Real-world Optimization Problems Research Articles

An Improved Teaching-Learning-Based Optimization Algorithm with Reinforcement Learning Strategy for Solving Optimization Problems.

This paper presents an improved teaching-learning-based optimization (TLBO) algorithm for solving optimization problems, called RLTLBO. First, a new learning mode considering the effect of the teacher is presented. Second, the Q-Learning method in reinforcement learning (RL) is introduced to build a switching mechanism between two different learning modes in the learner phase. Finally, ROBL is adopted after both the teacher and learner phases to improve the local optima avoidance ability of RLTLBO. These two strategies effectively enhance the convergence speed and accuracy of the proposed algorithm. RLTLBO is analyzed on 23 standard benchmark functions and eight CEC2017 test functions to verify the optimization performance. The results reveal that proposed algorithm provides effective and efficient performance in solving benchmark test functions. Moreover, RLTLBO is also applied to solve eight industrial engineering design problems. Compared with the basic TLBO and seven state-of-the-art algorithms, the results illustrate that RLTLBO has superior performance and promising prospects for dealing with real-world optimization problems. The source codes of the RLTLBO are publicly available at https://github.com/WangShuang92/RLTLBO.

An adaptive state transition algorithm with local enhancement for global optimization

State transition algorithm (STA) is an efficient and powerful metaheuristic method for solving global optimization problems, and it has been successfully applied in many engineering fields in the past few years. However, the basic STA has weak local search capability and shows slow convergence rate and low convergence accuracy in the later search stage. In view of the above shortcomings, an adaptive state transition algorithm (ASTA) with local enhancement is proposed in this paper. Firstly, the order of using state transformation operators and the optimal parameters of the operators are considered in each iteration of ASTA, and a statistical method is employed to adaptively select the optimal transformation operator and the parameter values of the optimal operator to speed up the search process. Then, an adaptive call strategy is adopted to determine its convergence to the neighborhood of the optimal solution and to decide whether to perform the quasi-Newton operator for local enhancement. Finally, the degree to which the current solution is close to the optimal solution is judged by the information of historical solutions, and an analytical solution is quickly obtained by calling the quadratic interpolation operator. The effectiveness of the proposed ASTA is checked, through a comparison with other metaheuristic methods, on 15 benchmark functions and several real-world optimization problems. Experimental results show that ASTA has a stronger search capability than the basic STA, STA variants, and some state-of-the-art metaheuristic methods.

Adaptive Bundle Methods for Nonlinear Robust Optimization

Currently, there are few theoretical or practical approaches available for general nonlinear robust optimization. Moreover, the approaches that do exist impose restrictive assumptions on the problem structure. We present an adaptive bundle method for nonlinear and nonconvex robust optimization problems with a suitable notion of inexactness in function values and subgradients. As the worst-case evaluation requires a global solution to the adversarial problem, it is a main challenge in a general nonconvex nonlinear setting. Moreover, computing elements of an ε-perturbation of the Clarke subdifferential in the [Formula: see text]-norm sense is in general prohibitive for this class of problems. In this article, instead of developing an entirely new bundle concept, we demonstrate how existing approaches, such as Noll’s bundle method for nonconvex minimization with inexact information [Noll D (2013) Bundle method for non-convex minimization with inexact subgradients and function values. Computational and Analytical Mathematics, Springer Proceedings Mathematics, vol. 50 (Springer, New York), 555–592.] can be modified to be able to cope with this situation. Extending the nonconvex bundle concept to the case of robust optimization in this way, we prove convergence under two assumptions: first, that the objective function is lower C1 and, second, that approximately optimal solutions to the adversarial maximization problem are available. The proposed method is, hence, applicable to a rather general setting of nonlinear robust optimization problems. In particular, we do not rely on a specific structure of the adversary’s constraints. The considered class of robust optimization problems covers the case that the worst-case adversary only needs to be evaluated up to a certain precision. One possibility to evaluate the worst case with the desired degree of precision is the use of techniques from mixed-integer linear programming. We investigate the procedure on some analytic examples. As applications, we study the gas transport problem under uncertainties in demand and in physical parameters that affect pressure losses in the pipes. Computational results for examples in large realistic gas network instances demonstrate the applicability as well as the efficiency of the method. Summary of Contribution: Nonlinear robust optimization is a relevant field of research as real-world optimization problems usually suffer from not precisely known parameters, for example, physical parameters that cannot be measured exactly. Currently, there are few theoretical or practical approaches available for general nonlinear robust optimization. Moreover, the methods that do exist impose restrictive assumptions on the problem structure. Writing nonlinear robust optimization tasks in minimax form, in principle, bundle methods can be used to solve the resulting nonsmooth problem. However, there are a number of difficulties to overcome. First, the inner adversarial problem needs to be solved to global optimality, which is a major challenge in a general nonconvex nonlinear setting. In order to cope with this, an adaptive solution approach, which allows for inexactness, is required. A second challenge is then that the computation of elements from an ε-neighborhood of the Clarke subdifferential is, in general, prohibitive. We show how an existing bundle concept by D. Noll for nonconvex problems with inexactness in function values and subgradients can be adapted to this situation. The resulting method only requires availability of approximate worst-case evaluations, and in particular, it does not rely on a specific structure of the adversarial constraints. To evaluate the worst case with the desired degree of precision, one possibility is the use of techniques from mixed-integer linear programming. In the course of the paper, we discuss convergence properties of the resulting method and demonstrate its efficiency by means of robust gas transport problems.

A fuzzy constraint handling technique for decomposition-based constrained multi- and many-objective optimization

The challenge in solving constrained multi-objective optimization problems (CMOPs) is how to balance minimizing objectives and satisfying constraints, especially when the infeasible region is very large. To address this issue, this work proposes a fuzzy constraint handling technique, which uses the fuzzy set theory to accurately characterize the difference between solutions on objective function values and constraint violation degrees. On this basis, a new concept, called “fuzzy advantage”, is introduced to comprehensively quantify the degree to which one solution is better than others, allowing the infeasible solutions with promising fitness to survive. The proposed method is integrated with a decomposition-based multi-objective evolutionary algorithm to verify its effectiveness. Compared with nine state-of-the-art MOEAs on a number of test problems and a real-world optimization problem, the proposed algorithm shows high competitiveness in solving a variety of CMOPs.

Internet of Medical Things (IoMT) and Reflective Belief Design-Based Big Data Analytics with Convolution Neural Network-Metaheuristic Optimization Procedure (CNN-MOP).

In recent times, the Internet of Medical Things (IoMT) is a new loomed technology, which has been deliberated as a promising technology designed for various and broadly connected networks. In an intelligent healthcare system, the framework of IoMT observes the health circumstances of the patients dynamically and responds to backings their needs, which helps detect the symptoms of critical rare body conditions based on the data collected. Metaheuristic algorithms have proven effective, robust, and efficient in deciphering real-world optimization, clustering, forecasting, classification, and other engineering problems. The emergence of extraordinary, very large-scale data being generated from various sources such as the web, sensors, and social media has led the world to the era of big data. Big data poses a new contest to metaheuristic algorithms. So, this research work presents the metaheuristic optimization algorithm for big data analysis in the IoMT using gravitational search optimization algorithm (GSOA) and reflective belief network with convolutional neural networks (DBN-CNNs). Here the data optimization has been carried out using GSOA for the collected input data. The input data were collected for the diabetes prediction with cardiac risk prediction based on the damage in blood vessels and cardiac nerves. Collected data have been classified to predict abnormal and normal diabetes range, and based on this range, the risk for a cardiac attack has been predicted using SVM. The performance analysis is made to reveal that GSOA-DBN_CNN performs well in predicting diseases. The simulation results illustrate that the GSOA-DBN_CNN model used for prediction improves accuracy, precision, recall, F1-score, and PSNR.

Niching chimp optimization for constraint multimodal engineering optimization problems

Two significant concerns need to be addressed to handle multimodal problems: classifying various local/global optima and preserving these optimum values until the termination. Besides, a comprehensive local search ability is also a need to achieve the exact global optima. Chimp Optimization Algorithm (ChOA) is a recently swarm intelligence algorithm that needs less parameter tuning. The ChOA, on the other hand, is prone to early convergence and fails to strike a balance between exploration and exploitation when it comes to resolving multimodal challenges. In order to overcome these concerns, this paper embeds the niching technique in ChOA (NChOA) that includes the personal best qualities of PSO and a local search technique. To evaluate the NChOA’s performance, we analyze it against fifteen frequently utilized multimodal numerical test functions, ten complex IEEE CEC06-2019 suit tests, and twelve constrained real-world optimization problems in a variety of engineering fields, including industrial chemical producer, process design and synthesis, mechanical design, power system, power-electronic, and livestock teed ration problems. The results indicate that the NChOA outperforms several benchmark algorithms and sixteen out of eighteen state-of-the-art algorithms by an average rank of Friedman test greater than 81% for 25 numerical functions and twelve engineering problems while outperforming jDE100 and DISHchain1e + 12 by 22% and 41%, respectively. The Bonferroni-Dunn and Holm tests demonstrated that NChOA outperforms all benchmark and state-of-the-art algorithms for all numerical functions and engineering tasks while performing comparably to jDE100 and DISHchain1e + 12. The proposed NChOA, we believe, can be used to address difficulties involving multimodal search spaces. Additionally, NChOA is more broadly applicable than rival benchmarks to a broader range of engineering applications.

Empirical Study of Data-Driven Evolutionary Algorithms in Noisy Environments

For computationally intensive problems, data-driven evolutionary algorithms (DDEAs) are advantageous for low computational budgets because they build surrogate models based on historical data to approximate the expensive evaluation. Real-world optimization problems are highly susceptible to noisy data, but most of the existing DDEAs are developed and tested on ideal and clean environments; hence, their performance is uncertain in practice. In order to discover how DDEAs are affected by noisy data, this paper empirically studied the performance of DDEAs in different noisy environments. To fulfill the research purpose, we implemented four representative DDEAs and tested them on common benchmark problems with noise simulations in a systematic manner. Specifically, the simulation of noisy environments considered different levels of noise intensity and probability. The experimental analysis revealed the association relationships among noisy environments, benchmark problems and the performance of DDEAs. The analysis showed that noise will generally cause deterioration of the DDEA’s performance in most cases, but the effects could vary with different types of problem landscapes and different designs of DDEAs.

A dynamic stochastic search algorithm for high-dimensional optimization problems and its application to feature selection

As the number of dimensions of an optimization problem increases, the process of deriving the solution becomes more complicated and difficult. Metaheuristic algorithms are effective methods for solving many optimization problems, whereas most of these algorithms perform poorly on high-dimensional problems. In this paper, a novel metaheuristic algorithm called Dynamic Stochastic Search (DSS) is proposed for high-dimensional optimization problems. To effectively execute the exploration (diversification) and exploitation (intensification) processes of DSS, a dynamic stochastic search process is designed by defining a stochastic search control factor, a search process based on the Gaussian distribution, two shrink modes inspired by the Whale Optimization Algorithm, and a balance mechanism derived from the Bat Algorithm. The proposed algorithm has the following advantages: no specific control parameters other than the population size and the maximum number of iterations, a simple structure, and less computational effort in the implementation. Analyzing the computational complexity of DSS demonstrates its simplicity. To evaluate the performance of DSS, twenty 300-dimensional and 3000-dimensional classical benchmark functions as well as thirty 100-dimensional CEC2014 benchmark functions are utilized. The statistical results prove the effectiveness and feasibility of DSS for high-dimensional optimization problems because it shows better convergence performance and higher efficiency than various advanced optimization algorithms. Moreover, the superiority of DSS in solving high-dimensional real-world optimization problems is validated by applying it to feature selection for ten real-world benchmark classification datasets from the UCI machine learning repository.

A hybrid Grasshopper Optimization Algorithm and Harris Hawks Optimizer for Combined Heat and Power Economic Dispatch problem

The Combined Heat and Power Economic Dispatch (CHPED) is a real-world optimization problem with several complex constraints that has been a topic of studies around energy systems and optimization processes. This paper attempts to conceptualize a potent algorithm by combining the Modified Grasshopper Optimization Algorithm (MGOA) and the Improved Harris Hawks Optimizer (IHHO) for attaining a better balance between the beginning stages of global search and the latter stages of global convergence. The proposed attempt is abbreviated as MGOA-IHHO. Firstly, the chaotic and Opposition-Based Learning (OBL) methods are invoked to generate the initial population. Second, the mathematical model of the conventional Grasshopper Optimization Algorithm (GOA) is modified using Sine–Cosine Acceleration Coefficients (SCAC) to simulate the global exploration at the initial iterations and graduating to the global convergence at the final stages of optimization. Hence, it is named MGOA. Finally, the adaptive search mechanism integrates the two improved search phases of HHO with a search phase of MGOA to improve the performance of the proposed optimization method. This mechanism investigates the best solution for the aging level of the individual during the optimal evaluation process for choosing an appropriate search phase in MGOA-IHHO. The intended effect of the proposed MGOA-IHHO method is verified with other nature-inspired methods on standard single-objective test functions including 23 benchmark problems, 30 test suits of IEEE Congress on Evolutionary Computation 2017 (CEC2017), and four CHPED problems. The statistical results ascertain that the proposed hybridized MGOA-IHHO is capable of providing promising results when compared with its variants and optimization algorithms introduced in the literature.

Solving Many-objective Constraint Real-World Optimization Problems with Multi-objective Optimization Algorithms

In real world engineering optimization problems many constraints must be considered due to the imperfect conditions of the systems or process. Therefore, constraint handling methods are integrated into optimization algorithms. However, since the constraints are succeeded by the algorithm, their value is not considered or watched. Alternatively, it is possible to convert constraints to objectives and these many-objective constraint real-world optimization problems are changed to many-objective optimization problems. In this research for this purpose five real world engineering design problems are converted into many-objective optimization problem which are Gear Train Design, Pressure Vessel Design, Two Bar Truss Design, Disc Brake Design and Vibrating Platform Design problems. The problems are solved by using multi-objective optimization algorithms (NSGA-II, MOEA/D, MOEA/D-DE, MPSO/D and MOPSO) and their performance is compared by using the hypervolume metric.

Many‐objective optimization by using an immune algorithm

Multiobjective optimization is important in practical engineering applications. With the increased number of objectives, multiobjective optimization becomes more challenging due to the difficulty of convergence in population selection. A number of many-objective evolutionary algorithms (MaOEAs) have been designed to enhance population selection, but studies selecting parents for evolution are still rare. Fortunately, multiobjective immune algorithms (MOIAs) provide a promising approach to select high-quality parents for evolution. However, the existing MOIAs are not effective for solving many-objective optimization problems (MaOPs), as these algorithms consider only the local information of solutions for cloning but ignore the global information of populations; consequently, the populations of these algorithms may easily be trapped in local optima. To solve this problem, this paper proposes a many-objective immune algorithm with a novel immune cloning operator. In this approach, the global information in the population is used to estimate the quality of each solution, and only a few offspring from high-quality parents are generated in each generation to improve the convergence and diversity of the population. When the proposed algorithm is compared with nine MaOEAs and six MOIAs on three MaOP benchmarks with 5, 10, and 15 objectives, the experimental results validate that the proposed algorithm obtains the best performance in most cases. Moreover, the effectiveness of the proposed algorithm is also validated on one real-world optimization problem.

A surrogate-assisted evolutionary algorithm for expensive many-objective optimization in the refining process

Computationally expensive optimization problems are difficult for an evolutionary algorithm within limited fitness evaluations, especially for many-objective optimization. To remedy this issue, a surrogate-assisted decomposition-based evolutionary algorithm is proposed in this work where the Kriging model is used to approximate each objective function. In order to balance exploration and exploitation, the model management strategy integrates the infill criterion with the distribution information of both weight vectors and population. Additionally, a one-by-one replacement strategy is developed to select a fixed number of training data to limit computational time for the model training as well as maintain the approximation accuracy. The empirical results show that the performance of the proposed algorithm is competitive to the state-of-the-art algorithms on a number of benchmarks. Finally, the proposed algorithm is applied for a real-world optimization problem in the refining process and exhibits superior performance.

SPMS-ALS: A Single-Point Memetic structure with accelerated local search for instance reduction

• SPMS-ALS is a single-point memetic structure for instance reduction. • SPMS-ALS proposes a domain specific accelerated local search based on Pattern Search. • SPMS-ALS is a memetic approach designed according to a bottom-up strategy. • SPMS-ALS can save up to 85% of the runtime and yet achieves an excellent performance. Real-world optimisation problems pose domain specific challenges that often require an ad-hoc algorithmic design to be efficiently addressed. The present paper investigates the optimisation of a key stage in data mining, known as instance reduction, which aims to shrink the input data prior to applying a learning algorithm. Performing a smart selection or creation of a reduced number of samples that represent the original data may become a complex large-scale optimisation problem, characterised by a computationally expensive objective function, which has been often tackled by sophisticated population-based metaheuristics that suffer from a high runtime. Instead, by following the Ockham’s Razor in Memetic Computing, we propose a Memetic Computing approach that we refer to as fast Single-Point Memetic Structure with Accelerated Local Search (SPMS-ALS). Using the k-nearest neighbours algorithm as base classifier, we first employ a simple local search for large-scale problems that exploits the search logic of Pattern Search, perturbing an n -dimensional vector along the directions identified by its design variables one by one. This point-by-point perturbation mechanism allows us to design a strategy to re-use most of the calculations previously made to compute the objective function of a candidate solution. The proposed Accelerated Local Search is integrated within a single-point memetic framework and coupled with a resampling mechanism and a crossover. A thorough experimental analysis shows that SPMS-ALS, despite its simplicity, displays an excellent performance which is as good as that of the state-of-the-art while reducing up to approximately 85% of the runtime with respect to any other algorithm that performs the same number of function calls.

Spintronics-compatible Approach to Solving Maximum-Satisfiability Problems with Probabilistic Computing, Invertible Logic, and Parallel Tempering

The search of hardware-compatible strategies for solving NP-hard combinatorial optimization problems (COPs) is an important challenge of today s computing research because of their wide range of applications in real world optimization problems. Here, we introduce an unconventional scalable approach to face maximum satisfiability problems (Max-SAT) which combines probabilistic computing with p-bits, parallel tempering, and the concept of invertible logic gates. We theoretically show the spintronic implementation of this approach based on a coupled set of Landau-Lifshitz-Gilbert equations, showing a potential path for energy efficient and very fast (p-bits exhibiting ns time scale switching) architecture for the solution of COPs. The algorithm is benchmarked with hard Max-SAT instances from the 2016 Max-SAT competition (e.g., HG-4SAT-V150-C1350-1.cnf which can be described with 2851 p-bits), including weighted Max-SAT and Max-Cut problems.

A two-archive model based evolutionary algorithm for multimodal multi-objective optimization problems

Multimodal multi-objective optimization (MMO) can offer more elegant solutions and provide diverse decisions to decision-makers in real world optimization problems. Many multimodal evolutionary mechanisms have been proposed to explore and exploit two solution spaces (i.e. decision space and objective space) in recent years. However, most existing methods only use single evolutionary operator to generate offsprings and ignore the advantage of using hybrid evolutionary algorithm. Moreover, it is still a great challenge to balance the effectiveness and efficiency simultaneously in the evolutionary process of MMO. In view of this, an efficient Two-Archive model based multimodal evolutionary algorithm is proposed in this paper. Two parallel offspring generation mechanisms based on competitive particle swarm optimizer and differential evolution are applied to expand two solution spaces with different evolutionary requirements. Moreover, niching local search scheme and reverse vector mutation strategy play roles in achieving better convergence and diversity. Finally, 22 MMO test problems are used to validate the superiority of the proposed method by comparing it with 5 state-of-the-art MMO algorithms. The proposed method is also expanded to solve 9 feature selection problems for validating the effectiveness of the proposed method on real world applications.

Enhanced Flow Direction Arithmetic Optimization Algorithm for mathematical optimization problems with applications of data clustering

Data clustering is one of the most common and challenging problems in the machine learning domain. It requires an efficient method to be addressed. This paper proposed a new version of the Flow Direction Algorithm (FDA) to solve various optimization problems. The proposed method is called FDAOA, which enhanced the performance of the original Flow Direction Algorithm by the arithmetic operators that have been used in the Arithmetic Optimization Algorithm (AOA). The main aim of the proposed FDAOA is to avoid the recognized weaknesses in the original methods; stuck in the local area, premature convergence, and weak equilibrium between the exploration and exploitation search mechanisms. The proposed method is tested on two sets of various problems to validate its performance. In the first set, twenty-three benchmark functions are used, which belong to three categories; seven unimodal functions, six multimodal functions, and ten fixed dimension functions. In the second set, eight common data clustering problems are used to prove the ability of the proposed FDAOA to deal with real-world optimization problems. The results of the proposed method are compared with other well-established methods, and the proposed FDAOA achieved promising output compared to the other methods on various tested problems. The proposed method got the optimal clustering solutions almost in all the tested data clustering problems with clear significant improvements against the other comparative methods.

Improved slime mould algorithm with elitist strategy and its application to structural optimization with natural frequency constraints

An improved slime mould algorithm (ISMA) is proposed and applied to the size optimization of truss structures with natural frequency constraints. The slime mould algorithm is a recently proposed metaheuristic inspired by the morphological changes of the acellular slime mould Physarum polycephalum while foraging. This algorithm has been successfully applied to some real-world optimization problems in science and industry. However, it is found that the classical SMA suffers from slow convergence and often converges prematurely to non-optimal solutions, especially for large-scale optimization problems. Compared to the classical SMA, two main improvements are introduced in the proposed ISMA: (1) In the replacement phase of the ISMA, an elitist strategy is adopted to replace the generational replacement strategy of the classical SMA. The elitist strategy aims to increase the convergence rate of the ISMA. (2) A slight modification is made to the exploration phase of the classical SMA to ensure a vast exploration of the search space. The suggested modification enables the ISMA to overcome the shortcoming of the premature convergence of the classical SMA. Finally, the efficiency and robustness of the ISMA are demonstrated through three large-scale benchmark dome trusses with natural frequency constraints. To our knowledge, this is the first time to apply SMA to structural optimization. It is shown that the proposed ISMA overcomes the problems of premature convergence and slow convergence rate of the classical SMA. Numerical results show that the ISMA outperforms the classical SMA and shows superior or comparable performance to other reported methods.

A covariance-based Moth–flame optimization algorithm with Cauchy mutation for solving numerical optimization problems

Moth–Flame Optimization (MFO) algorithm, which is inspired by the navigation method of moths, is a nature-inspired optimization algorithm. The MFO is easy to implement and has been used to solve many real-world optimization problems. However, the MFO cannot balance exploration and exploitation well, and the information exchange between individuals is limited, especially in solving some complex numerical problems. To overcome these disadvantages of the MFO in solving the numerical optimization problems, a covariance-based Moth–Flame Optimization algorithm with Cauchy mutation (CCMFO) is proposed in this paper. In the CCMFO, the concept of covariance is used to transform the individuals of the moths and flames from the original space to the eigenspace and update the positions of moths, which can better improve the information exchange ability of the flames and moths in the eigenspace. In addition, Cauchy mutation is utilized to improve the exploration. And the CCMFO is compared with the other 22 algorithms on CEC 2020 test suite. The test results show that the CCMFO is better than other population-based optimization algorithms and MFO variants in search performance, while its performance is statistically similar to CEC competition algorithms. Furthermore, the CCMFO is compared with the other 12 algorithms on CEC 2020 real-world constrained optimization problems, and the results show that the CCMFO can effectively solve real-world constrained optimization problems. Finally, the CCMFO is used to optimize the tracking controller parameters of continuous casting mold vibration displacement. The experimental results based on the experimental platform show that the CCMFO can effectively reduce the difficulty of parameter selection and improve the tracking accuracy.

Dynamic multi-swarm differential learning harris hawks optimizer and its application to optimal dispatch problem of cascade hydropower stations

Harris hawks optimization (HHO) algorithm inspired by the cooperative behavior and chasing style of harris’ hawks in nature called surprise pounce is a relatively novel swarm intelligent optimization algorithm. Due to its simplicity and efficiency, the canonical HHO has displayed promising performance on a large number of continuous optimization problems and real-world optimization problems. However, how to balance contradictions between the exploration and exploitation capabilities and alleviate the premature convergence are two critical concerns that need to be dealt with in the HHO study. To address these two drawbacks, improve the optimization performance, and broaden its application domain, a dynamic multi-swarm differential learning Harris hawks optimizer (DMSDL-HHO) is proposed in this paper. To efficiently maintain the population diversity, the whole population is divided into many small sub-swarms, which are regrouped periodically, and information is exchanged among the swarms. In each generation, the differential evolution operator (including mutation, crossover, and selection operators) based on the personal historical best position is merged into each sub-swarm to augment the exploration capability, while the Quasi-Newton method as a local searcher is used to enhance the exploitation capability. Besides, aiming to prevent the algorithm from falling into local optima to some extent, the differential mutation operator candidate pool strategy is introduced into the late stage of the search process. Thus, different individuals in the same population can conduct distinct search behaviors in each generation, and the same individual can perform various search behaviors in different generations. The proposed algorithm is tested on 23 classic test functions and 30 CEC2014 benchmark functions and is compared with quite a few state-of-the-art algorithms in terms of often-used performance metrics with the help of statistical analysis, diversity measurement, exploration–exploitation investigations, ranking statistics, and Wilcoxon Signed Rank Test (WSRT). The experimental results verify the superior performance of the embedded strategies on balancing the exploration capability and the exploitation capability. In addition, the DMSDL-HHO is applied to the optimal dispatch problem of cascade hydropower stations (ODPCHS) based on a novel constraints handling method designed in this paper to demonstrate its good practicability and performance. The experimental results of a case study on the optimal dispatch problem of China’s Wujiang cascade hydropower stations show that DMSDL-HHO can obtain better and more reliable optimal results than the canonical HHO and other compared algorithms. Moreover, the convergence speed of DMSDL-HHO is also competitive in contrast to other algorithms. Therefore, it can be concluded that DMSDL-HHO is a promising alternative tool for solving complex continuous optimization problems and real-world optimization problems with complex constraints.

Criminal Search Optimization Algorithm: A Population-Based Meta-Heuristic Optimization Technique to Solve Real-World Optimization Problems

Criminal Search Optimization Algorithm: A Population-Based Meta-Heuristic Optimization Technique to Solve Real-World Optimization Problems