Low carbon manufacturing has received increasingly more attention in the context of global warming. The flexible job shop scheduling problem (FJSP) widely exists in various manufacturing processes. Researchers have always emphasized manufacturing efficiency and economic benefits while ignoring environmental impacts. In this paper, considering carbon emissions, a multi-objective flexible job shop scheduling problem (MO-FJSP) mathematical model with minimum completion time, carbon emission, and machine load is established. To solve this problem, we study six variants of the non-dominated sorting genetic algorithm-III (NSGA-III). We find that some variants have better search capability in the MO-FJSP decision space. When the solution set is close to the Pareto frontier, the development ability of the NSGA-III variant in the decision space shows a difference. According to the research, we combine Pareto dominance with indicator-based thought. By utilizing three existing crossover operators, a modified NSGA-III (co-evolutionary NSGA-III (NSGA-III-COE) incorporated with the multi-group co-evolution and the natural selection is proposed. By comparing with three NSGA-III variants and five multi-objective evolutionary algorithms (MOEAs) on 27 well-known FJSP benchmark instances, it is found that the NSGA-III-COE greatly improves the speed of convergence and the ability to jump out of local optimum while maintaining the diversity of the population. From the experimental results, it can be concluded that the NSGA-III-COE has significant advantages in solving the low carbon MO-FJSP.

Evolutionary Algorithms (EAs) based Unmanned Aerial Vehicle (UAV) path planners have been extensively studied for their effectiveness and high concurrency. However, when there are many obstacles, the path can easily violate constraints during the evolutionary process. Even if a single waypoint causes a few constraint violations, the algorithm will discard these solutions. In this paper, path planning is constructed as a multi-objective optimization problem with constraints in a three-dimensional terrain scenario. To solve this problem in an effective way, this paper proposes an evolutionary algorithm based on multi-level constraint processing (ANSGA-III-PPS) to plan the shortest collision-free flight path of a gliding UAV. The proposed algorithm uses an adaptive constraint processing mechanism to improve different path constraints in a three-dimensional environment and uses an improved adaptive non-dominated sorting genetic algorithm (third edition—ANSGA-III) to enhance the algorithm’s path planning ability in a complex environment. The experimental results show that compared with the other four algorithms, ANSGA-III-PPS achieves the best solution performance. This not only validates the effect of the proposed algorithm, but also enriches and improves the research results of UAV path planning.

Swarm-based algorithm can successfully avoid the local optimal constraints, thus achieving a smooth balance between exploration and exploitation. Salp swarm algorithm (SSA), as a swarm-based algorithm on account of the predation behavior of the salp, can solve complex daily life optimization problems in nature. SSA also has the problems of local stagnation and slow convergence rate. This paper introduces an improved salp swarm algorithm, which improve the SSA by using the chaotic sequence initialization strategy and symmetric adaptive population division. Moreover, a simulated annealing mechanism based on symmetric perturbation is introduced to enhance the local jumping ability of the algorithm. The improved algorithm is referred to SASSA. The CEC standard benchmark functions are used to evaluate the efficiency of the SASSA and the results demonstrate that the SASSA has better global search capability. SASSA is also applied to solve engineering optimization problems. The experimental results demonstrate that the exploratory and exploitative proclivities of the proposed algorithm and its convergence patterns are vividly improved.

Proposing new strategies to improve the optimization performance of differential evolution (DE) is an important research study. The jSO algorithm was the announced winner of the Congress on Evolutionary Computation (CEC) 2017 competition on numerical optimization, and is the state-of-the-art algorithm in the SHADE (Success-History based Adaptive Differential Evolution) algorithm series. However, the jSO algorithm converges prematurely in the search space with different dimensions and is prone to falling into local optimum during evolution, as well as the problem of decreasing population diversity. In this paper, a modified jSO algorithm (MjSO) is proposed which is based on cosine similarity with parameter adaptation and a novel opposition-based learning restart mechanism incorporated with symmetry to address the above problems, respectively. Moreover, it is well known that parameter setting has a significant impact on the performance of the algorithm and the search process can be divided into two symmetrical parts. Hence, a parameter control strategy based on a symmetric search process is introduced in the MjSO. The effectiveness of these designs is supported by presenting a population clustering analysis, along with a population diversity measure to evaluate the performance of the proposed algorithm, three state-of-the-art DE variant algorithms (EBLSHADE, ELSHADE-SPACMA, and SALSHADE-cnEPSin) and two original algorithms (jSO and LSHADE) are compared with it, for solving 30 CEC’17 benchmark functions and three classical engineering design problems. The experimental results and analysis reveal that the proposed algorithm can outperform other competitions in terms of the convergence speed and the quality of solutions. Promisingly, the proposed method can be treated as an effective and efficient auxiliary tool for more complex optimization models and scenarios.

Particle swarm optimization (PSO) has the disadvantages of easily getting trapped in local optima and a low search accuracy. Scores of approaches have been used to improve the diversity, search accuracy, and results of PSO, but the balance between exploration and exploitation remains sub-optimal. Many scholars have divided the population into multiple sub-populations with the aim of managing it in space. In this paper, a multi-stage search strategy that is dominated by mutual repulsion among particles and supplemented by attraction was proposed to control the traits of the population. From the angle of iteration time, the algorithm was able to adequately enhance the entropy of the population under the premise of satisfying the convergence, creating a more balanced search process. The study acquired satisfactory results from the CEC2017 test function by improving the standard PSO and improved PSO.

Single objective optimization algorithms are the foundation of establishing more complex methods, like constrained optimization, niching and multi-objective algorithms. Therefore, improvements to single objective optimization algorithms are important because they can impact other domains as well. This paper proposes a method using turning-based mutation that is aimed to solve the problem of premature convergence of algorithms based on SHADE (Success-History based Adaptive Differential Evolution) in high dimensional search space. The proposed method is tested on the Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions for all SHADE, L-SHADE, and jSO algorithms. The effectiveness of the method is verified by population diversity measure and population clustering analysis. In addition, the new versions (Tb-SHADE, TbL-SHADE and Tb-jSO) using the proposed turning-based mutation get apparently better optimization results than the original algorithms (SHADE, L-SHADE, and jSO) as well as the advanced DISH and the jDE100 algorithms in 10, 15, and 20 dimensional functions, but only have advantages compared with the advanced j2020 algorithm in 5 dimensional functions.