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In recent years, grey models based on fractional-order accumulation and/or derivatives have attracted considerable research interest because they offer better performance in handling limited samples with uncertainty than integer-order grey models; however, there remains room for improvement. This paper considers a more flexible and general structure for the fractional grey model by incorporating a generalized fractional-order derivative (GFOD) that complies by memory effects, resulting in the development of a generalized fractional grey model (denoted as GFGM(1,1)). Specifically, we comprehensively analyse the modelling mechanism of the proposed GFGM(1,1) model, involving model parameter estimation and time response function derivation, and discuss the link between the proposed approach and existing special cases. Then, to further improve the efficacy of the proposed approach, four mainstream metaheuristic algorithms are employed to ascertain the orders of fractional accumulation and derivatives. Finally, we carry out a series of simulation studies and a real-world application case to demonstrate the applicability and advantage of the our approach. The numerical results show that GFGM(1,1) outperforms other benchmarks, and some significant insights are obtained from the numerical experiments.

Task scheduling is one of the major issues in cloud computing environment. Efficient task scheduling is substantial to attain cost-effective execution and improve resource utilization. The task scheduling problem is classified to be a nondeterministic polynomial time (NP)-hard problem. This feature attracts researchers to utilize nature inspired metaheuristic algorithms. Initializing searching solutions randomly is one of the key features in such optimization algorithms. However, assisting metaheuristic algorithms with effective initialized solutions can significantly improve its performance. In this paper, an improved initialization of particle swarm optimization (PSO) using heuristic algorithms is proposed. Longest job to fastest processor (LJFP) and minimum completion time (MCT) algorithms are used to initialize the PSO. The performance of the proposed LJFP-PSO and MCT-PSO algorithms are evaluated in minimizing the makespan, total execution time, degree of imbalance, and total energy consumption metrices. Moreover, the performance of the proposed algorithms is compared with recent task scheduling methods. Simulation results revealed the effectiveness and superiority of the proposed LJFP-PSO and MCT-PSO compared to the conventional PSO and comparative algorithms.

There is an acute need to evaluate the energy consumption of buildings in response to climate change. The “occupant” factor has been largely overlooked in building energy analysis. This research aims at investigating occupancy existence in the office environment using a hybrid artificial neural network with metaheuristic algorithms for improved energy management. It proposes and compares three classification models, namely particle swarm optimization (PSO), gravitational search algorithm (GSA), and hybrid PSO-GSA in combination with the feedforward neural network (FFNN). The inputs to these models are data related to temperature, humidity, light, and carbon dioxide emissions. Two data sets are used for testing the models while the office door is open and closed. The capabilities of the optimized models are evaluated using best, average, median, and standard deviation of the mean squared error. Most of the performance metrics indicate that the FFNN-PSO-GSA model exhibits better performance compared to the other models using the two datasets. The proposed model yields a classification accuracy ranging between 98.47-98.73% using one predictor (i.e., temperature). Besides, it yields an accuracy ranging between 85.45-94.03% using temperature and CO2 predictors. It can be concluded that the FFNN combined with PSO and GSA algorithms can be a useful tool for occupancy detection modeling.

This paper presents a new optimization procedure to consider uncertainty in complex optimization problems, where conventional mathematical programming strategies are not efficient. This methodology consists in using evolutionary algorithms based on metaheuristic optimization tools. The proposed sequence involves the generation of random values to consider the stochastic behavior of uncertain parameters in the mathematical model. Likewise, a subcode was developed in visual basic for applications to manipulate the decision variables generated by the evolutionary algorithm and the post evaluation of the performance of the objective functions. The used metaheuristic optimization algorithm was the improved multi-objective differential evolution optimization algorithm. To prove the efficiency of the proposed optimization strategy, three case studies are analyzed, which involve the solution of single-objective and bi-objective optimization problems. This optimization procedure offers attractive solutions to the specified goals.

Recently, studies have focused on optimization as a method to reach the finest conditions for metal forming processes. This study tests various optimization techniques to determine the optimum conditions for single point incremental forming (SPIF). SPIF is a die-less forming process that depends on moving a tool along a path designed for a specific feature. As it involves various parameters, optimization based on experimental studies would be costly, hence a finite element model (FE-model) for the SPIF process is developed and validated through experimental results. In the second phase, statistical analyses based on the response surface method (RSM) are conducted. The optimum conditions are determined using the desirability optimization method, in addition to two metaheuristic optimization algorithms, namely genetic algorithm (GA) and particle swarm optimization (PSO). The results of all optimization techniques are compared to each other and a confirmation test using the FE-model is subsequently performed.

Flow-shop scheduling is an extremely popular optimization model in industrial production, where each job must be scheduled on a series of machines following an identical process. The optimal criter...

Metaheuristic algorithms are widely used in various fields of optimization engineering. These algorithms have become popular because of their ability to explore and exploit solutions in various problem areas. The Spotted Hyena Optimizer (SHO) algorithm is a metaheuristic algorithm inspired by the life of spotted hyenas, introduced by Dhiman and Kumar (2017) to solve continuous optimization problems. Various studies have been performed based on changes in the SHO algorithm to solve various problems due to its effectiveness and success in solving continuous problems. This paper aims to comprehensively survey the application of the SHO algorithm in solving various optimization problems. In this paper, SHO algorithms are categorized based on hybridization, improvement, SHO variants, and optimization problems. This study invites researchers and developers of meta-heuristic algorithms to employ the SHO algorithm for solving diverse problems since it is a simple and robust algorithm for solving intricate and NP-hard problems. Based on the studies, it was concluded that the SHO algorithm had been used more in optimization problems. The purpose of optimization problems is to find optimal solutions and finding global points in the problem environment. Also, the SHO algorithm establishes a good trade-off between the exploration and extraction stages. Based on the done studies and investigations, properties and factors of the SHO algorithm are better than another meta-heuristic algorithms, which has increased its adaptability and flexibility in different fields.

Ngày nay, thiết kế tối ưu công trình sử dụng thuật toán metaheuristic được sử dụng một cách thường xuyên hơn nhờ hiệu quả vượt trội của các thuật toán tối ưu này trong việc giải quyết các bài toán có độ phức tạp cao. Nhờ những ưu điểm đó, có khá nhiều thuật toán tối ưu đã và đang được đề xuất. Tuy nhiên, tùy thuộc vào đặc điểm của từng dạng bài toán tối ưu khác nhau mà hiệu quả của thuật toán sẽ khác nhau. Trong bài báo này, bài toán tối ưu của khung thép sử dụng phân tích phi tuyến đã được xem xét. Bốn thuật toán tối ưu sử dụng phổ biến gần đây cho dạng bài toán này được xem xét so sánh bao gồm: bản nâng cấp thuật toán tiến hóa vi phân (EpDE), bản nâng cấp thuật toán tối ưu va chạm giữa các vật chất (ECBO), kỹ thuật tìm kiếm hài hòa (HS) và thuật toán Rao. Một khung thép phẳng 5 tầng được tối ưu với hàm mục tiêu là tổng khối lượng và điều kiện ràng buộc cả về khả năng chịu tải và về chuyển vị lệch tầng. Kết quả tính toán cho thấy, thuật toán EpDE không chỉ tìm kiếm được kết quả tối ưu tốt nhất mà tốc độ tối ưu cũng tốt nhất trong bốn thuật toán.

In this paper, a novel flower pollination algorithm (FPA) is implemented to solve the problem of combined economic emission dispatch (CEED) in the power system. The FPA is a new metaheuristic optimization technique, which takes a biological approach to flower pollination. The FPA mimics the characteristics of flower pollination according to the survival of the fittest concept. CEED represents a combination of the emission and economic dispatch functions, formulated into a single function using the penalty factor. In this paper, the effect of valve point loading in the power system network is considered to obtain minimum fuel cost, minimum emissions, and optimum power generation. The performance of the proposed algorithm is evaluated using two test systems, namely 10 and 14 generating units by contemplating the valve point loading effect as well as transmission loss. The results of the 10 and 14 system units are compared with a learning-based optimization technique to demonstrate the effectiveness of the FPA. The findings reveal that the proposed FPA gives better performance than other algorithms with minimum fuel cost and emissions.

This paper reports a study of the flowshop scheduling problem with two machines where a set of tasks must be scheduled on a set of machines respecting the same fixed order. The objective was to des...

Nowadays, mixed-model assembly lines (MMALs) are extensively applied to manufacture different products with no need for the changeover of the whole lines to satisfy the diversified preferences of c...

Purpose Optimal placement of static VAR compensator (SVC) devices not only improves the voltage profile (VP) but also reduces the active power loss (APL) and enhances the voltage stability (VS) through injecting appropriate VARs at optimal buses. The traditional mathematical methods may not provide global best solution and pose difficulties in handling multi-objective SVC placement (SVCP) problem with complex constraints and forcefully place all the given number of SVCs in the system without assessing their real requirements in enhancing the chosen performances. The purpose of this paper is to formulate the SVCP as a multi-objective optimization problem and solve it using a metaheuristic algorithm for global best solution. Design/methodology/approach The proposed SVCP method uses improved harmony search optimization (IHSO) with dissonance-avoiding mechanism for obtaining the global best solution through driving away the solution from the sub-optimal traps. In addition, the method uses a self-adaptive technique for optimally tuning the IHSO parameters and places only the required number of SVCs from the given number of SVCs. Findings This paper presents the results of the proposed method for 14, 30 and 57 bus systems and exhibits that the proposed method outperforms the existing SVCP methods in achieving the desired performances. Originality/value This paper proposes a new self-adaptive IHSO based SVCP method for optimally placing only the required number of SVCs with a goal of attaining the global best performances.

Metaheuristic algorithms are successful methods of optimization. The firefly algorithm is one of the known metaheuristic algorithms used in a variety of applications. Recently, a new and efficient version of this algorithm was introduced as NEFA, which indicated a good performance in solving optimization problems. However, the introduced attraction model in this algorithm may not provide good coverage of the search space and thus trap the algorithm in a local optimum. In this paper, a new and efficient improved firefly algorithm called INEFA is proposed to improve the performance of NEFA. In INEFA, a new model of attraction is introduced in which each firefly can be attracted to brighter fireflies located in different areas of the search space, using the clustering concept to classify fireflies. To evaluate the performance of INEFA, it was used to optimize several known benchmark functions. The results were compared with the results of the firefly algorithm and some of its known improvements. The comparison of results indicated the significant power of INEFA compared to the algorithms. It was used to evaluate its application in solving a constrained optimization problem. The comparison results showed that INEFA performs better than most of the compared algorithms.

Considering ergonomic factors in assembly line balancing problems can significantly improve human ergonomic conditions. In this study, a two-stage framework is developed to balance a mixed-model parallel U-shaped assembly line by considering ergonomic risks. In the first stage, according to various ergonomic standards and using the best-worst method and ELECTRE TRI, ergonomic risks of each task are identified and each task is classified into hard, normal, or easy class. In the second stage, a mathematical model of the problem is developed by considering a new objective function to level the number of tasks of each class between stations. This objective ensures that the tasks of each class are distributed equally among stations, resulting in having a roughly equal number of hard, normal, and easy tasks in each station. To solve the problem, a constraint programming model and a heuristic algorithm are developed. Numerical results show that the proposed objective function can level ergonomic risks well. The performance of the proposed solution approaches is examined against six different metaheuristic algorithms. Numerical results indicate the superiority of the constraint programming model for small and medium-size problems and that of the heuristic algorithm for large-size problems.

The complexity of an optimization problem is determined by its decision and objective spaces. Over the past few decades, a large number of works have focused on the performance improvement of metaheuristic algorithms via the objective space, whereas studies related to the decision space have attracted little attentions. Moreover, metaheuristic algorithms may not obtain satisfactory results within an entire feasible region, even if sufficient computational resources are available. Therefore, reducing the search space (i.e., finding a trust region) may be an effective method to ensure that the convergence is sufficiently close to the global optimal region. However, inappropriate subspace size may also weaken the performance of algorithms except for ones with a sufficiently small search space. To alleviate aforementioned problems, a variable search space (VSS) strategy based on a sequential trust region determination approach is proposed in this paper. In the VSS, the entire optimization process is divided into two stages: the first stage is to use an optimization approach for sequentially finding the trust domain of each variable and then determine the best-matched subspace; the second stage is to employ the optimization method for searching an optimal/near-optimal solution within the found trust region. The effectiveness of the VSS is evaluated using two widely used test suites, that is, IEEE CEC2014 and BBOB2012. Experimental results indicate that improving the algorithm performance is an important method for tackling problems, but locating a trust region is also beneficial for metaheuristic algorithms to improve the solution precision, especially for complex optimization problems.

Infrastructure development is followed by an increase in demand for ready-mix concrete (RMC). Some failures in delivering RMC on time would delay construction performance or the truck would need to wait at the construction site, so the delivered concrete became useless if it exceeded the concrete setting time limit. This research optimizes the supply chain of ready mix concrete based on real-time data from a batching plant in Surabaya by using the metaheuristic method. The metaheuristic method used in this research are Particle Swarm Optimization (PSO) and Symbiotic Organisms Search (SOS), and also compares the performance of both metaheuristic algorithms, because both algorithms have proven effective in solving various optimization problems. The objective function of this research is to minimize the total waiting times of mixer trucks. The results showed that the SOS algorithm has better performance than the PSO algorithm, which gets lower total waiting times of 100,863 hours.

This study proposes a scenario-based mixed-integer programming model to investigate the responsive-resilient inventory-location problem under uncertainty. The proposed model minimizes the total costs and makes decisions about the location, allocation, and inventory problems. The literature showed that simultaneous consideration of responsiveness and resilience measures has been ignored by the researchers. Hence, to fill this gap, this study considers responsiveness and resilience measures in the proposed model. Also, since the uncertainty exists in the nature of the research problem due to changes in the business environment, this paper applies the queuing theory and robust fuzzy stochastic optimization to cope with uncertainty. At first, the existed uncertainty in lead time and demand is tackled by employing the queuing theory, and some performance measures of the system are calculated. Then, the achieved results are incorporated into the fuzzy robust stochastic model. As the problem is an NP-Hard, this study develops several metaheuristic algorithms to solve the proposed model in a reasonable time. Then, the applicability of the proposed model and efficiency of the developed algorithms are shown by several numerical examples. Eventually, several sensitivity analyses are conducted on some important parameters of the model, and useful managerial insights are provided.

Compliant mechanisms are crucial parts in precise engineering but modeling techniques are restricted by a high complexity of their mechanical behaviors. Therefore, this paper devotes an optimal design method for compliant mechanisms. The integration method is a hybridization of statistics, finite element method, artificial intelligence, and metaheuristics. In order to demonstrate the superiority of the method, one degree of freedom is considered as a study object. Firstly, numerical datasets are achieved by the finite element method. Subsequently, the main design parameters of the mechanism are identified via analysis of variance. Desirability of both displacement and frequency of the mechanism is determined, and then, they are embedded inside a fuzzy logic system to combine into a single fitness function. Then, the relationship between the fine design variables and the fitness function is modeled using the adaptive network-based fuzzy inference system. Next, the single fitness function is maximized via moth-flame optimization algorithm. The optimal results determined that the frequency is 79.517 Hz and displacement is 1.897 mm. In terms of determining the global optimum solution, the current method is compared with the Taguchi, desirability, and Taguchi-integrated fuzzy methods. The results showed that the current method is better than those methods. Additionally, the devoted method outperforms the other metaheuristic algorithms such as TLBO, Jaya, PSOGSA, SCA, ALO, and LAPO in terms of faster convergence. The result of this study will be considered to apply for multiple-degrees-of-freedom compliant mechanisms in future work.

In this study, the capability of the recently introduced moth swarm algorithm (MSA) was compared with two robust metaheuristic algorithms: the harmony search (HS) algorithm and the imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared for optimization of the complex problem of four-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms. Sensitivity analysis was performed to determine the appropriate values of the algorithms’ parameters. The statistical indices coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), normalized MSE (NMSE), mean absolute percentage error (MAPE), and Willmott’s index of agreement (d) were used to compare the algorithms’ performance. The results showed that MSA was the superior algorithm for solving all benchmark functions in terms of obtaining the optimal value and saving CPU usage. ICA and HS were ranked next. When the dimensions of the problem were increased, the performance of ICA and HS dropped but MSA has still performed extremely well. In addition, the minimum CPU usage and the best solutions for the optimal operation of the four-reservoir system were obtained by MSA, with values of 269.7 seconds and 308.83, which are very close to the global optimum solution. Corresponding values for ICA were 486.73 seconds and 306.47 and for HS were 638.61 seconds and 264.61, which ranked them next. Similar results were observed for the 10-reservoir system; the CPU time and optimal value obtained by MSA were 722.5 seconds and 1,195.58 while for ICA they were 1,421.62 seconds and 1,136.22 and for HS they were 1,963.41 seconds and 1,060.76. The R2 and RMSE values achieved by MSA were 0.951 and 0.528 for the four-reservoir system and 0.985 and 0.521 for the 10-reservoir system, which demonstrated the outstanding performance of this algorithm in the optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the 12 algorithms investigated, MSA was the best, and it is recommended as a robust and promising tool in the optimal operation of multi-reservoir systems. HIGHLIGHTS This is the first application of robust MSA in the optimization of water resources.; The capability of 11 metaheuristic algorithms in optimization of multi-reservoir systems was compared.; MSA was the superior model in terms of CPU time and obtaining the optimal solution.

The usability of robots is expanding day by day as it is capable of doing complex and hazardous tasks better and faster than human beings. To increase the capacity of robot modernization of its motion is inexorable, and finding the obstacle-free and shortest path for the robot in minimum time becomes essential. To solve this mobile robot path planning problem, many exact, heuristic and metaheuristic algorithms were designed and developed. Here, a metaheuristic algorithm based on chemical reaction optimization (CRO) is proposed to find the obstacle-free minimum path in minimum computational time. To get this outcome, basic operators of CRO are redesigned and two new repair operators have been introduced. These repair operators help to reduce the path length, increase the path smoothness and minimize the number of points in a path, respectively,. They have great influence because the four fundamental operators of CRO are not sufficient enough to produce better results in all situations. To prove the supremacy of the proposed algorithm, the results are compared with ant colony optimization algorithm, probabilistic road map method, particle swarm optimization algorithm and genetic algorithm. The comparison shows that the proposed algorithm has the best results in the improvement of path length, smoothness and execution time. The superiority of the proposed algorithm over the compared algorithms has been proven using a statistical test. Besides this, the empirical outcomes of 10 complex maps are revealed in this research work for which nobody did any experiment in our conjecture.

This paper presents a new computational procedure for optimization of structures subjected to dynamic loads. The optimization problem is formulated with discrete design variables that represent the members from a table of commercially available members. Also, the requirements in the American Institute of Steel Construction (AISC) manual are formulated as constraints. This results in a nondifferentiable optimization problem. In the new procedure, the dynamic load is transformed into equivalent static loads (ESLs). Then the static response optimization problem having discrete design variables is solved using a metaheuristic optimization algorithm. Three methods to calculate the ESLs are investigated. It is found that the ESL cycles cannot converge to the final design. Therefore after a few ESL cycles, the original dynamic loads need to be used in the optimization process. Four example problems are solved to analyze the procedure. Based on this analysis, it is concluded that the new procedure is more efficient compared to a procedure that does not use the ESL cycles because it reduces the total CPU effort to obtain the final design. Also, better final designs are found. The reason is that many more designs are analyzed very efficiently with the ESL procedure.

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer linear programming (MILP) formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization (PSO) is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic.

Incremental industrialization and urbanization is the cause of enhanced energy use as it increases the building of new lines and more inductive loads. As a result, the transmission system losses increased, and the magnitudes of voltage profile values deviated from the stated value, resulting in increased cost of active power generation. To mitigate these issues, adequate reactive power compensation in the transmission line and bus systems should be done. Reactive power is regulated by the proper position of the Flexible AC Transmission System (FACTS). Unified Power Flow Controller (UPFC) is a voltage converter system that increases the voltage profile and reduces loss. In this paper, the optimal power flow solution is considered using a FACTS device based on Multi Population Modified Jaya (MPMJ) optimization algorithm. Using the Analytical Hierarchy Process (AHP) system, the optimal position of the UPFC device is determined by considering the most useful objective function provided by priorities and weighting factors. Therefore, on the standard IEEE-57 bus test system, the proposed MPMJ optimization algorithm is implemented with UPFC for optimal fuel cost values of generation, real power loss, voltage deviation and sum of squared voltage stability index. The result obtained by the proposed algorithm is contrasted with the recent literature algorithm.

Population structure has an impact on the performance of metaheuristic algorithms. To better improve the performance of differential evolution (DE), an elite-guided hierarchical differential evolution algorithm (EHDE) is proposed. First, an elite-guided hierarchical mutation mechanism is presented, which integrates elite elements into the hierarchical population structure. During each generation, the population is divided into three groups according to fitness values, each group playing a unique role in its hierarchy. The best individual on the top layer is used to avoid the local optimal by random reinitialization or Levy flight. The (k − 1) elite individuals on the middle layer focus on the local search around the best individual. The remaining non-elite individuals on the bottom layer pay more attention to a more considerable range search by the guidance of the k elite individuals. Second, to accommodate diverse optimization problems and seek the balance between exploration and exploitation, the adaptive strategy of EHDE control parameters has added the random component and the time-varying component. Finally, for the sake of evaluating the performance of EHDE, sensitivity analysis to the size of elite individuals, efficiency analysis of the control parameters adaptive strategy, and comparisons with nine advanced DE variants and three non-DE algorithms on 29 universal benchmark function in terms of convergence accuracy and convergence speed have been taken out. All the obtained results show that the proposed EHDE has excellent optimization performance.

The bin-packing problem (BPP) is an age-old NP-hard combinatorial optimization problem, which is defined as the placement of a set of different-sized items into identical bins such that the number of containers used is optimally minimized. Besides, different variations of the problem do exist in practice depending on the bins dimension, placement constraints, and priority. More so, there are several important real-world applications of the BPP, especially in cutting industries, transportation, warehousing, and supply chain management. Due to the practical relevance of this problem, researchers are consistently investigating new and improved techniques to solve the problem optimally. Nature-inspired metaheuristics are powerful algorithms that have proven their incredible capability of solving challenging and complex optimization problems, including several variants of BPPs. However, no comprehensive literature review exists on the applications of the metaheuristic approaches to solve the BPPs. Therefore, to fill this gap, this article presents a survey of the recent advances achieved for the one-dimensional BPP, with specific emphasis on population-based metaheuristic algorithms. We believe that this article can serve as a reference guide for researchers to explore and develop more robust state-of-the-art metaheuristics algorithms for solving the emerging variants of the bin-parking problems.

In this paper, we study a novel risk measure, which is a copula-based extension of tail value-at-risk (TVaR). This measure is called dependent tail value-at-risk (DTVaR), which is a generalization of TVaR. Moreover, we describe a second conditional tail moment of the tail distribution with the center being the DTVaR itself, which is called the dependent conditional tail variance (DCTV). Both DTVaR and DCTV contain two contraction parameters, which make them much more flexible than some of the more familiar measures of risk, such as TVaR and conditional tail variance (CTV). We derive analytical formulas of the DTVaR and DCTV for exponential risk associated with another risk where their dependence structure is represented by Farlie-Gumbel-Morgenstern (FGM) copula. This paper proposes an optimization method for DTVaR by applying two metaheuristic algorithms: spiral optimization (SpO) and particle swarm optimization (PSO). Furthermore, we perform SpO and PSO by utilizing DCTV and CTV to estimate two contraction parameters that maximize DTVaR. This work presents an application of DTVaR optimization in predicting the DTVaR of energy risk of New York Harbor (NYH) gasoline associated with energy risk of West Texas Intermediate (WTI) crude oil. We find that the values of the objective function using both algorithms converge to zero, which implies that the SpO and PSO algorithms are very suitable for application to DTVaR optimization. However, according to the values of the objective function, we find that the PSO algorithm is more suitable than the SpO algorithm in optimizing DTVaR.

Support Vector Regression (SVR) is often used in forecasting. Adjustment of parameters in the SVR affects the results of forecasting. This study aims to analyze the SVR method that is optimized using Harris Hawks Optimization (HHO), hereinafter referred to as HHO-SVR. The HHO-SVR was evaluated using five benchmark datasets to determine the performance of this method. The HHO process is also compared based on the type of kernel and other metaheuristic algorithms. The results showed that the HHO-SVR has almost the same performance as other methods but is less efficient in terms of time. In addition, the type of kernel also affects the process and results.

Modified Adaptive Weight Approach (MAWA) is one of the simplest methods used for solving time-cost optimization problems. This type of optimization problem, categorized as multi-objective optimization, can be solved with metaheuristic algorithms. Here, metaheuristic algorithms evaluate a randomly generated solution set, referred to as population, within the boundary condition of a solution space. The weight factor values determined by MAWA are applied to all solutions in the population without distinguishing the solutions in that population. However, the potential solutions in the population indicate different fitness properties concerning solution space. In this paper to solve time-cost optimization problems, new adaptive weight formulations are proposed. In contrast to MAWA, the novelty of this study’s formulations is to adaptively detect the weight factor value, depending on the solution‘s fitness in the population. The results obtained from the numerical experiments examined in this study show that the proposed formulations can improve the performance of MAWA and can find identical or slightly different Pareto results for investigated multi-objective optimization problems.

In cloud computing, task scheduling plays a major role and the efficient schedule of tasks can increase the cloud system efficiency. To successfully meet the dynamic requirements of end-users’ applications, advanced scheduling techniques should be in place to ensure optimal mapping of tasks to cloud resources. In this paper, a modified Henry gas solubility optimization (HGSO) is presented which is based on the whale optimization algorithm (WOA) and a comprehensive opposition-based learning (COBL) for optimum task scheduling. The proposed method is named HGSWC. In the proposed HGSWC, WOA is utilized as a local search procedure in order to improve the quality of solutions, whereas COBL is employed to improve the worst solutions by computing their opposite solutions and then selecting the best among them. HGSWC is validated on a set of thirty-six optimization benchmark functions, and it is contrasted with conventional HGSO and WOA. The proposed HGSWC has been proved to perform better than the comparison algorithms. Moreover, the performance of HGSWC has also been tested on a set of synthetic and real workloads including fifteen different task scheduling problems. The results obtained through simulation experiments demonstrate that HGSWC finds near optimal solutions with no computational overhead as well as outperforms six well-known metaheuristic algorithms.

To improve ant colony optimization (ACO) for traveling salesman problem (TSP), its two main strategies which are tour construction and pheromone updating have been modified, and one modified ACO (MACO) has been proposed. For the first strategy (tour construction strategy), one new method to construct tours by combining paths of two meeting ants has been applied. And for second strategy (pheromone updating strategy), one new method to polarize pheromone density of all paths has been proposed. Based on the applications for 40 standard benchmark TSP instances (datasets) ranging from 29 to 13,509 cities, the good performance of the MACO is verified. To verify the MACO deeply, based on the applications for some standard TSP instances, the computing results of MACO are compared with three typical state-of-the-art algorithms based on ACO methods. Moreover, based on the applications for some standard TSP instances, the computing results of MACO are compared with 10 state-of-the-art metaheuristic algorithms. The comparison studies show that the MACO can attain the optimal solution with higher accuracy, no matter how complicated the TSPs are. And its performance is the best, comparing to all state-of-the-art algorithms. At last, two new strategies used in MACO have been analyzed comprehensively by the applications for 25 TSPs. The results show that the first strategy is mainly used to improve the computing efficiency, and the second one is mainly used to improve the computing effect.

In this paper, two optimal operation plans of a cascaded reservoir system with four hydropower plants are studied for reaching the highest power energy of all the power plants. In the first plan, called local optimization plan, optimal water discharge of each upstream hydropower plant is determined first and the optimal discharge is then used as input data for determining optimal water discharge of other downstream hydropower plants. In the second plan, called global optimization plan, optimal water discharge of all hydropower plants is simultaneously determined. For reaching the highest total power energy of the system, nine methods consisting of moth swarm algorithm, Harris hawks optimization, cuckoo search algorithm (CSA), snap drift cuckoo search algorithm (SD-CSA), stochastic fractal search algorithm, parasitism predation algorithm, marine predator algorithm, tunicate swarm algorithm, and the proposed improved cuckoo search algorithm (ICSA) are implemented. Among the methods, the proposed ICSA is first developed by improving the exploitation phase of CSA. The comparisons of power energy from each hydropower plant for the two plans indicate that local optimization plan is more useful for upstream plants but for downstream plants, whereas global optimization plan is more useful for downstream plants. For the purpose of reaching the highest total power energy for the whole system, the global optimization plan is more effective because it reaches higher power energy than local optimization plan. For investigating the improvement of the proposed method over CSA and SD-CSA, the three methods are run for seven benchmark functions and for the global optimization plan with different population sizes and different iteration numbers. As a result, it is recommended that global optimization plan should be applied for all hydropower plants in cascaded systems and downstream plants with higher power energy can share benefit to upstream ones. In addition, one of the most effective methods that should be recommended for implementing global optimization plan is the proposed ICSA.

For optimally designing water distribution networks (WDNs), the nondeterministic polynomial hard problem, a novel hybrid model, is introduced with the combined features of evolutionary and ...

In the modern world, wireless body area networks (WBANs) play an essential role in psychological and biomedical applications. The use of WBANs in medical applications is limited due to various issues related to the sensors, viz., irregularity in data production, replacement and recharging of their batteries and the energy consumed by the networks. This manuscript addresses how these problems can be solved along with optimization of the energy consumption through efficient design of the system by applying routing protocols and heuristic-based optimization algorithms. In this paper, the particle swarm optimization (PSO) algorithm is a heuristic search algorithm that relies on an upgrade mechanism of the velocity and position of swarms. Although PSO has excellent exploration capability in global search, it becomes quickly stuck in local minima. To enhance the local search function of the current PSO algorithm, a simulated annealing (SA) algorithm has been incorporated in the exploitation phase. The newly developed hybrid PSO-SA (hPSO-SA) algorithm is validated with other state-of-the-art nature-inspired algorithms on eighteen benchmarks and five real engineering design problems. The statistical results of the proposed hPSO-SA algorithm are promising and indicate very good efficiency. The paper also aims at the application of the proposed algorithm to the WBAN design problem for minimization of the energy consumption through better selection of the relay node. The proposed hPSO-SA algorithm outperforms twelve other metaheuristic algorithms, taking hybrid variants for comparison.

Selection of useful bands plays a very important role in hyperspectral image classification. In the past decade, metaheuristic algorithms have been used as promising methods for solving this problem. However, many metaheuristic algorithms may provide unsatisfactory performance due to their slow or premature convergence. Therefore, how to develop algorithms well balancing the exploration and exploitation, and find the suitable bands precisely is still a challenge. In this paper, a new hybrid global optimization algorithm, which is based on the Wind Driven Optimization (WDO) and Cuckoo Search (CS) is proposed to solve hyperspectral band selection problems. Both WDO and CS have strong searching ability and require less control parameters, but easily suffer from premature convergence due to loss of diversity of population. The proposed approach uses the Chebyshev chaotic map to initialize the population at initial step. The population is divided into two subgroups and WDO and CS are adopted for these two subgroups independently. By division, these two subgroups can share suitable information and utilize each other’s pros, thus avoid premature convergence, and obtain best optimal solution. Furthermore, the Levy flight step size in CS algorithm is adaptively adjusted based on fitness value and current iteration number, which helps in boosting the convergence speed of algorithm. The experimental results on three standard benchmark datasets namely, Pavia University, Botswana and Indian Pines, prove the superiority of the proposed approach over standard WDO and CS approaches as well as the other traditional approaches in terms of classification accuracy with fewer bands.

This paper represents the modified version of spotted hyena optimizer (SHO) to improve the performance. The spiral moment and astrophysics concepts are utilized in the proposed algorithm. The spiral moment is used to enhance the intensification capability of SHO. The concept of astrophysics is incorporated in SHO to improve both diversification and intensification. The performance of the proposed algorithm is compared with five well-known metaheuristic algorithms over CEC 2015 benchmark test functions. The results depict that the proposed algorithm outperforms the others in terms of fitness function value. The effects of scalability and sensitivity analysis have also been investigated. The proposed algorithm is also applied to two constrained engineering design problems. The experimental result shows that the proposed algorithm performs better than the other algorithms.

Hazardous wastes’ volume produced by human activities has increased in recent years. Consequently, associated risks involved in the treatment, recycling, disposing, and transportation of these hazardous materials have become more attractive for the researchers. In this study, we propose a new model for hazardous waste location routing problem. Appending the service time window and workload balance to the previous mathematical models can be taken into account as the major contributions of this study. Three objective functions including two systematic goals (cost and risk) and one social goal (workload balancing) have been considered for the model. Compatibility between wastes and a heterogeneous fleet of vehicles, which are rarely investigated in the literature, is discussed in this paper. Since the proposed model is classified as a multi-objective model, three multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm II (PESA-II), and Strength Pareto Evolutionary Algorithm II (SPEA-II) are employed. As two other innovations, an adaptive penalty function is developed and the PESA-II is modified by removing replicated solutions from its archive and their obtained results are discussed. Finally, by experimenting a number of test problems in different sizes, it is demonstrated that proposed modified PESA-II and SPEA-II perform better than NSGA-II in most of comparison metrics including feasible answers exploration, CPU time, spacing metric, inverted generational distance, quality metric, etc., whereas, NSGA-II creates more spread Pareto frontiers which are suitable for decision-maker to choose, from among a range of different options.

In this paper, a Joint set-up procedure for tuning metaheuristic algorithms’ parameters is proposed. The approach is applied to a genetic algorithm (GA) and tested further on the artificial bee colony (ABC) algorithm. The joint influence of parameters (the crossover and mutation probabilities for GA and the number of population and limit for ABC) on the performance of the algorithms is investigated. As a case study, a model parameter identification of an E. coli fed-batch cultivation process is considered. E. coli is one of the most commonly used bacteria for producing medical substances in the pharmaceutical industry. The development of an effective model of a fed-batch cultivation process is very important. The processes in a bioreactor are usually described by a system of parametric nonlinear differential equations. The model parameter identification is a difficult optimization problem, which cannot be solved by applying traditional numerical methods. Feasibilities of GA and ABC for a model parameter identification of a nonlinear fed-batch cultivation process based on real experimental data are presented. The application of the proposed Joint set-up approach leads to a significant improvement in the performance of GA and ABC. As a result, a reasonable enhancement of the E. coli cultivation model accuracy is achieved. The main advantage of the tuning procedure, which searches an optimal set of values of GA and ABC control parameters, focusing on promising intervals of variation of the parameter values and refining their ranges, is that the computational efforts are reduced by more than 60% for the ABC algorithm and more than 90% for GA.

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the \textit{q}-stripe TSP with $q \geq 1$, the objective function sums the costs for travelling from one customer to each of the next \textit{q} customers along the tour. The resulting \textit{q}-stripe TSP generalizes the TSP and forms a special case of the Quadratic Assignment Problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The proposed algorithm has two main components, which are construction and improvement phases. The construction phase generates a solution using Greedy Randomized Adaptive Search Procedure (GRASP) while the optimization phase improves the solution with several variants of Variable Neighborhood Search, both coupled with a technique called Shaking Technique to escape from local optima. In addition, Adaptive Memory is integrated into our algorithms to balance between the diversification and intensification. To show the efficiency of our proposed metaheuristic algorithms, we extensively experiment on benchmark instances. The results indicate that the developed algorithms can produce efficient and effective solutions at a reasonable computation time.

Cloud computing delivers practical solutions for long-term image archiving systems. Cloud data centers consume enormous amounts of electrical energy that increases their operational costs. This shows the importance of investing on energy consumption techniques. Dynamic placement of virtual machines to appropriate physical nodes using metaheuristic algorithms is among the methods of reducing energy consumption. In metaheuristic algorithms, there should be a balance between both exploration and exploitation aspects so that they can find better solutions in a search space. Exploration means looking for a solution in a wider area, while exploitation is producing new solutions from existence ones. Artificial bee colony optimization, which is a biological metaheuristic algorithm, is a sign-oriented approach. It has a strong exploration ability, but a relatively weaker exploitation power. On the other hand, tabu search is a popular algorithm that shows better exploitation in comparison with ABC. In this study, cloud computing environments are detailed with an allocation protocol for efficient energy and resource management. The technique of energy-aware allocation splits data centers (DCs) resources among client applications end routes to enhance energy efficacy of DCs and also achieves anticipated quality of service (QoS) for everyone. Heuristic protocols are exercised for optimizing the distribution of resources to upgrade the efficiency of DC. In the current paper, energy-aware resources allotment technique is employed and optimized in clouds via a new approach called Tabu Job Master (JM). Tabu JM claims the benefits of some variables and also rapid convergence speeds. Results are duly achieved for energy consumption—the count of virtual machines (VMs) migration and also makespan. The results shown by Tabu JM are benchmarked by using genetic algorithm (GA), artificial bee colony (ABC), ABC with crossover and technique of mutation, the basic tabu search techniques, and Tabu Job Master.

In this paper, optimal load dispatch problem under competitive electric market (OLDCEM) is solved by the combination of cuckoo search algorithm (CSA) and a new constraint handling approach, called modified cuckoo search algorithm (MCSA). In addition, we also employ the constraint handling method for salp swarm algorithm (SSA) and particle swarm optimization algorithm (PSO) to form modified SSA (MSSA) and modified PSO (MPSO). The three methods have been tested on 3-unit system and 10-unit system under the consideration of payment model for power reserve allocated, and constraints of system and generators. Result comparisons among MCSA and CSA indicate that the proposed constraint handling method is very useful for metaheuristic algorithms when solving OLDCEM problem. As compared to MSSA, MPSO as well as other previous methods, MCSA is more effective by finding higher total benefit for the two systems with faster manner and lower oscillations. Consequently, MCSA method is a very effective technique for OLDCEM problem in power systems.

This paper presents the application of two metaheuristic algorithms (Exchange Market Algorithm and Ant Lion Optimizer) in solving the DC optimal power flow problem. The objective of this study is t...

A recent metaheuristic algorithm, such as Whale Optimization Algorithm (WOA), was proposed. The idea of proposing this algorithm belongs to the hunting behavior of the humpback whale. However, WOA suffers from poor performance in the exploitation phase and stagnates in the local best solution. Grey Wolf Optimization (GWO) is a very competitive algorithm comparing to other common metaheuristic algorithms as it has a super performance in the exploitation phase while it is tested on unimodal benchmark functions. Therefore, the aim of this paper is to hybridize GWO with WOA to overcome the problems. GWO can perform well in exploiting optimal solutions. In this paper, a hybridized WOA with GWO which is called WOAGWO is presented. The proposed hybridized model consists of two steps. Firstly, the hunting mechanism of GWO is embedded into the WOA exploitation phase with a new condition which is related to GWO. Secondly, a new technique is added to the exploration phase to improve the solution after each iteration. Experimentations are tested on three different standard test functions which are called benchmark functions: 23 common functions, 25 CEC2005 functions and 10 CEC2019 functions. The proposed WOAGWO is also evaluated against original WOA, GWO and three other commonly used algorithms. Results show that WOAGWO outperforms other algorithms depending on the Wilcoxon rank-sum test. Finally, WOAGWO is likewise applied to solve an engineering problem such as pressure vessel design. Then the results prove that WOAGWO achieves optimum solution which is better than WOA and Fitness Dependent Optimizer (FDO)., Comment: 28 pages

The moth search algorithm (MS) is a novel intelligent optimization algorithm based on moth population behavior, which can solve many problems in different fields. However, the algorithm is easy to fall into local optimization when solving complex optimization problems. This study develops a new hybrid moth search-fireworks algorithm (MSFWA) to solve numerical and constrained engineering optimization problems. The explosion and mutation operators from the fireworks algorithm are introduced into the MS, which not only preserves the advantages of fast convergence and strong exploitation capability of the algorithm, but also significantly enhances the exploration capability. The performance of the MSFWA is tested using 23 benchmark functions. The hybrid algorithm is superior to other highly advanced metaheuristic algorithms for most benchmark functions, demonstrating the characteristics of fast convergence and high stability. Finally, the ability of the MSFWA to solve practical constrained problems is evaluated on six well-known engineering application problems. Compared with other optimization algorithms, the MSFWA is very competitive in its solution of these complex and constrained practical problems.

This paper proposes an improved coyote optimization algorithm (ICOA) for optimizing the location and sizing of solar photovoltaic distribution generation units (PVDGUs) in radial distribution systems. In the considered problem, four single objectives consisting of total power losses, capacity of all PVDGUs, voltage profile index, and harmonic distortions are minimized independently while satisfying branch current limits, voltage limits, and harmonic distortion limits exactly and simultaneously. The performance of the proposed ICOA method has been improved significantly since two improvements were carried out on the two new solution generations of the conventional coyote optimization algorithm (COA). By finding four single objectives from two IEEE distribution power systems with 33 buses and 69 buses, the impact of each proposed improvement and two proposed improvements on the real performance of ICOA has been investigated. ICOA was superior to COA in terms of capability of finding higher quality solutions, more stable search ability, and faster convergence speed. Furthermore, we have also applied five other metaheuristic algorithms consisting of biogeography-based optimization (BBO), genetic algorithm (GA), particle swarm optimization algorithm (PSO), sunflower optimization (SFO), and salp swarm algorithm (SSA) for dealing with the same problem and evaluating further performance of ICOA. The result comparisons have also indicated the outstanding performance of ICOA because it could find much better results than these methods, especially SFO, SSA, and GA. Consequently, the proposed ICOA is a very effective method for finding the optimal location and capacity of PVDGUs in radial distribution power systems.

Kernel partial least squares regression (KPLS) is a technique used in several scientific areas because of its high predictive ability. This article proposes a methodology to simultaneously estimate both the parameters of the kernel function and the number of components of the KPLS regression to maximize its predictive ability. A metaheuristic optimization problem was proposed taking the cumulative cross-validation coefficient as an objective function to be maximized. It was solved using nature-inspired metaheuristic algorithms: the genetic algorithm, particle swarm optimization, grey wolf optimization and the firefly algorithm. To validate the results and have a reference measure of the efficiency of the nature-inspired metaheuristic algorithms, derivative-free optimization algorithms were also applied: Hooke-Jeeves and Nelder-Mead. The metaheuristic algorithms estimated optimal values of both of the kernel function parameters and the number of components in the KPLS regression.

The efficiency of a Variable neighborhood search metaheuristic for continuous global optimization problems greatly depends on geometric shape of neighborhood structures used by the algorithm. Among the neighborhoods defined by balls in ?p, 1 ?p ? ? metric, we tested the ?1, ?2, and ?? ball shape neighborhoods, for which there exist efficient algorithms for obtaining uniformly distributed points. On many challenging high-dimensional problems, our exhaustive testings showed that, popular and the easiest for implementation, ?? ball shape of neighborhoods performed the worst, and much better efficiency was obtained with ?1 and ?2.