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Locating multiple roots of nonlinear equation systems (NESs) remains a challenging and meaningful task in the numerical optimization community. Although a large number of NES-solving approaches have been put forward, they can only find the roots of one NES at a time. In this paper, we develop a novel NES-solving algorithm based on evolutionary multitasking referred to as EMNES, the goal of which is to effectively find the multiple roots of multiple different NESs simultaneously in a single run through knowledge sharing and transfer. Specifically, firstly a NES-solving framework based on evolutionary multitasking is proposed. Then an efficient multi-task evolutionary algorithm based on neighborhood-based speciation differential evolution for NESs is designed. Finally, combining Gaussian distribution and uniform distribution, a novel resource release strategy is proposed to release the found roots to improve resource utilization and increase population diversity. Numerous experimental results reveal that the proposed EMNES algorithm can achieve a higher root rate and success rate when compared with several well-established algorithms on thirty NESs. Furthermore, simulation results on a more complex test set show that the proposed EMNES is able to locate more roots than most comparison algorithms. • An evolutionary multitasking NES-solving framework is proposed. • Relationship of different NESs is established by a unified search space. • An adaptive mutation strategy with knowledge transfer is presented. • A novel resource release strategy is developed to improve the utilization of computing resources. [ABSTRACT FROM AUTHOR]

The performance of photovoltaic (PV) system relies on the accurate determination of unknown parameters in PV models, such as photo-generated current, diode current, and resistance. These unknown parameters may vary with different temperature and irradiance conditions, which greatly increases the difficulty of identifying these unknown parameters. Although some parameter identification methods have been proposed to solve such a problem, the accuracy and reliability of solutions obtained by these methods suffers from great challenges when temperature and irradiance are changing. In this paper, a simple and effective approach called success-history adaptation differential evolution with linear population size reduction (L-SHADE) and decomposition referred as (L-SHADED), is presented to accurately and reliably identify the unknown parameters of PV models under different temperature and irradiance. In L-SHADED, firstly, an unknown parameters decomposition technique is used to reduce the complexity of the problem. Then an advanced evolutionary algorithm L-SHADE is employed to identify the optimal unknown parameter values. The performance of proposed L-SHADED has been investigated by testing two single-diode-based PV modules (multi-crystalline KC200GT and mono-crystalline SM55) under different temperature and irradiance. The experimental comparison results demonstrate that proposed L-SHADED is almost 10 times smaller in RMSE than other methods. Furthermore, the coefficient of determination of L-SHADED reaches 1.0 in almost all conditions, which indicates that the parameters identified by L-SHADED are quite accurate. • An effective unknown parameters decomposition technique is proposed. • The L-SHADE algorithm is used to optimize the non-linear unknown parameters. • A simple yet effective approach for parameter identification of PV models is provided. • The statistical results demonstrate the effectiveness of proposed L-SHADED. [ABSTRACT FROM AUTHOR]

Evolutionary multitasking has attracted much attention in the field of evolutionary computing. Most of the existing multitasking evolutionary algorithms aim at solving unconstrained multitasking optimization problems. The study on constrained multitasking optimization problems is scarce. However, in practical applications, lots of optimization problems contain constraints. In this paper, an adaptive archive-based multifactorial evolutionary algorithm is proposed to solve constrained multitasking optimization problems. First, an archiving strategy is proposed to store infeasible solutions with better objective function values. With this strategy, useful information on infeasible solutions can be exploited to accelerate the convergence rate. Second, the random mating probability is adjusted through an adaptive strategy to facilitate positive knowledge transfer. Finally, a new mutation strategy is proposed to promote convergence by mutating some random individuals and replacing the individuals with the largest constraint violation. By comparing existing constrained multitasking evolutionary algorithms and some constrained single-task evolutionary algorithms, the results reveal the effectiveness of the proposed algorithm in solving constrained multitasking optimization problems. • An evolutionary algorithm for constrained multitasking optimization. • An archiving strategy that promotes convergence via saving valuable infeasible solutions. • An adaptive strategy that promotes positive knowledge transfer via adaptively adjusting random mating probability. • A mutation strategy that promotes convergence by replacement of the worst individuals. • Extensive experiments that confirmed the effectiveness and superiority of our proposed algorithm. [ABSTRACT FROM AUTHOR]

An important factor in constrained multi-objective evolutionary algorithms (CMOEAs) is how to make optimal use of the information of feasible and infeasible solutions. To fully utilize these promising solutions, this paper proposes an archive-based two-stage evolutionary algorithm, called AT-CMOEA, for solving constrained multi-objective optimization problems (CMOPs). AT-CMOEA divides the evolutionary process into two stages — exploration and exploitation. The purpose of the exploration stage is to encourage a broader exploration of the search space to discover some promising regions, which is achieved by two populations with different priorities of constraints and objectives. In the exploitation stage, the goal is to obtain a set of well-distributed Pareto-optimal solutions by utilizing the useful archived information found during the exploration stage, allowing the search resources to be focused on the region of interest. Then, the two populations cooperatively converge to the constrained Pareto front (CPF). Comprehensive experiments on a series of benchmark test problems and three real-world CMOPs demonstrate the competitiveness of our method when compared with other representative algorithms in terms of effectiveness and reliability in finding a set of well-distributed optimal solutions. [ABSTRACT FROM AUTHOR]

Competitive multitasking optimization (CMTO) is a special multitasking optimization paradigm that has been recently proposed. In the CMTO problems, the objective values of all tasks are competitive, and the purpose of CMTO is to find an optimal solution for multiple tasks. However, existing algorithms designed for the CMTO problems perform poorly since their resource allocation strategies are prone to incorrect task selection. To remedy this drawback, this paper proposes an improved multitasking adaptive differential evolution, which can be featured as: (i) a success-history based resource allocation strategy is proposed; (ii) an adaptive random mating probability control strategy is devised to adapt to different task combinations; (iii) an adaptive multitasking differential evolution operator is designed to enhance the searchability. To evaluate the performance of the proposed method, three CMTO benchmark test suites and two real-world optimization problems are chosen. Compared with other related methods, the results show that the proposed method achieved better performance empirically. • Competitive multitasking optimization has good practical significance. • A powerful competitive multitasking evolutionary algorithm is proposed. • A success-history based resource allocation strategy is designed. • An improved differential evolution operator is used to enhance searchability. • An adaptive RMP control strategy is devised for different task combinations. [ABSTRACT FROM AUTHOR]

The balance between multiple objectives and various constraints is the key to solving constrained multi-objective optimization problems (CMOPs). When dealing with CMOPs with complex feasible regions, some evolutionary algorithms suffer from great challenges in converging to the constrained Pareto front (CPF) with well-distributed feasible solutions. To address this issue, this paper proposes a dual-population based bidirectional coevolution algorithm, called DBC-CMOEA, which aims to converge to the CPF using promising solutions explored from both feasible and infeasible regions. To do so, DBC-CMOEA maintains two populations and an archive, where the dual-population is complementary in the search process and the archive is used to retain promising feasible and infeasible solutions, thus facilitating information exchange between these two populations. For updating the archive, a nondominated sorting procedure and an angle-based selected scheme are conducted to store infeasible and feasible solutions, as they can help to maintain the diversity of the search and find more feasible regions. To evolve the CPF from the bidirectional side of the feasible region, a novel mating selection strategy is used to choose appropriate mating parents. In comparison with some related constraint multi-objective optimization algorithms on a number of benchmark problems, experimental results show that the proposed algorithm performs better than the state-of-the-art constrained multi-objective evolutionary optimizers. • A cooperative dual-population algorithm is proposed for solving CMOPs. • Constraints are handled in three different ways to explore the search space. • A brand-new selection strategy is applied to select the mating parents. • A novel archive update strategy is designed to retain the promising information. [ABSTRACT FROM AUTHOR]

The widespread existence of constrained multi-objective optimization problems (CMOPs) in practical applications encourages researchers to devote more efforts to the development of constrained multi-objective evolutionary algorithms (CMOEAs). An efficient way of handling CMOPs is to balance the satisfaction of constrains and the optimization of objective functions. Although many approaches have been designed to this end, most of them are still unable to handle CMOPs with diverse characteristics effectively. To remedy this issue, a simple and generic two-stage framework is proposed in this paper to achieve better efficiency and versatility for CMOPs. Specifically, the whole search process is simply divided into two stages with different purposes: (i) Stage 1 focuses on approaching the unconstrained Pareto front (PF) and storing the obtained feasible solutions in the archive. During stage 1 , the archive is updated to promote convergence and diversity; (ii) Stage 2 is mainly designed to obtain the constrained PF of CMOPs. First, the solutions in the archive are used to form the initial population. Afterwards, the constrained Pareto front (CPF) is extensively explored. Based on this framework, a CMOEA, referred to as C-TSEA, is presented. Fifty-seven instances in five benchmark test suites are chosen to evaluate the performance of our approach. Compared with seven advanced CMOEAs, the results demonstrate the superiority or at least competitiveness of C-TSEA. The generality of the proposed framework is also verified by integrating other methods in the proposed framework. • A simple and generic two-stage framework is proposed for CMOPs. • C-TSEA is presented based on the framework to effectively solve CMOPs. • Fifty-seven CMOPs are chosen to extensively evaluate its performance. • C-TSEA gets better or competitive results compared with other methods. [ABSTRACT FROM AUTHOR]