Amid the global push for sustainable development, rising market demands have necessitated a multiregional, multiobjective, and flexible production model. Against this backdrop, this article investigates the multiobjective distributed flow shop group scheduling problem by formulating a mathematical model and introducing an advanced memetic algorithm integrated with reinforcement learning (RLMA). The RLMA involves a novel cooperative crossover operation in conjunction with the nature of the coupled problems to extensively explore the solution space. Additionally, the Sarsa algorithm enhanced with eligibility traces guides the selection of optimal schemes during the local enhancement phase. To ensure a balance between convergence and diversity, a solution selection strategy based on penalty-based boundary intersection decomposition is utilized. Furthermore, the increasing-efficiency and reducing-consumption strategies integrating a rapid evaluation mechanism are designed by dynamically changing the machine speed to balance economic and sustainability metrics. Comprehensive numerical experiments and comparative analyses demonstrate that the proposed RLMA surpasses existing state-of-the-art algorithms in addressing this complex problem.

Flexible job shop scheduling problem (FJSP) is one of the challenging issues in industrial systems. In this study, we propose a bi-population balancing multi-objective evolutionary algorithm, to solve the distributed FJSPs from a steelmaking system, with considering the fuzzy processing time and crane transportation processes. Two objectives are considered simultaneously, including minimization of the maximum fuzzy completion time and the energy consumption during machine processing and crane transportation. Firstly, the mathematical model is formulated for the considered problem. Then, an efficient problem-specific initialization heuristic is developed. To balance the convergence and diversity abilities, a novel crossover operator and two cooperative population environmental selection mechanisms are developed. In addition, an efficient population size adaptive adjustment mechanism is designed. Then, an enhanced local search heuristic is developed to further improve the searching abilities. Finally, a set of randomly generated instances based on realistic industrial processes are tested, and through comprehensive computational comparison and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several presented algorithms.Note to Practitioners—In practical manufacturing processes, the processing times for each job should not be considered as deterministic values because of the disruption events, such as machine breakdown, resource limitation, and machine maintenance. Therefore, the fuzzy scheduling should be considered in many industrial procedures. This study considered multi-objective optimization flexible job shop with energy and robotic transportations, where the fuzzy makespan and energy consumptions are minimized simultaneously. Two populations balancing the convergence and diversity abilities are developed. Efficient problem-specific heuristics are designed to enhance the searching performance. The proposed methods can be generalized and applied to many applications considering both the realistic constraints and objectives.

Multimodal multiobjective optimization problems (MMOPs) are commonly seen in real-world applications. Many evolutionary algorithms have been proposed to solve continuous MMOPs. However, little effort has been made to solve combinatorial (or discrete) MMOPs. Searching for equivalent Pareto-optimal solutions in the discrete decision space is challenging. Moreover, the true Pareto-optimal solutions of a combinatorial MMOP are usually difficult to know, which has limited the development of its optimizer. In this article, we first propose a test problem generator for multimodal multiobjective traveling salesman problems (MMTSPs). It can readily generate MMTSPs with known Pareto-optimal solutions. Then, we propose a novel evolutionary algorithm to solve MMTSPs. In our proposed algorithm, we develop two new edge assembly crossover operators, which are specialized in searching for superior solutions to MMTSPs. Moreover, the proposed algorithm uses a new environmental selection operator to maintain a good balance between the objective space diversity and decision space diversity. We compare our algorithm with five state-of-the-art designs. Experimental results convincingly show that our algorithm is powerful in solving MMTSPs.

Handling energy resource management (ERM) in today’s energy systems is complex and challenging due to uncertainties arising from the high penetration of distributed energy resources. Such penetration introduces various uncertain factors, such as renewable energy, energy storage, and electric vehicles, making it difficult for traditional mathematical methods to find effective solutions. However, Evolutionary Algorithms (EAs) have shown good performance in solving this problem. Therefore, in this paper, a self-adaptive collaborative differential evolution algorithm (SADEA) is proposed to solve the ERM problem under uncertainty. In SADEA, a three-stage adaptive collaboration strategy, includes boundary randomization stage, knowledge-assisted collaboration stage, and range restructuration stage, is used to generate collaborative solutions. The collaborative solutions generated in the above stages will jointly participate in the perturbation of DE strategies to explore promising solutions. In addition, different DE strategies are selected according to count values and random factors. At the end of the algorithm, boundary control, elite selection and retention are used to ensure the legitimacy and robustness of solutions. The proposed SADEA is compared to several state-of-the-art algorithms on a real-world distribution network located in Salamanca, Spain. The results show that SADEA is superior to its competitors in terms of the objective function, ranking index, and convergence. In summary, the proposed algorithm is effective to handle the ERM problem under uncertainty.

Sustainable scheduling within the manufacturing field has garnered substantial attention from both academia and industry. The escalating market demands have heightened requirements on the flexibility of production modes, multi-zone, and multi-objective. In this context, our study explores the intricacies of the multi-objective distributed flow shop group scheduling problem with sequence-dependent setup times, aiming to concurrently optimize makespan and total energy consumption (DFm|group, sdst|#(Cmax, TEC) ). Firstly, a mathematical model is constructed to analyze problem characteristics. Subsequently, we introduce a collaborative multi-objective evolutionary algorithm driven by indicators (CMOEA/I). In CMOEA/I, an indicator-driven approach is proposed for solution selection, which approximates the Pareto front based on the convergence indicator, while screening potential solutions based on the spread indicator. Furthermore, a collaborative model and local search are developed by incorporating the intrinsic linkages of factories, groups, and jobs. Additionally, to further explore the potential non-dominated solutions, a speed variation strategy is devised based on the pivots of decreasing speed to save energy and increasing speed to reduce makespan. An extensive set of simulation experiments is conducted on a diverse range of test instances. Through meticulous statistical analysis, the outcomes demonstrate that the CMOEA/I exhibits efficacy when contrasted with other advanced algorithms.

Automated guided vehicles (AGVs) have become indispensable transportation tools in intelligent production workshops. The current AVG scheduling system has almost no processing capacity for temporary special cases and mostly depends on the path planning part to solve them, which can only reduce the cost waste caused to a certain extent. In this article, a dynamic AGV scheduling model is proposed, including an aperiodic departure method and a real-time task list update method. Compared with the static AGV scheduling model, the new model can reassign the AGVs for new tasks and special cases. A discrete invasive weed optimization (DIWO) algorithm with parameter adaptation and computing time adaptation is used to prove the effectiveness of the new model. The proposed model is verified by the cases from actual production workshops, which proves the effectiveness of the proposed dynamic AGV scheduling model for the special cases.

A multi-modal multi-objective optimization problem (MMOP) may have equivalent Pareto optimal solutions. These solutions are different in the decision space but correspond to the same objective vector. Searching for equivalent Pareto optimal solutions with evolutionary algorithms is a hot topic in recent years. However, most existing researches are about continuous MMOPs, whereas there are few studies on discrete MMOPs. In this paper, we discuss the property of the multi-modal multi-objective traveling salesman problem and present a set of test problems. Then, we propose an evolutionary optimizer to solve the problem. Experimental results show that our evolutionary optimizer can find more equivalent Pareto optimal solutions than traditional multi-objective evolutionary optimizers on the test problems.

Multi-modal multi-objective optimization problems may have different Pareto optimal solutions with the same objective vector. A number of evolutionary multi-modal multiobjective algorithms have been developed to solve these problems. They aim to search for a Pareto optimal solution set with good diversity in both the objective and decision spaces. Although the normalization in both the objective and decision spaces is very important for these algorithms, there are few studies on this topic. In this paper, we investigate the effect of four normalization methods on two evolutionary multi-modal multiobjective algorithms. Six distance minimization problems are chosen as test problems. The experimental results show that the effect of normalization in evolutionary multi-modal multiobjective optimization is algorithm- and problem-dependent.

In this article, we propose a hybrid artificial bee colony (ABC) algorithm to solve a parallel batching distributed flow-shop problem (DFSP) with deteriorating jobs. In the considered problem, there are two stages as follows: 1) in the first stage, a DFSP is studied and 2) after the first stage has been completed, each job is transferred and assembled in the second stage, where the parallel batching constraint is investigated. In the two stages, the deteriorating job constraint is considered. In the proposed algorithm, first, two types of problem-specific heuristics are proposed, namely, the batch assignment and the right-shifting heuristics, which can substantially improve the makespan. Next, the encoding and decoding approaches are developed according to the problem constraints and objectives. Five types of local search operators are designed for the distributed flow shop and parallel batching stages. In addition, a novel scout bee heuristic that considers the useful information that is collected by the global and local best solutions is investigated, which can enhance searching performance. Finally, based on several well-known benchmarks and realistic industrial instances and via comprehensive computational comparison and statistical analysis, the highly effective performance of the proposed algorithm is favorably compared against several algorithms in terms of both solution quality and population diversity.

This paper presents a novel migrating birds optimization (NMBO) algorithm for solving the lot-streaming flowshop scheduling problem with minimizing makespan. The proposed NMBO algorithm utilizes discrete job permutations to represent solutions, and applies multiple neighborhoods based on insert and swap operators to improve the leading solution. Two new crossover operators, i.e., similar job order with artificial chromosome crossover, and similar block order crossover are employed to obtain solutions for the rest migrating birds. An initialization scheme based on the problem-specific heuristics is presented to generate an initial population with a certain level of quality and diversity. A local search based on the insert neighborhood is embedded to improve the algorithm's local exploitation ability. NMBO is compared with the existing discrete invasive weed optimization, estimation of distribution algorithm and modified MBO algorithms based on the well-known lot-streaming flow shop benchmark. The computational results and comparison demonstrate the superiority of the proposed NMBO algorithm for the lot-streaming flow shop scheduling problems with makespan criterion.

Local Pareto optimal solutions may exist in multi-modal multi-objective optimization problems. Traditional multi-objective evolutionary algorithms usually try to escape from local Pareto optima. However, these solutions may be good enough for the decision makers and are additional options if Pareto optimal solutions are infeasible. In this paper, we modify our previous double-niched evolutionary algorithm (DNEA) to search for local Pareto optimal solutions. The new version is termed as DNEA-L. We apply DNEA-L to 3- and 4-objective polygon-based problems with local Pareto optima. The experimental results show that DNEA-L is efficient to find a large number of local Pareto optimal solutions with good diversity.

The vehicle routing problem (VRP) has been researched during recent years, which has also been applied in many industrial fields, such as the logistics system, the industrial production horizons. Many of realistic constraints such as time window for each customer, and different types of vehicles have also been considered in recent literatures. In this study, we consider the two constraints and propose an improved brain storm optimization (BRO) algorithm. In the proposed algorithm, firstly, a novel solution representation is developed considering the synchronized visits constraint. Then, a well-designed decoding method is designed. Experimental comparisons with efficient algorithms on the well-known benchmarks showed that the proposed algorithm is efficient and effective.

In various flow shop scheduling problems, it is very common that a machine suffers from breakdowns. Under this situation, a robust and stable suboptimal scheduling solution is of more practical interest than a global optimal solution that is sensitive to environmental changes. However, blocking lot-streaming flow shop (BLSFS) scheduling problems with machine breakdowns have not yet been well studied up to date. This paper presents, for the first time, a multiobjective model of the above problem including robustness and stability criteria. Based on this model, an evolutionary multiobjective robust scheduling algorithm is suggested, in which solutions obtained by a variant of single-objective heuristic are incorporated into population initialization and two novel crossover operators are proposed to take advantage of nondominated solutions. In addition, a rescheduling strategy based on the local search is presented to further reduce the negative influence resulted from machine breakdowns.The proposed algorithm is applied to 22 test sets, and compared with the state-of-the-art algorithms without machine breakdowns. Our empirical results demonstrate that the proposed algorithm can effectively tackle BLSFS scheduling problems in the presence of machine breakdowns by obtaining scheduling strategies that are robust and stable.