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The estimation of distribution algorithm (EDA) has recently emerged as a promising alternative to the traditional evolutionary algorithms for solving combinatorial optimization problems. In this paper, an estimation of distribution algorithm with multiple intensification strategies (EDA-MIS) is proposed to solve a typical kind of hybrid flow-shop scheduling problem. The two-stage heterogeneous hybrid flow-shop scheduling problem is investigated. The sequence-dependent setup time at the first stage is also considered. In the proposed EDA-MIS, the initial population is constructed through the heuristic method and random strategy. An order matrix is established to estimate the probabilistic model of promising solutions. Then the solutions of the algorithm are evolved through the processes of selection, recombination, sampling, and local search. The obtained results indicate that the EDA-MIS provides good solutions in the aspects of solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) and Estimation of distribution algorithm (EDA) exhibit complementary superiority in solving complex continuous optimization and engineering problems. The design of appropriate strategies coordinated with the two algorithms to balance exploration and exploitation is conducive to obtaining high-precision solutions. A knowledge-driven co-evolutionary algorithm assisted by a cross-regional interactive learning mechanism (KCACIL) is proposed to achieve a comprehensive collaboration between the algorithms, diverse strategies, and cross-regional individuals. Various elite-guided mutation strategies and a self-feedback strategy based on successful experience in light of implicit knowledge are devoted to fulfilling self-learning and cross-regional interactive learning to accomplish individual collaboration and knowledge transfer in the three regions. Reinforcement learning based on ε − g r e e d y and simulated annealing is employed as feedback on the cross-regional individual information to promote the collaboration between opposition-based learning, interaction learning mechanism, and the revised strategy of inferior solutions with small Q values and high distance density. The dynamic self-adaptive adjustment strategies of multiple parameters are adopted to balance diversity and convergence. KCACIL is verified on the CEC 2014, 2017, 2020 benchmark test suites, and engineering applications. Experimental results indicate KCACIL is superior to the state-of-the-art comparison algorithms. • A knowledge-driven comprehensive co-evolutionary algorithm is proposed. • Cross-regional interactive learning with adaptive parameters is introduced. • A collaboration of strategies guided by reinforcement learning is implemented. • The learning mechanisms based on intra-regional implicit knowledge are designed. • Two improvement strategies of solutions specific to the phenomenon are employed. [ABSTRACT FROM AUTHOR]

A co-evolutionary migrating birds optimization algorithm based on online learning policy gradient (CMBO-PG) is proposed to address complex continuous real-parameter optimization problems. In CMBO-PG, a Gaussian estimation of distribution algorithm (GEDA), which enhances the exploitation tendency, is utilized to generate the solutions of the leading flock. The neighborhood solutions of the following flock are produced by a multi-strategy learning mechanism to promote exploration capability. The co-evolution of the leading flock and following flock is realized by the information-sharing mechanism and the operation of destruction and construction to keep the balance of exploration and exploitation. The nonlinear selection of mutation strategies is laborious due to the differences in the ability to address optimization problems. In the mechanism of multi-strategy learning, a long short-term memory (LSTM) is adopted as a selector of mutation strategies to predict the selection probability of three mutation strategies. The evolutionary procedure of the following flock is modeled as a Markov decision process (MDP). The policy gradient (PG) is employed as a model optimizer to control the parameters of LSTM based on the historical feedback information. The performance of CMBO-PG is testified on the CEC 2017 benchmark test suite. The experimental results show that CMBO-PG is superior to the 12 comparison algorithms, including state-of-art algorithms. [ABSTRACT FROM AUTHOR]

• A novel cooperative learning fruit fly optimization algorithm (HGCLFOA) is proposed. • The hierarchical guidance strategy for local search is implemented in the olfactory search. • The inferior solution repairing (ISR) strategy is employed to modify the search direction. • The hybrid GEDA with previous information is applied to guide the evolution in vision search. • A probability selection strategy based on feedback of objective space is introduced. The fruit fly optimization algorithm (FOA) has drawn enormous attention from researchers and practitioners in the computation intelligence domain for the benefits of simple implementation mechanism and few parameters tuning requirement of FOA. However, FOA is hard to adapt directly to address complex continuous problems. A hierarchical guidance strategy assisted fruit fly optimization algorithm with cooperative learning mechanism (HGCLFOA) is proposed in this study. The population is divided into elitist and inferior subpopulations with the fitness of objective function. The population center is re-designed as an elitist subpopulation to maintain the diversity of the population. In the olfaction search stage, the hierarchical guidance strategy is introduced for local search according to the difference of solution qualities to assign inferior individuals to elitist individuals on different levels. Meanwhile, the inferior information is applied by the inferior solutions repairing strategy to deflect the prediction of the elitist subpopulation for preventing HGCLFOA from falling into the local optimum. In the vision search stage, a hybrid Gaussian distribution estimation strategy is adopted to extract the elitist information of previous generations to predict the distribution of potential elitist individuals in the next generation. The exploration and exploitation of the HGCLFOA are balanced by the cooperation between elitist subpopulation and inferior subpopulation. A random walk strategy is activated to assist the elitist solutions to jump out the local optimal. The parameters of the HGCLFOA are calibrated by DOE and ANOVA methods. The experimental results demonstrated that the HGCLFOA outperformed the classical FOA and state-of-arts variants of FOA. [ABSTRACT FROM AUTHOR]