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Nowadays, economic and environmental concerns in production have become increasingly significant. To address these issues, the Combined Economic and Emission Dispatch (CEED) problem has been introduced to optimize the power generation process by considering fuel cost and emitted substances. However, due to the nonlinearity and nonconvexity of the objective function, the optimization of CEED remains a challenge. In this paper, we develop a Reinforcement Learning-based Adaptive Differential Evolution (RLADE) algorithm to enhance the optimization performance. The mutation strategy and crossover probability of RLADE are optimized using Reinforcement Learning (RL) to respectively ensure better convergence speed and searchability. Additionally, two modifications of RL, namely the adaptive population size-based state division and fitness-ranking-based reward mechanism, are proposed to improve the accuracy of state division and reward calculation in RL. The experiments conducted in this paper consider two objective formulation methods of CEED problems, namely the quadratic and cubic criterion functions. The mean values and standard deviations of the obtained solutions were utilized to assess the performance of RLADE, as well as other comparative algorithms, namely DE algorithm and two RL-based DE variants. The results clearly demonstrate that RLADE surpasses its counterparts with proportion of 100%, 85.7%, and 100% for the 6-unit and 11-unit quadratic CEED problems, as well as cubic criterion functions, in terms of both search accuracy and convergence ability. Furthermore, the significance of RLADE's superiority is confirmed through the Wilcoxon's signed rank test. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper develops a robust strategy based on integrating three mutation phases and adapted control parameters into the Adaptive Guided Differential Evolution algorithm called (mAGDE) to improve diversity and exploration of the original AGDE. The mAGDE performance is evaluated using IEEE CEC'2020 test suite. Furthermore, the mAGDE is employed to identify the solid oxide fuel cell (SOFC) model optimal parameters. Two modes of SOFC operation are investigated, steady and transient states. The results obtained from the proposed mAGDE are compared with a number of recent, well-established and reputed meta-heuristics, including Particle swarm optimization, Teaching learning-based optimization, Whale optimization algorithm, Harris hawks optimization, Marine predators algorithm, Archimedes optimization algorithm, Differential evolution, and the original AGDE. Additionally, the statistical parameters that measure the performance of the proposed optimizer and the other competitors are calculated. The main finding demonstrated the preference and robustness of the suggested mAGDE in constructing the SOFC circuit that closely converges to the actual one. During the steady-state operation, the best fitness value obtained via the suggested mAGDE for operation at 1273 K is 2.2995E−06, while in the transient-state operation, the best SMSE is 1.04. The average cost function is decreased by 43.33% compared to the one obtained by the original AGDE. From the aforementioned assessments, it can be concluded that the proposed mAGDE is outstanding and promising. • This paper introduces a modified mAGDE based on the integration of a modified three-phases AGDE with the DE_SPA algorithm. • A modified three-phases AGDE has been introduced to maintain diversity and convergence of the evolutionary process. • The CEC'2020 test suite problems are used to demonstrate the performance mAGDE against other competitors. • Applying for first time mAGDE to identify the optimal parameters of SOFC model. • The robustness of the proposed strategy-based mAGDE is proved. [ABSTRACT FROM AUTHOR]

Differential evolution is one of the most powerful stochastic real-parameter optimization algorithms currently, and its performance depends heavily on control parameters and mutation strategy. In recent years, methods to select favorable parameters control and mutation strategy when solving various optimization problems have attracted increasing attention. To choose an appropriate mutation strategy and control parameters for a given optimization problem, in this paper, a Adaptive Differential Evolution Algorithm Based on Deeply-Informed Mutation Strategy and Restart Mechanism (ADEDMR) is proposed, and the ADEDMR algorithm has the following characteristics: First, a deeply-informed mutation strategy is proposed, which takes into account the information of suboptimal solutions discarded by selection and inherits the advantages of the powerful "DE/target-pbest/1/bin", aiming to obtain a better perceptual landscape of the target function and improve the candidate diversity of the trial vector. Second, according to the evolution process, the segmentation method is used to control F , which alleviates the scaling of F in the wrong direction, and makes the newly generated F fit more accurately. Third, a new population restart mechanism is adopted to further enhance population diversity by adaptively enhancing the search ability of hopeless individuals and randomly replacing some inferior individuals with wavelet walks. To evaluate the performance of our proposed algorithm, comparative experiments are conducted on 72 benchmark functions from the CEC2014, CEC2017 and CEC2022 test suites. Experimental results show that the proposed ADEDMR has higher convergence accuracy, better optimization ability when solving high-dimensional complex functions, and is competitive with six recent strong DE variants. [ABSTRACT FROM AUTHOR]

Multi-UAV (unmanned aerial vehicle)-supported mobile edge computing system deploys multiple UAVs as flight edge clouds for large-scale users. In this system, how to optimize the deployment of UAVs is important for providing good service for all mobile users. Specifically, for each mobile user, we need to determine whether the task can be performed locally or on the drone (i.e., the unload decision) and how much resources should be allocated. In this paper, a new two-level optimization method is proposed for UAV deployment and task scheduling problem to minimize the system energy consumption. The proposed algorithm is named TSHGHSDE algorithm, in which a few features are designed to enhance the algorithm performance. Firstly, a two-stage optimization strategy is proposed based on HS-DE algorithm. In the early stage, HS algorithm is used for the local search in a limited space, and the DE algorithm is employed for the global search in the late stage. Secondly, we design an effective control parameter to adjust the search process, which aims to effectively combine the local search ability of HS algorithm and the global search ability of DE algorithm. Thirdly, a novel encoding mechanism is proposed in the process of the UAV deployment optimization. A global search strategy is designed to enhance the performance of the proposed algorithm. To assess the performance of the proposed algorithm, some well-known algorithms are used for comparison in experiments. The results demonstrate that the proposed algorithm performs better in terms of the search efficiency, search accuracy and stability. • A two-stage optimization strategy is proposed based on HS-DE algorithm. • An effective control parameter is designed to balance the local and global search ability. • A novel encoding mechanism is proposed in the process of the UAV deployment optimization. • A global search strategy is designed to enhance the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The population structure of differential evolution (DE) algorithm cannot maintain the diversity of the population to the greatest extent and help the population avoid to fall into the local optima in time. In this paper, a co-evolutionary multi-swarm adaptive differential evolution algorithm, namely ECMADE is proposed to solve the premature convergence and search stagnation. First of all, in terms of population structure, based on the parallel distributed framework, ECMADE randomly and evenly divides the population into exploration subpopulation, development subpopulation, and auxiliary subpopulation, and introduces an adaptive information exchange mechanism so that subpopulations can escape local optima in time. Then, a multi-operator parallel search strategy is proposed to keep population diversity and meet the optimization needs of different problems. Finally, an adaptive adjustment mechanism of control parameters is developed, through recent elite parameter archive and weight distribution to fully mine successful parameter information, and generate control parameters with a high success rate for the current evolutionary stage. In order to prove the effectiveness of the ECMADE, 10 test functions and portfolio optimization problem are selected in here. The experiment results show that the ECMADE can effectively solve these test functions, the accuracy and efficiency is superior to those of two classical DE algorithms. The actual application results show that the ECMADE can significantly improve the ability of portfolio to resist extreme losses, which proves the effectiveness and feasibility of the ECMADE once again. The ECMADE has better optimization performance by comparing with some well-known algorithms in term of the solution quality, robustness and space distribution. It provides a new algorithm for solving complex optimization problems. [ABSTRACT FROM AUTHOR]

The shape optimization of interpolation curves is a crucial and intractable technique in scientific visualization, data analysis, manufacturing and computer-aided design and is potentially used in many engineering fields involving geometric modeling. In this paper, an enhanced hybrid tunicate swarm algorithm (TSA) is used to optimize the shape of complex rational quartic interpolation spline (RQI-spline, for short) curves. Firstly, to modify the shape of the interpolation curve more flexibly, a novel multi-parameter RQI-spline curve with local and global shape parameters is presented. Then the corresponding combined RQI-spline curves with 2th-order parametric continuity denoted C 2 are constructed. In addition, considering that the optimization of shape parameters for RQI-spline curves is a complex optimization problem, an enhanced hybrid version of TSA called DQTSA is developed. The introduction of differential evolution and quadratic interpolation strategies enhances the ability of the TSA to jump out of local minima, thus effectively solving the shape parameter optimization of RQI-spline curves. DQTSA and some popular comparison algorithms are used to solve the set of 23 benchmark functions and CEC2019 test functions. The experimental results show that DQTSA performs the best in 7 (30.43%) of the 23 test problems, while DQTSA performs the best in 3 of the 10 CEC2019 suites. Meanwhile, applying DQTSA to three engineering optimization problems, the best value, mean and significantly better than other search algorithms are obtained from 20 optimized designs, which verifies the applicability and stability of DQTSA in solving engineering optimization problems. Finally, the proposed DQTSA is used to solve the shape optimization model for the combined C 2 RQI-spline curve. Numerical results find that DQTSA obtains the optimal RQI-spline curve with minimum energy. Some representative numerical examples illustrate that DQTSA is a potentially excellent algorithm for solving curve optimization. • A novel C2 rational quartic interpolation spline (RQI-spline, for short) curves are constructed. • An enhanced tunicate swarm algorithm called DQTSA is presented. • The superiority of DQTSA is verified by comparing with popular intelligent algorithms. • Shape optimization model of C2 RQI-spline curves is established. • The DQTSA algorithm is applied to the solutions of the established optimization model. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved version of JADE by h ybridizing the JADE algorithm with a G aussian t ail, a modified hunger games search (HGS) algorithm, and a distance-based multi-population (DbMP) approach named as HJADE-GT. In the proposed algorithm, two sets of operators (modified HGS operator and JADE operator with Gaussian tail) are utilized to generate offspring to further enhance the exploration and exploitation abilities. DbMP approach is proposed to make full use of feedback information from the whole population. In HJADE-GT, the main population is divided into three fixed-size subpopulations: exploration subpopulation, balanced subpopulation, and exploitation subpopulation. Secondly, a modified HGS operator is incorporated into the exploration subpopulation to improve global searchability. Thirdly, the JADE operator with a Gaussian tail is utilized to enhance the ability of exploitation subpopulation. Finally, the DbMP approach is utilized for the balanced subpopulation to choose an appropriate operator for current individuals to make full use of feedback information from the exploration subpopulation and exploitation subpopulation. In the experimental studies, it is demonstrated that the proposed algorithm presents competitive performance with 13 well-known algorithms, including jDE, SaDE, JADE, MPEDE, SHADE, CoDE, SaJADE, iLSHADE, jSO, CMAES, MGFPA, ESSA, and PPSO on CEC2017 benchmark functions. Four engineering problems and three dynamic economic emission dispatch (DEED) problems were utilized to verify the performance of HJADE-GT, and the experiments on DEED problems confirm that HJADE-GT is an efficient algorithm to solve engineering and large-scale constrained DEED problems. [ABSTRACT FROM AUTHOR]

Land readjustment and redistribution (LR) is an important approach used to realize development plans by converting rural lands to urban land and also providing urban infrastructure. The LR problem, which is a complex challenging real-world problem, is a discrete optimization problem because its structure is similar to TSP (Traveling Salesman Problem) and scheduling problems which are combinatorial optimization problems. Since classical mathematical methods are insufficient for solving NP (Nondeterministic Polynomial) optimization problems due to time limitations, meta-heuristic optimization algorithms are commonly utilized for solving these kinds of problems. In this paper, meta-heuristic algorithms including genetic, particle swarm, differential evolution, artificial bee, and tree seed algorithms are utilized for solving LR problems. The stated meta-heuristic algorithms are used by applying spatial-based crossover and mutation operators depending upon the LR problem on each algorithm. Moreover, a synthetic dataset is used to ensure that the quality of the solution obtained is acceptable to everyone, to prove an optimal solution easily. By utilizing the suggested spatial-based crossover and mutation operators, finding the ideal solution is aimed using the synthetic dataset. In addition, five different modifications on TSA (Tree-Seed Algorithm) are performed and used to solve LR problems. All the modified versions of TSA are carried out only by changing the mechanism of seed reproduction. The novel TSA approaches are respectively named as tcTSA (tournament current), tbTSA (tournament best), pbTSA (personal-best based), t2TSA (double tournament), and elTSA (elitism based). In the experimental studies, the hybrid approach, which includes the crossover and mutation operators, is successfully applied in all of the algorithms under equal conditions for a fair comparison. According to experimental results performed using the dataset, it can be clearly stated that especially t2TSA outperforms all the algorithms in terms of performance and time. [ABSTRACT FROM AUTHOR]

Search-based algorithms are a recent research hotspot for solving path coverage (PC), which is the most critical and challenging problem in the field of automated test case generation (ATCG). There remains a large research space for achieving ATCG-PC's goal of finding a set of test cases covering all possible paths with as little computational overhead as possible. In contrast to two existing research approaches of testing different search-based algorithms and developing different fitness functions, this paper proposes two learning strategies based on a hypercube (termed HBL and THBL), which are inspired by a problem-specific knowledge expressed by the mathematical formulas of different fitness functions for ATCG-PC. The hypercubes of HBL and THBL are developed via an opposition-based learning strategy around the current best solution. The two learning strategies can guide search-based algorithms to search for test cases that cover uncovered paths. Two improved differential evolutionary algorithms based on HBL and THBL are then proposed to solve ATCG-PC. Experimental studies on thirty instances generated by eight classical benchmark programs and six fog computing benchmark programs show that the proposed algorithms achieve highest path coverage with fewer test cases and less running time than some compared state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The extremely sensitive and highly non-linear search space of interplanetary transfer trajectory design brings about big challenges on global optimization. As a representative, the current known best solution (fuel consumption) of the global trajectory optimization problem designed by the European space agency is very hard to be found. To deal with this difficulty, a powerful differential evolution with the guided movement for population, named G_DE is proposed in this paper. G_DE employs a two-stage evolutionary process, which concentrates on learning global structure in the earlier process, and tends to self-adaptively probe the structures of numerous local spaces at a later stage. During these two stages, four guidance strategies related to the learning from the population distribution are proposed. The experimental test results show that G_DE can find the current known best solutions of Cassini1 and Sagas directly. For the newly proposed GTOP-X problem, G_DE has found state-of-the-art solutions for four encounter sequences, and using five gravity assists, G_DE found encounter sequences with fuel consumption as low as 1.5676 km/s. The experimental test on 10D CEC2017 problems proves G_DE has a comparable performance with recently proposed differential evolution variant. [ABSTRACT FROM AUTHOR]