data demonstrates that CSO offers solutions of better quality in comparison with several well-practiced algorithms like genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), artificial bee colony (ABC), covariance matrix adaptation evolution strategy (CMA-ES), teaching and learning based optimization (TLBO) and water cycle algorithm (WCA). The experiments on high-dimensional problems reveal that CSO algorithm also outperforms significantly a number of algorithms designed specifically for high dimensional global optimization problems.

Solving high-dimensional global optimization problems using an improved sine cosine algorithm

The sine cosine algorithm (SCA) is a relatively novel population-based optimization technique that has been proven competitive with other algorithms and it has received significant interest from researchers in different fields. However, similar to other population-based algorithms, SCA tends to be trapped in local optima and unbalanced exploitation. Additionally, to our limited knowledge, the present SCA and its variants have not been applied to the high-dimensional global optimization problems. This paper presents an improved version of the SCA (ISCA) for solving high-dimensional problems. A modified position-updating equation by introducing inertia weight is proposed to accelerate convergence and avoid falling into the local optima. In addition, to balance the exploration and exploitation of the SCA, we present a new nonlinear conversion parameter decreasing strategy based on the Gaussian function. The effectiveness of the proposed ISCA is evaluated using 24 benchmark high-dimensional (D = 30, 100, 500, 1000, and 5000) functions, large-scale global optimization problems from the IEEE CEC2010 competition, and several real-world engineering applications. The comparisons show that the proposed ISCA can better escape from local optima with faster convergence than both the traditional SCA and other population-based algorithms.

Self-adaptive fruit fly optimizer for global optimization

A self-adaptive fruit fly optimization (SFFO) algorithm is presented for solving high-dimensional global optimization problems. Unlike the conventional self-adaptive swarm intelligence algorithms that try to modify the values of control parameters during the run by taking the actual search process into account, the proposed SFFO algorithm self-adaptively adjusts its search along an appropriate decision variable from its previous experience in generating promising solutions. The presented self-adaptive method significantly improves the intensive search capability of the fruit fly optimization algorithm around promising areas that are problem and search process dependent. Extensive computational simulations and comparisons are performed based on a set of 40 benchmark functions from the literature. The computational results show that the proposed SFFO is a new state-of-the-art algorithm for global optimization.

Calibrating one-dimensional velocity model for downhole microseismic monitoring using station-pair differential arrival times based on the differential evolution method

For microseismic monitoring, in order to obtain accurate microseismic locations, a good estimation of the velocity model for the region covering the monitoring stations and microseismic sources is crucial. Perforation shots are generally used to estimate a velocity model suitable for microseismic location. However, the origin times of the perforation shots are generally not accurate. To mitigate the effect of inaccurate origin times of perforation shots on calibrating the velocity model, we propose to search for a velocity model fitting for station-pair differential arrival times instead of absolute arrival times from perforation shots. Another advantage of using station-pair differential arrival times is that waveform cross-correlation can be used to estimate more accurate differential times because of waveform similarity among stations for perforation shots. Due to high nonlinearity of the objective function for estimating one-dimensional velocity model, the differential evolution (DE) method for solving high-dimensional global optimization problems is utilized in the optimization. Compared to the grid-search method, the DE method is much more efficient. Synthetic tests based on a downhole microseismic monitoring system show the effectiveness of the proposed method to recover the velocity model. We also test our DE-based method by using perforation shots for a real microseismic monitoring project. Compared to the well sonic velocity model, station-pair differential arrival times are better fitted and perforation shots are also more accurately relocated with the calibrated velocity model.

Modeling and Optimizing Tensile Strength and Yield Point on a Steel Bar Using an Artificial Neural Network With Taguchi Particle Swarm Optimizer

A Taguchi particle swarm optimization (TPSO) with a three-layer feedforward artificial neural network (ANN) is used to model and optimize the chemical composition of a steel bar. The novel contribution of a TPSO is the use of a Taguchi method mechanism to exploit better solutions in the search space through iterations, the use of the conventional non-linear PSO to increase convergence speed, and the use of random movement for particle diversity. The exploration and exploitation capability of the TPSO were confirmed by performance comparisons with other PSO-based algorithms in solving high-dimensional global numerical optimization problems. Experiments in this paper showed that the TPSO provides higher computational efficiency and higher robustness when solving problems involving seven non-linear benchmark functions, including three unimodal functions, one multimodal functions, two rotated functions, and one shifted functions. The results for the computational experiments show that the TPSO outperforms other PSO-based algorithms reported in the literature. Finally, the results obtained by a TPSO-based ANN model of the chemical composition of the steel bar were consistent with the actual data. That is, the proposed TPSO with three-layer feedforward ANN can be used in practical applications.

Parallel differential evolution with self-adapting control parameters and generalized opposition-based learning for solving high-dimensional optimization problems

Solving high-dimensional global optimization problems is a time-consuming task because of the high complexity of the problems. To reduce the computational time for high-dimensional problems, this paper presents a parallel differential evolution (DE) based on Graphics Processing Units (GPUs). The proposed approach is called GOjDE, which employs self-adapting control parameters and generalized opposition-based learning (GOBL). The adapting parameters strategy is helpful to avoid manually adjusting the control parameters, and GOBL is beneficial for improving the quality of candidate solutions. Simulation experiments are conducted on a set of recently proposed high-dimensional benchmark problems with dimensions of 100, 200, 500 and 1,000. Simulation results demonstrate that GjODE is better than, or at least comparable to, six other algorithms, and employing GPU can effectively reduce computational time. The obtained maximum speedup is up to 75.

Improved differential evolution algorithm based on Laplace distribution mutation

To improve the optimum speed and optimization accuracy of Differential Evolution Algorithm(DEA),an improved DEA was proposed.In this algorithm,a new mutation operator following the Laplace distribution was used during the mutation,and both the mutation strategy and the crossover probability could be gradually self-adapted to fit different phases of evolution by learning from their previous successful experience.Experimental studies were carried out on five classical Benchmark functions,and the computational results show that the algorithm has faster convergence,higher accuracy and stronger robustness,and it is suitable to solve high-dimensional complex global optimization problems.

A line search approach for high dimensional function optimization

This paper proposes a modified line search method which makes use of partial derivatives and re-starts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high dimensional benchmark functions, we illustrate that the proposed Line Search Re-Start (LSRS) approach is very suitable for high dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 10,000 dimensions clearly illustrate that the proposed approach performs very well for the tested high dimensional functions.

Dynamic differential evolution algorithm with random mutation

The dynamic Differential Evolution(DE) algorithm with random mutation was proposed.In this algorithm,the mutation strategies of DE/rand/1 and DE/best/1 were combined by linear decreased weight convex combination strategy to produce a new mutation strategy so as to dynamically use the advantages of DE/rand/1 and DE/best/1.In order to improve the global optimization ability of DE algorithm,exponent increased crossover probability operator,linear decreasing scaling factor and random mutation mechanism were introdunced.The test results on the four standard test functions show that the new algorithm has fast convergence,high accuracy and more robustness,more suitable to solve high-dimensional complex global optimization problems.

A novel global optimization technique for high dimensional functions

Several types of line search methods are documented in the literature and are well known for unconstraint optimization problems. This paper proposes a modified line search method, which makes use of partial derivatives and restarts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high-dimensional benchmark functions, we illustrate that the proposed line search restart (LSRS) approach is very suitable for high-dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 2000 dimensions clearly illustrate that the proposed approach performs very well for the tested high-dimensional functions. © 2009 Wiley Periodicals, Inc.