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The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization. [ABSTRACT FROM AUTHOR]

The invasive weed algorithm (IWO) is a meta-heuristic algorithm, which is an effective and promising optimiser to address the optimisation problems. In this study, a hybrid algorithm based on the self-adaptive invasive weed algorithm (IWO) and differential evolution algorithm (DE), named SIWODE, is proposed to address the continuous optimisation problems. In the proposed SIWODE, first, the two parameters are adaptively proposed to improve the convergence speed of the algorithm. Second, the crossover and mutation operations are introduced in SIWODE to improve the population diversity and increase the exploration capability during the iterative process. Furthermore, a local perturbation strategy is presented to improve exploitation ability during the late process. The exploration and exploitation ability of the algorithm is effectively balanced by cooperative mechanisms. The experiment results of SIWODE show that the SIWODE has the superior searching quality and stability than other mentioned approaches. [ABSTRACT FROM AUTHOR]

Water Wave Optimisation algorithm (WWO) is a new swarm-based metaheuristic inspired by shallow wave models for global optimisation. In this paper, an enhanced WWO, which combines with multiple assistant strategies (EWWO), is proposed. First, the random opposition-based learning (ROBL) mechanism is introduced to generate the initial population with high quality. Second, a new modified operation is designed and embedded into propagation operation to balance the global exploration and the local exploitation. Third, the covariance matrix self-adaptation evolution strategy (CMA-ES) is employed by the refraction operation to further strengthen the local exploitation. Furthermore, the diversity of the population is maintained in the evolution process by using a crossover operator. The experiment results based on CEC 2017 benchmarks indicate that the EWWO outperforms the state-of-the-art variant algorithms of the WWO and the standard WWO. [ABSTRACT FROM AUTHOR]

The large-scale real value problem in continuous and discrete optimization problems is a challenging issue for researchers and practitioners in the manufacturing domain. An improved artificial bee colony algorithm (ABC) combined with multi-agent reinforcement learning (called MARLABC) is presented for addressing the large-scale real value optimization problem in this study. Two stages including the training and the testing are introduced in the MARLABC via the multi-agent central controller to improve the convergence speed and local exploitation capability of the algorithm. The optimal strategy pool is constructed by training procedures via the multi-agent central controller with Q-learning mechanism. The effective strategy is selected from the optimal strategy pool for each agent during the testing process in the multi-agent central controller. The elite agents in the training population are reserved to generate the testing population to guide the search. The MARLABC algorithm is compared with the ABC variants and state-of-art algorithms on CEC 2017 benchmark problems. The stability and effectiveness of the MARLABC algorithm are confirmed by the experimental results. [ABSTRACT FROM AUTHOR]

• A distributed no-wait flow shop scheduling problem with due windows is proposed. • A discrete knowledge-guided learning fruit fly optimization is designed. • The KNEH dw based on no-wait problem property knowledge is introduced. • A probability knowledge model with learning and feedback is designed. • The variable neighborhood descent (VND) strategy is employed. The distributed no-wait flow shop scheduling problem with due windows (DNWFSPDW) is a novel and considerable model for modern production chain and large manufacturing industry. The object of total weighted earliness and tardiness (TWET dw) is a common cost indicator in application. A discrete knowledge-guided learning fruit fly optimization algorithm (DKLFOA) is proposed in this study to minimize TWET in DNWFSPDW. A knowledge-based structural initialization method (KNEH dw) is proposed to construct an effective initial solution. In the KNEH dw , the property that the job has no waiting time between processing machines in the no-wait flow shop scheduling problem is abstracted as knowledge to instruct jobs to be placed in possible positions. The swarm center expands from a single individual to an elitist swarm in the vision search stage. A probability knowledge model is established based on the sequence relationship of jobs in the elite population. The feedback information in the iterative process using the probabilistic knowledge model leads the population to search in the direction with a high success rate. The inferior individuals are allocated to the corresponding elite individuals for the local search in the olfactory search stage. The knowledge of weight in due windows is utilized to avoid invalid search during the iteration process. The variable neighborhood descent (VND) strategy is adopted in the local search to enhance the accuracy of the proposed algorithm and jump out of the local optimal. The design of experimental method (DOE) is introduced to calibrate the parameters in the algorithm. The simulation results show that DKLFOA has advantages for solving DNWFSPDW problems comparing with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

An improved Jaya algorithm named surrogate-assisted Jaya algorithm based on optimal directional guidance and historical learning mechanism (SDH-Jaya) is proposed in this study to address the continuous optimization problems. In the SDH-Jaya, a surrogate-assisted model combined with the polynomial model and radial basis model built by the individual with real fitness is introduced to decrease the expensive computational simulations and accelerate the convergence speed. Two co-evolutionary mechanisms, which are named assisted co-evolutionary mechanism and self-learning co-evolutionary mechanism, are proposed to optimize the surrogate model and evolutionary population. Search directions and steps of the SDH-Jaya are adjusted adaptively by the differential vector resulting from the best solution and worst solution in the candidates at each generation. The historical population stored in an archive is selected randomly to provide new search areas for improving the diversity of the population during the evolution process of the SDH-Jaya. The performance of SDH-Jaya is tested on CEC2017 benchmark problems. The experimental results reveal that the effectiveness of the SDH-Jaya algorithm outperforms the classical Jaya algorithm, its variants, and state-of-the-art algorithms in terms of the quality of solution and execution time. • The SDH-Jaya based on optimal directional guidance and historical learning is proposed. • A surrogate-assisted model is introduced in the SDH-Jaya. • The co-evolutionary and self-learning mechanism are incorporated in the surrogate model. • The differential vector is utilized to adjust the search directions and steps. • The historical population stored in the archive is adopted to generate new search areas. [ABSTRACT FROM AUTHOR]

Brain storm optimization algorithm (BSO), which is inspired by brain storm process of human, has been adopted as an efficient optimizer for various complex problems. A reinforcement learning brain storm optimization algorithm (RLBSO) to improve the performance of BSO is proposed in this paper. Four mutation strategies are designed to enhance the search capability of the algorithm in different stages. Elites are adopted as the guidance to ensure the quality of the population. The global best is utilized to guide the search direction of individuals. The cluster centers are employed to improve the exploitation ability of the algorithm. The historical individuals are utilized to the increase the diversity of the population. The Q-learning mechanism is introduced to guide the selection of strategies according to the historical information fed back by the corresponding strategies. A self-learning mechanism, which is based on the evolutionary state of the population and the experience of previous successful individuals, is utilized to determine the update method of individual. The RLBSO algorithm is tested on the CEC 2017 benchmark test suite and a practical engineering problem. The results show that RLBSO has better performance than the other state of the arts algorithms. • A reinforcement learning brain storm optimization algorithm (RLBSO) is proposed. • Four mutation strategies are introduced to increase the ability of global search. • Q-learning is utilized to guide the algorithm to the appropriate evolution strategy. • A self-learning strategy is utilized to determine the update method of the individual. • The RLBSO algorithm is tested on the CEC 2017 benchmark test suite. [ABSTRACT FROM AUTHOR]

• An ensemble discrete differential evolution (EDE) algorithm is proposed. • Two different heuristic methods and one random strategy are introduced into EDE. • The mutation, crossover and selection operators are redesigned to assist the EDE algorithm. • An elitist retain strategy is introduced into the framework of EDE algorithm. • The parameters of the EDE algorithm are calibrated by the design of experiments (DOE) method. The distributed blocking flowshop scheduling problem (DBFSP) plays an essential role in the manufacturing industry and has been proven to be as a strongly NP-hard problem. In this paper, an ensemble discrete differential evolution (EDE) algorithm is proposed to solve the blocking flowshop scheduling problem with the minimization of the makespan in the distributed manufacturing environment. In the EDE algorithm, the candidates are represented as discrete job permutations. Two heuristics method and one random strategy are integrated to provide a set of desirable initial solution for the distributed environment. The front delay, blocking time and idle time are considered in these heuristics methods. The mutation, crossover and selection operators are redesigned to assist the EDE algorithm to execute in the discrete domain. Meanwhile, an elitist retain strategy is introduced into the framework of EDE algorithm to balance the exploitation and exploration ability of the EDE algorithm. The parameters of the EDE algorithm are calibrated by the design of experiments (DOE) method. The computational results and comparisons demonstrated the efficiency and effectiveness of the EDE algorithm for the distributed blocking flowshop scheduling problem. [ABSTRACT FROM AUTHOR]

• A two-stage evolution strategy is proposed for solving multi-objective problem. • The convergence and diversity should be balanced in multi-objective optimization. • A local searching method can improve the diversity of solutions in the space. • Experimental results have been presented by using statistical method. The balance of convergence and diversity plays a significant role to the performance of multi-objective evolutionary algorithms (MOEAs). The MOEA/D is a very popular multi-objective optimization algorithm and has been used to solve various real world problems. Like many other algorithms, the MOEA/D also has insufficient ability of convergence and diversity when tackling certain complex multi-objective optimization problems (MOPs). In this paper, a novel algorithm named MOEA/D-TS is proposed for effectively solving MOPs. The new algorithm adopts two stages evolution strategies, the first stage is focused on pushing the solutions into the area of the Pareto front and speeding up its convergence ability, after that, the second stage conducts in the operating solution's diversity and makes the solutions distributed uniformly. The performance of MOEA/D-TS is validated in the ZDT, DTLZ and IMOP problems. Compared with others popular and variants algorithms, the experimental results demonstrate that the proposed algorithm has advantage over other algorithms with regard to the convergence and diversity in most of the tested problems. [ABSTRACT FROM AUTHOR]