Large-scale Global Optimization Research Articles

Intelligent Scheduling Methodology for UAV Swarm Remote Sensing in Distributed Photovoltaic Array Maintenance.

In recent years, the unmanned aerial vehicle (UAV) remote sensing technology has been widely used in the planning, design and maintenance of urban distributed photovoltaic arrays (UDPA). However, the existing studies rarely concern the UAV swarm scheduling problem when applied to remoting sensing in UDPA maintenance. In this study, a novel scheduling model and algorithm for UAV swarm remote sensing in UDPA maintenance are developed. Firstly, the UAV swarm scheduling tasks in UDPA maintenance are described as a large-scale global optimization (LSGO) problem, in which the constraints are defined as penalty functions. Secondly, an adaptive multiple variable-grouping optimization strategy including adaptive random grouping, UAV grouping and task grouping is developed. Finally, a novel evolutionary algorithm, namely cooperatively coevolving particle swarm optimization with adaptive multiple variable-grouping and context vector crossover/mutation strategies (CCPSO-mg-cvcm), is developed in order to effectively optimize the aforementioned UAV swarm scheduling model. The results of the case study show that the developed CCPSO-mg-cvcm significantly outperforms the existing algorithms, and the UAV swarm remote sensing in large-scale UDPA maintenance can be optimally scheduled by the developed methodology.

Large-Scale Evolutionary Optimization Approach Based on Decision Space Decomposition

The identification of decision variable interactions has a crucial role in the final outcome of the algorithm in the large-scale optimization domain. It is a prerequisite for decomposition-based algorithms to achieve grouping. In this paper, we design a recognition method with higher efficiency and grouping accuracy. It is based on the decomposition strategy of min hash to solve large-scale global optimization (LSGO) problems, called MHD. Our proposed method focuses on discovering the interactions of decision variables through min hash and forming subcomponents with a principle that the interdependencies between these subcomponents are maintained at a minimal level. This is described as follows: first, the min hash performs several permutations of the vector composed of decision variables. Second, the index value of the first non-zero row of the vector after rearrangement is found to obtain the new feature vector. Third, the probability of identical data at each position is calculated based on the new feature vector to decide whether there are some certain interactions between the decision variables. The advantages of min hash are: simpler computation and greater efficiency improvement than comparison between two or two decision variables; ability to find similar decision variables very quickly; and ability to cluster decision variables in a simple way. Therefore, the efficiency as well as the reliability of MHD is guaranteed. On the accuracy aspect, the proposed algorithm performs well in various types of the large-scale global optimization benchmark test function. Finally, the experimental results analysis and summarize the performance competitiveness of our proposed MHD algorithm from several aspects when it is used within a co-evolutionary framework.

An innovative quadratic interpolation salp swarm-based local escape operator for large-scale global optimization problems and feature selection

An innovative quadratic interpolation salp swarm-based local escape operator for large-scale global optimization problems and feature selection

Black-Box Optimization Revisited: Improving Algorithm Selection Wizards Through Massive Benchmarking

Existing studies in black-box optimization suffer from low generalizability, caused by a typically selective choice of problem instances used for training and testing of different optimization algorithms. Among other issues, this practice promotes overfitting and poor-performing user guidelines. We address this shortcoming by introducing in this work a general-purpose algorithm selection wizard that was designed and tested on a previously unseen breadth of black-box optimization problems, ranging from academic benchmarks to real-world applications, from discrete over numerical to mixed-integer problems, from small to very large-scale problems, from noisy over dynamic to static problems, etc. Not only did we use the already very extensive benchmark environment available in Nevergrad, but we also extended it significantly by adding a number of additional benchmark suites, including Pyomo, Photonics, large-scale global optimization (LSGO), and MuJoCo. Our wizard achieves competitive performance on all benchmark suites. It significantly outperforms previous state-of-the-art algorithms on some of the suites, including YABBOB and LSGO. Its excellent performance is obtained without any task-specific parametrization. The algorithm selection wizard, all of its base solvers, as well as the benchmark suites are available for reproducible research in the open-source Nevergrad platform.

CCFR3: A cooperative co-evolution with efficient resource allocation for large-scale global optimization

Cooperative co-evolution (CC) adopts the divide-and-conquer strategy to decompose an optimization problem, which can decrease the difficulty of solving large-scale optimization problems. Each decomposed subproblem is solved by a subpopulation. According to the contributions of the subpopulations to the improvement of the best overall objective value, the CC algorithms select the subpopulation with the greatest contribution to undergo evolution. In the existing CC algorithms, the contribution evaluation cannot adapt to solve the optimization problem, which may decrease the performance of CC. In this paper, we propose a new CC framework named CCFR3, which can adaptively evaluate the contribution of a subpopulation in each co-evolutionary cycle. CCFR3 can allocate computational resources among subpopulations more frequently than other contribution-based CC algorithms. The subpopulations can have more chances to undergo evolution, which is beneficial to speed up the convergence of CC and enhance the performance of CC on obtaining the global optimal solution. Our experimental results and analysis suggest that CCFR3 is a competitive solver for large-scale optimization problems.

An Efficient and Robust Improved Whale Optimization Algorithm for Large Scale Global Optimization Problems

As an efficient meta-heuristic algorithm, the whale optimization algorithm (WOA) has been extensively applied to practical problems. However, WOA still has the drawbacks of converging slowly, and jumping out from extreme points especially for large scale optimization problems. To overcome these defects, a modified whale optimization algorithm integrated with a crisscross optimization algorithm (MWOA-CS) is proposed. In MWOA-CS, each dimension of the optimization problem updates its position by randomly performing improved WOA or crisscross optimization algorithm during the entire iterative process. The improved WOA adopts the new nonlinear convergence factor and nonlinear inertia weight to tune the ability of exploitation and exploration. To analyze the performance of MWOA-CS, a series of numerical experiments were performed on 30 test benchmark functions with dimension ranging from 300 to 1000. The experimental results revealed that the presented MWOA-CS provided better convergence speed and accuracy, and meanwhile, displayed a significantly more effective and robust performance than the original WOA and other state of the art meta-heuristic algorithms for solving large scale global optimization problems.

A Novel Memetic Algorithm Based on Multiparent Evolution and Adaptive Local Search for Large-Scale Global Optimization.

In many fields, including management, computer, and communication, Large-Scale Global Optimization (LSGO) plays a critical role. It has been applied to various applications and domains. At the same time, it is one of the most challenging optimization problems. This paper proposes a novel memetic algorithm (called MPCE & SSALS) based on multiparent evolution and adaptive local search to address the LSGO problems. In MPCE & SSALS, a multiparent crossover operation is used for global exploration, while a step-size adaptive local search is utilized for local exploitation. A new offspring is generated by recombining four parents. In the early stage of the algorithm execution, global search and local search are performed alternately, and the population size gradually decreases to 1. In the later stage, only local searches are performed for the last individual. Experiments were conducted on 15 benchmark functions of the CEC′2013 benchmark suite for LSGO. The results were compared with four state-of-the-art algorithms, demonstrating that the proposed MPCE & SSALS algorithm is more effective.

DMDE: Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition large-scale global optimization

DE algorithms have outstanding performance in solving complex problems. However, they also have highlighted the need for an effective approach to alleviating the risk of premature convergence and loss of population diversity, particularly for non-decomposition large-scale global optimization (N-LSGO) problems. In this study, first, the multi-trial vector (MTV) approach is improved by adding a population diversity component, then, a diversity-maintained multi-trial differential evolution (DMDE) algorithm is proposed using the improved approach for N-LSGO problems. The DMDE algorithm produces solutions during six phases: initializing, subpopulation constructing, movement, evaluating and updating, archiving, and diversity maintaining. In initializing, the population is located in the search space and partitioned into three subpopulations using a success-rate based policy. Then, the subpopulations are independently evolved using the proposed meaningful search strategies to decrease the risk of stagnation. The DMDE algorithm introduces an archiving mechanism to maintain population diversity, which prevents premature convergence. Finally, the individuals' behavior is analyzed using the diversity maintaining phase, and those dimensions that have lost their diversity will be enriched. The effectiveness and scalability of the DMDE algorithm are evaluated using benchmark functions CEC 2018 with dimensions 30, 50, and 100 and CEC 2013 with dimension 1000 as LSGO problems. Moreover, the performance of the proposed algorithm was statistically analyzed using Wilcoxon signed-rank sum, ANOVA, and the Friedman tests. In addition, the applicability of the DMDE was assessed by solving seven well-known real-world problems including large-scale problems selected mostly from test-suite CEC 2020. In all experiments and tests, several well-known and N-LSGO algorithms have competed with DMDE through which the comparison results prove that the proposed DMDE algorithm is superior to competitor algorithms.

Parallel Cooperative Coevolutionary Grey Wolf Optimizer for Path Planning Problem of Unmanned Aerial Vehicles.

The path planning of Unmanned Aerial Vehicles (UAVs) is a complex and hard task that can be formulated as a Large-Scale Global Optimization (LSGO) problem. A higher partition of the flight environment leads to an increase in route’s accuracy but at the expense of greater planning complexity. In this paper, a new Parallel Cooperative Coevolutionary Grey Wolf Optimizer (PCCGWO) is proposed to solve such a planning problem. The proposed PCCGWO metaheuristic applies cooperative coevolutionary concepts to ensure an efficient partition of the original search space into multiple sub-spaces with reduced dimensions. The decomposition of the decision variables vector into several sub-components is achieved and multi-swarms are created from the initial population. Each sub-swarm is then assigned to optimize a part of the LSGO problem. To form the complete solution, the representatives from each sub-swarm are combined. To reduce the computation time, an efficient parallel master-slave model is introduced in the proposed parameters-free PCCGWO. The master will be responsible for decomposing the original problem and constructing the context vector which contains the complete solution. Each slave is designed to evolve a sub-component and will send the best individual as its representative to the master after each evolutionary cycle. Demonstrative results show the effectiveness and superiority of the proposed PCCGWO-based planning technique in terms of several metrics of performance and nonparametric statistical analyses. These results show that the increase in the number of slaves leads to a more efficient result as well as a further improved computational time.

A particle swarm optimizer with multi-level population sampling and dynamic p-learning mechanisms for large-scale optimization

Large-scale optimization, which has received much attention in recent years, is inherently a challenging problem. This paper proposes a particle swarm optimizer with multi-level population sampling and dynamic p-learning mechanisms to address the problem. The multi-level sampling mechanism in the proposed method is developed for supporting a balanced evolutionary search. The mechanism works by partitioning the particles of swarm into multi-levels based on their fitness before each generation of evolution. A subset of swarm is then dynamically sampled from the particles at various levels for evolution such that encouraging exploration at the beginning of evolution while exploitation towards the end of evolution, thus appropriately searching the space. The dynamic p-learning mechanism, on the other hand, is introduced to allow efficient particle learning while preserving the swarm diversity during evolution. In this mechanism, each particle is devised to learn from one of the top 100p% particles of the sub-swarm and the value of p associated with each particle is dynamically adjusted during evolution. By employing the above two mechanisms, the resulting method aims to appropriate search the solution space of large-scale global optimization problem for identifying the optimal or near-optimal solution. The performance of the proposed method has been evaluated on CEC’2010 and CEC’2013 benchmark suites for large-scale optimization and compared with related methods. Our results confirm the merits of the devised mechanisms in the proposed method. The results also show that our method can achieve a superior performance and outperform related methods.

An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping

An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping

Comparing SSALEO as a Scalable Large Scale Global Optimization Algorithm to High-Performance Algorithms for Real-World Constrained Optimization Benchmark

The Salp Swarm Algorithm (SSA) outperforms well-known algorithms such as particle swarm optimizers and grey wolf optimizers in complex optimization challenges. However, like most meta-heuristic algorithms, SSA suffers from slow convergence and stagnation in the best local solution. In this study, a Salp swarm algorithm (SSA) is combined with a local escaping operator (LEO) to overcome some inherent limitations of the original SSA. SSALEO is a novel search technique that accounts for population diversity, the imbalance between exploitation and exploration, and the SSA algorithm’s premature convergence. By implementing LEO in SSALEO, the search slowdown in SSA is eliminated, and the local search efficiency of swarm agents is improved. The proposed SSALEO method is tested using the CEC 2017 benchmark with 50 and 100 decision variables, seven CEC2008lsgo test functions with 200, 500, and 1000 decision variables, and its performance was compared to other metaheuristic algorithms (MAs) and advanced algorithms, including seven Salp swarm variants. The comparisons show that SSA greatly benefits from LEO by enhancing the quality and accelerating its solutions’ convergence rate. The SSALEO was then assessed using a benchmark set of seven well-known constrained design challenges in various engineering domains defined in the CEC 2020 conference benchmark. Friedman and Wilcoxon rank-sum statistical tests are also used to examine the results. ACCORDING TO EXPERIMENTAL DATA AND STATISTICAL TESTS, the SSALEO algorithm is very competitive and often superior to the algorithms used in the studies. Further, the proposed approach can be viewed as a special LSGO optimizer whose performance exceeds that of specialized state-of-the-art algorithms like CMA-ES and SHADE.

Performance Analysis of Simulated Annealing and Genetic Algorithm on systems of linear equations

Problem solving and modelling in traditional substitution methods at large scale for systems using sets of simultaneous equations is time consuming. For such large scale global-optimization problem, Simulated Annealing (SA) algorithm and Genetic Algorithm (GA) as meta-heuristics for random search technique perform faster. Therefore, this study applies the SA to solve the problem of linear equations and evaluates its performances against Genetic Algorithms (GAs), a population-based search meta-heuristic, which are widely used in Travelling Salesman problems (TSP), Noise reduction and many more. This paper presents comparison between performances of the SA and GA for solving real time scientific problems. The significance of this paper is to solve the certain real time systems with a set of simultaneous linear equations containing different unknown variable samples those were simulated in Matlab using two algorithms-SA and GA. In all of the experiments, the generated random initial solution sets and the random population of solution sets were used in the SA and GA respectively. The comparison and performances of the SA and GA were evaluated for the optimization to take place for providing sets of solutions on certain systems. The SA algorithm is superior to GA on the basis of experimentation done on the sets of simultaneous equations, with a lower fitness function evaluation count in MATLAB simulation. Since, complex non-linear systems of equations have not been the primary focus of this research, in future, performances of SA and GA using such equations will be addressed. Even though GA maintained a relatively lower number of average generations than SA, SA still managed to outperform GA with a reasonably lower fitness function evaluation count. Although SA sometimes converges slowly, still it is efficient for solving problems of simultaneous equations in this case. In terms of computational complexity, SA was far more superior to GAs.

Dynamic Model and Intelligent Maximum Power Point Tracking Approach for Large‐Scale Building‐Integrated Photovoltaic System

Due to the complex surrounding environments, unpredictable occupants’ behaviors, and the photovoltaic (PV) module degradation after years of operation, the fast and accurate maximum power point tracking (MPPT) of building‐integrated photovoltaic (BIPV) system is very difficult. Herein, the MPPT of a huge BIPV system is modeled as a large‐scale global optimization (LSGO) problem, in which all the variables are proven to be separable. Then, a novel differential evolution (DE) algorithm with the “DE/Current‐to‐Tbest/Current‐to‐Gbest/1” mutation operation (DE‐TG1) is developed to optimize the aforementioned separable LSGO−MPPT model. In addition, the problem of PV module degradation and its effect on the LSGO‐MPPT model are analyzed in detail. To reduce the influence of PV degradation on MPPT accuracy, the dynamic LSGO−MPPT model is developed by introducing the annual drift rates into the proposed LSGO−MPPT model. Finally, the developed methodologies are comprehensively tested by simulation experiments. Experimental results show that the developed DE‐TG1 algorithm significantly outperforms the other state‐of‐the‐art algorithms on separable LSGO problems. In addition, result of the experiments also indicates that with the cooperation of the DE‐TG1 algorithm and the dynamic LSGO−MPPT model, the effective MPPT control of a large‐scale BIPV system can be obtained with accurate and robust performance.

An improved weighted optimization approach for large-scale global optimization

It is a great challenge for ordinary evolutionary algorithms (EAs) to tackle large-scale global optimization (LSGO) problems which involve over hundreds or thousands of decision variables. In this paper, we propose an improved weighted optimization approach (LSWOA) for helping solve LSGO problems. Thanks to the dimensionality reduction of weighted optimization, LSWOA can optimize transformed problems quickly and share the optimal weights with the population, thereby accelerating the overall convergence. First, we concentrate on the theoretical investigation of weighted optimization. A series of theoretical analyses are provided to illustrate the search behavior of weighted optimization, and the equivalent form of the transformed problem is presented to show the relationship between the original problem and the transformed one. Then the factors that affect problem transformation and how they take affect are figured out. Finally, based on our theoretical investigation, we modify the way of utilizing weighted optimization in LSGO. A weight-sharing strategy and a candidate solution inheriting strategy are designed, along with a better allocation of computational resources. These modifications help take full advantage of weighted optimization and save computational resources. The extensive experimental results on CEC’2010 and CEC’2013 verify the effectiveness and scalability of the proposed LSWOA.

Cooperative Coevolution with Two-Stage Decomposition for Large-Scale Global Optimization Problems

Cooperative coevolution (CC) is an effective framework for solving large-scale global optimization (LSGO) problems. However, CC with static decomposition method is ineffective for fully nonseparable problems, and CC with dynamic decomposition method to decompose problems is computationally costly. Therefore, a two-stage decomposition (TSD) method is proposed in this paper to decompose LSGO problems using as few computational resources as possible. In the first stage, to decompose problems using low computational resources, a hybrid-pool differential grouping (HPDG) method is proposed, which contains a hybrid-pool-based detection structure (HPDS) and a unit vector-based perturbation (UVP) strategy. In the second stage, to decompose the fully nonseparable problems, a known information-based dynamic decomposition (KIDD) method is proposed. Analytical methods are used to demonstrate that HPDG has lower decomposition complexity compared to state-of-the-art static decomposition methods. Experiments show that CC with TSD is a competitive algorithm for solving LSGO problems.

Guest Editorial Evolutionary Computation Meets Deep Learning

Deep learning is a timely research direction in machine learning, where breakthrough progress has been made in both academe and industries, bringing promising results in speech recognition, computer vision, industrial control and automation, etc. The motivation of deep learning is primarily to establish a model to simulate the neural connection structure of the human brain. While dealing with complex tasks, deep learning adopts a number of transformation stages to deliver the in-depth description and interpretation of the data. Deep learning achieves exceptional power and flexibility by learning to represent the task through a nested hierarchy of layers, with more abstract representations formed successively in terms of less abstract ones. One of the key issues of existing deep learning approaches is that the meaningful representations can be learned only when their hyperparameter settings are properly specified beforehand, and general parameters are learned during the training process. Until now, not much research has been dedicated to automatically set the hyperparameters, and accurately find the globally optimal general parameters. However, this problem can be formulated as optimization problems, including discrete optimization, constrained optimization, large-scale global optimization, and multiobjective optimization, by engaging mechanisms of evolutionary computation.

Wild Geese Algorithm: A novel algorithm for large scale optimization based on the natural life and death of wild geese

In numerous real-life applications, nature-inspired population-based search algorithms have been applied to solve numerical optimization problems. This paper focuses on a simple and powerful swarm optimizer, named Wild Geese Algorithm (WGA), for large-scale global optimization whose efficiency and performance are verified using large-scale test functions of IEEE CEC 2008 and CEC 2010 special sessions with high dimensions D ​= ​100, 500, 1000. WGA is inspired by wild geese in nature and models various aspects of their life such as evolution, regular cooperative migration, and fatality. The effectiveness of WGA for finding the global optimal solutions of high-dimensional optimization problems is compared with that of other methods reported in the previous literature. Experimental results show that the proposed WGA has an efficient performance in solving a range of large-scale optimization problems, making it highly competitive among other large-scale optimization algorithms despite its simpler structure and easier implementation. The source code of the proposed WGA algorithm is publicly available at github.com/ebrahimakbary/WGA.

Fly visual evolutionary neural network solving large‐scale global optimization

Neurophysiologic achievements claimed that the fly visual system could naturally contribute to a type of artificial computation model which used motion-sensitive neurons to detect the local movement direction changes of moving objects. It, however, still remains open how the neurons' information-processing mechanisms and the inspirations of swarm intelligence can be integrated to serve an interdisciplinary topic between computer vision and intelligence optimization-visual evolutionary neural networks. Hereby, a fly visual evolutionary neural network is developed to solve large-scale global optimization (LSGO), inspired by swarm evolution and the characteristics of fly visual perception. It includes two functional modules, of which one is to generate global and local motion direction activities of visual neural nodes, and the other takes the activities as learning rates to update the nodes' states by a population-like evolutionary strategy. Also, it is used to optimize the structure of a multilayer perceptron to acquire a sample classification model. The theoretical results indicate that the network is convergent and meanwhile the computational complexity mainly depends on the size of the input layer and the dimension of LSGO. The comparative experiments have verified that the network is an extremely competitive optimizer for LSGO problems.

Image-based benchmarking and visualization for large-scale global optimization

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an image-based visualization framework, without dimension reduction, that visualizes the solutions to large-scale global optimization problems as images is proposed. In the proposed framework, the pixels visualize decision variables while the entire image represents the overall solution quality. This framework affords a number of benefits over existing visualization techniques including enhanced scalability (in terms of the number of decision variables), facilitation of standard image processing techniques, providing nearly infinite benchmark cases, and explicit alignment with human perception. To the best of the authors’ knowledge, this is the first realization of a dimension-preserving, scalable visualization framework that embeds the inherent relationship between decision space and objective space. The proposed framework is utilized with different mapping schemes on an image-reconstruction problem that encompass continuous, discrete, constrained, dynamic, and multi-objective optimization. The proposed framework is then demonstrated on arbitrary benchmark problems with known optima. Experimental results elucidate the flexibility and demonstrate how valuable information about the search process can be gathered via the proposed visualization framework. Results of a user survey strongly support that users perceive a correlation between objective fitness values and the quality of the corresponding images generated by the proposed framework.