Evolutionary algorithms have shown their promise in coping with many-objective optimization problems. However, the strategies of balancing convergence and diversity and the effectiveness of handling problems with irregular Pareto fronts are still far from perfect. To address these issues, this paper proposes an adaptive sorting-based evolutionary algorithm based on the idea of decomposition. Firstly, we propose an adaptive sorting-based environmental selection strategy. Solutions in each subpopulation (partitioned by reference vectors) are sorted based on their convergence. Those with better convergence are further sorted based on their diversity, then being selected according to their sorting levels. Secondly, we provide an adaptive promising subpopulation sorting-based environmental selection strategy for problems which may have irregular Pareto fronts. This strategy provides additional sorting-based selection effort on promising subpopulations after the general environmental selection process. Thirdly, we extend the algorithm to handle constraints. Finally, we conduct an extensive experimental study on the proposed algorithm by comparing with start-of-the-state algorithms. Results demonstrate the superiority of the proposed algorithm.

With respect to multicriteria group decision‐making (MCGDM) problems in which the experts have different priority levels, the criteria values are in the form of Pythagorean fuzzy uncertain linguistic variables (PFULVs), and the information about weights of experts and criteria is completely unknown, a novel decision‐making method is developed. Firstly, the concept of PFULV is defined, and some operational laws, score function, accuracy function, and normalized Hamming distance of PFULVs are presented. Then, to aggregate information given by all experts, the Pythagorean fuzzy uncertain linguistic prioritized weighted averaging aggregation (PFULPWAA) operator and the Pythagorean fuzzy uncertain linguistic prioritized weighted geometric aggregation (PFULPWGA) operator are proposed. Furthermore, in order to get a comprehensive evaluation value for each alternative, the Pythagorean fuzzy uncertain linguistic Maclaurin symmetric mean aggregation (PFULMSMA) operator and the weighted PFULMSMA (WPFULMSMA) operator are proposed. Moreover, to obtain the information about the weights of criteria, the model based on grey relational analysis (GRA) method is established. Finally, a method of MCGDM with PFULVs is developed, and an application example is given to illustrate the validity and feasibility of the provided procedure.

The article selects socioeconomic data related to 146 prefecture-level cities included in nine city clusters from 2014 to 2018 to establish a city-level socioeconomic system in China. A sensitivity analysis of regional entrepreneurship and economic quality development based on system dynamics was conducted to explore the changes in regional entrepreneurship and economic quality development over time and their sensitivity factors. In this way, the dynamic evolution mechanism of the system can be portrayed, and the optimization of the system can be achieved through the coordination of the factors within the system. The article sets up three scenarios to explore the fluctuations in regional entrepreneurship and economic quality development when three sensitive factors, namely, business environment, financial services scale, and innovation environment, change. Findings: There are differences in the development of cities within city clusters. The business environment and high-quality economic development of the central cities within the city cluster are stronger than those of the non-central cities. Therefore, regions should focus on synergistic development within city clusters when formulating related policies. The variation of regional entrepreneurship development and economic quality development, after a factor in the system is changed, is asymmetric. Because the sensitivity of different urban clusters and the way they are affected by sensitive factors varies, the state should pay more attention to the adaptability of cities when formulating corresponding policy measures and adapt its policy measures to the sensitivity characteristics of each region according to local conditions.

The purpose of this paper is to provide an effective solution method for the truck and trailer routing problem (TTRP) which is one of the important NP-hard combinatorial optimization problems due to its multiple real-world applications. It is a generalization of the famous vehicle routing problem (VRP), involving a group of geographically scattered customers served by the vehicle fleet including trucks and trailers. The meta-heuristic solution approach based on bat algorithm (BA) in which a local search procedure performed by five different neighborhood structures is developed. Moreover, a self-adaptive (SA) tuning strategy to preserve the swarm diversity is implemented. The effectiveness of the proposed SA-BA is investigated by an experiment conducted on 21 benchmark problems that are well known in the literature. Computational results indicate that the proposed SA-BA algorithm is computationally efficient through comparison with other existing algorithms found from the literature according to solution quality. As for the actual computational time, the SA-BA algorithm outperforms the others. However the scaled computational time of SA-BA algorithm underperforms the other algorithms. In this work the authors show that the proposed SA-BA is effective as a method for the TTRP problem. To our knowledge, the bat algorithm has not been earlier applied, as in this work, to solve the TTRP problem.