Mathematics

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22 pages, 3303 KiB

Open AccessArticle

A Decentralized Optimization Algorithm for Multi-Agent Job Shop Scheduling with Private Information

by Xinmin Zhou, Wenhao Rao, Yaqiong Liu and Shudong Sun

Mathematics 2024, 12(7), 971; https://doi.org/10.3390/math12070971 - 25 Mar 2024

Viewed by 474

The optimization of job shop scheduling is pivotal for improving overall production efficiency within a workshop. In demand-driven personalized production modes, achieving a balance between workshop resources and the diverse demands of customers presents a challenge in scheduling. Additionally, considering the self-interested behaviors [...] Read more.

The optimization of job shop scheduling is pivotal for improving overall production efficiency within a workshop. In demand-driven personalized production modes, achieving a balance between workshop resources and the diverse demands of customers presents a challenge in scheduling. Additionally, considering the self-interested behaviors of agents, this study focuses on tackling the problem of multi-agent job shop scheduling with private information. Multiple consumer agents and one job shop agent are considered, all of which are self-interested and have private information. To address this problem, a two-stage decentralized algorithm rooted in the genetic algorithm is developed to achieve a consensus schedule. The algorithm allows agents to evolve independently and concurrently, aiming to satisfy individual requirements. To prevent becoming trapped in a local optimum, the search space is broadened through crossover between agents and agent-based block insertion. Non-dominated sorting and grey relational analysis are applied to generate the final solution with high social welfare. The proposed algorithm is compared using a centralized approach and two state-of-the-art decentralized approaches in computational experiments involving 734 problem instances. The results validate that the proposed algorithm generates non-dominated solutions with strong convergence and uniformity. Moreover, the final solution produced by the developed algorithm outperforms those of the decentralized approaches. These advantages are more pronounced in larger-scale problem instances with more agents. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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14 pages, 299 KiB

Open AccessArticle

Branch-and-Bound and Heuristic Algorithms for Group Scheduling with Due-Date Assignment and Resource Allocation

by Hongyu He, Yanzhi Zhao, Xiaojun Ma, Zheng-Guo Lv and Ji-Bo Wang

Mathematics 2023, 11(23), 4745; https://doi.org/10.3390/math11234745 - 23 Nov 2023

Viewed by 593

Abstract

Green scheduling that aims to enhance efficiency by optimizing resource allocation and job sequencing concurrently has gained growing academic attention. To tackle such problems with the consideration of scheduling and resource allocation, this paper considers a single-machine group scheduling problem with common/slack due-date [...] Read more.

Green scheduling that aims to enhance efficiency by optimizing resource allocation and job sequencing concurrently has gained growing academic attention. To tackle such problems with the consideration of scheduling and resource allocation, this paper considers a single-machine group scheduling problem with common/slack due-date assignment and a controllable processing time. The objective is to decide the optimized schedule of the group/job sequence, resource allocation, and due-date assignment. To solve the generalized case, this paper proves several optimal properties and presents a branch-and-bound algorithm and heuristic algorithms. Numerical experiments show that the branch-and-bound algorithm is efficient and the heuristic algorithm developed based on the analytical properties outruns the tabu search. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

19 pages, 314 KiB

Open AccessArticle

Study on Scheduling Problems with Learning Effects and Past Sequence Delivery Times

by Hongyu He, Yanzhi Zhao, Xiaojun Ma, Yuan-Yuan Lu, Na Ren and Ji-Bo Wang

Mathematics 2023, 11(19), 4135; https://doi.org/10.3390/math11194135 - 30 Sep 2023

Cited by 1 | Viewed by 538

Abstract

In this paper, we study a single-machine green scheduling problem with learning effects and past-sequence-dependent delivery times. The problem can be properly applied to tackle green manufacturing where production and delivery time are variable and highly subject to process-reengineering. Our goal is to [...] Read more.

In this paper, we study a single-machine green scheduling problem with learning effects and past-sequence-dependent delivery times. The problem can be properly applied to tackle green manufacturing where production and delivery time are variable and highly subject to process-reengineering. Our goal is to determine the optimal sequence such that total weighted completion time and maximum tardiness are minimized. For the general case, we provide the analysis procedure of lower bound, and also propose the heuristic and branch-and-bound algorithms. Furthermore, computational experiments are conducted to demonstrate the effectiveness of our algorithms. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

18 pages, 320 KiB

Open AccessArticle

Delivery Times Scheduling with Deterioration Effects in Due Window Assignment Environments

by Rong-Rong Mao, Yi-Chun Wang, Dan-Yang Lv, Ji-Bo Wang and Yuan-Yuan Lu

Mathematics 2023, 11(18), 3983; https://doi.org/10.3390/math11183983 - 19 Sep 2023

Cited by 2 | Viewed by 545

Abstract

In practical problems, in addition to the processing time of the job, the impact of the time required for delivering the service to customers on the cost is also considered, i.e., delivery time, where the job processing time is a simple linear function [...] Read more.

In practical problems, in addition to the processing time of the job, the impact of the time required for delivering the service to customers on the cost is also considered, i.e., delivery time, where the job processing time is a simple linear function of its starting time. This paper considers the impact of past-sequence-dependent delivery times (which can be referred to as

p s d d t

) on the studied objectives in three types of due windows (common, slack and different due windows). This serves to minimize the weighted sum of earliness, tardiness, starting time and size of due window, where the weights (coefficients) are related to the location. Through the theoretical analysis of the optimal solution, it is found that these three problems can be solved in time

O (N \log N)

, respectively, where N is the number of jobs. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

17 pages, 3817 KiB

Open AccessArticle

Effective Improved NSGA-II Algorithm for Multi-Objective Integrated Process Planning and Scheduling

by Xiaoyu Wen, Qingbo Song, Yunjie Qian, Dongping Qiao, Haoqi Wang, Yuyan Zhang and Hao Li

Mathematics 2023, 11(16), 3523; https://doi.org/10.3390/math11163523 - 15 Aug 2023

Cited by 3 | Viewed by 1042

Abstract

Integrated process planning and scheduling (IPPS) is important for modern manufacturing companies to achieve manufacturing efficiency and improve resource utilization. Meanwhile, multiple objectives need to be considered in the realistic decision-making process for manufacturing systems. Based on the above realistic manufacturing system requirements, [...] Read more.

Integrated process planning and scheduling (IPPS) is important for modern manufacturing companies to achieve manufacturing efficiency and improve resource utilization. Meanwhile, multiple objectives need to be considered in the realistic decision-making process for manufacturing systems. Based on the above realistic manufacturing system requirements, it becomes increasingly important to develop effective methods to deal with multi-objective IPPS problems. Therefore, an improved NSGA-II (INSGA-II) algorithm is proposed in this research, which uses the fast non-dominated ranking method for multiple optimization objectives as an assignment scheme for fitness. A multi-layer integrated coding method is adopted to address the characteristics of the integrated optimization model, which involves many optimization parameters and interactions. Elite and mutation strategies are employed during the evolutionary process to enhance population diversity and the quality of solutions. An external archive is also used to store and update the Pareto solution. The experimental results on the Kim test set demonstrate the effectiveness of the proposed INSGA-II algorithm. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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25 pages, 3878 KiB

Open AccessArticle

A GA-Based Scheduling Method for Civil Aircraft Distributed Production with Material Inventory Replenishment Consideration

by Xumai Qi, Dongdong Zhang, Hu Lu and Rupeng Li

Mathematics 2023, 11(14), 3135; https://doi.org/10.3390/math11143135 - 16 Jul 2023

Cited by 1 | Viewed by 969

Abstract

The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft [...] Read more.

The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft distributed production is necessary, but previous studies have not taken material inventory into account sufficiently. This article proposes a scheduling method for civil aircraft distributed production that aims to minimize the production time to complete all the jobs in a large production station under the condition of material inventory replenishment. Firstly, we analyze the factors constraining civil aircraft production efficiency, and formulize the production scheduling problem into the Resource-Constrained Project Scheduling Problem model with Inventory Replenishment (RCPSP-IR). Precedence constraints and resource constraints, especially the inventory constraints, are mainly considered in RCPSP-IR. To solve the corresponding scheduling problem, the Genetic Algorithm (GA) is applied and multiple approaches are introduced to handle the complex constraints and avoid local optimum. Finally, we applied the proposed scheduling method to a case study of a jet twin-engine civil aircraft production of COMAC. The results of the case study show that the proposed method can give a nearly optimal scheduling strategy to be applied to actual civil aircraft production. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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15 pages, 2995 KiB

Open AccessArticle

Modeling and Heuristically Solving Group Train Operation Scheduling for Heavy-Haul Railway Transportation

by Weiya Chen, Qinyu Zhuo and Lu Zhang

Mathematics 2023, 11(11), 2489; https://doi.org/10.3390/math11112489 - 28 May 2023

Cited by 3 | Viewed by 1268

Abstract

In light of the improvements to the capacity and timeliness of heavy-haul railway transportation that can be organized through group trains originating at a technical station, we address a group train operation scheduling problem with freight demand importance via a newly proposed mixed [...] Read more.

In light of the improvements to the capacity and timeliness of heavy-haul railway transportation that can be organized through group trains originating at a technical station, we address a group train operation scheduling problem with freight demand importance via a newly proposed mixed integer programming model and a simulated annealing algorithm. The optimization objective of the mixed integer programming model is to minimize the weighted sum of the transportation cost and the total cargo travel time under the condition of matching freight supply and demand within the optimization period. The main constraints are extracted from the supply and demand relations, the cargo delivery time commitment, the maintenance time, and the number of locomotives. A simulated annealing algorithm was constructed to generate the grouping scheme, the stopping scheme and the running schedule of group trains. A numerical experiment based on a real heavy-haul railway configuration was employed to verify the efficacy of the proposed model and heuristics algorithm. The results show that the proposed methodology can achieve high-quality solutions. The case results reveal that the freight volume increased by 2.03%, the departure cost decreased by CNY 337,000, the transportation cost which results from the difference in the supply and demand matching increased by CNY 27,764, and the total cargo travel time decreased by 40.9%, indicating that group train operation can create benefits for both railway enterprises and customers. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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33 pages, 1375 KiB

Open AccessArticle

Dynamic Evaluation of Product Innovation Knowledge Concerning the Interactive Relationship between Innovative Subjects: A Multi-Objective Optimization Approach

by Fanshun Zhang, Zhuorui Zhang, Quanquan Zhang and Xiaochun Zhu

Mathematics 2023, 11(9), 2105; https://doi.org/10.3390/math11092105 - 28 Apr 2023

Viewed by 1312

Abstract

Product innovation knowledge, in prior studies, has been subjectively evaluated by a single stakeholder, resulting in a notable bias toward the chosen solution. Specifically, the selected product innovation solution may fail to incorporate the interests and demands of innovation subjects, potentially leading to [...] Read more.

Product innovation knowledge, in prior studies, has been subjectively evaluated by a single stakeholder, resulting in a notable bias toward the chosen solution. Specifically, the selected product innovation solution may fail to incorporate the interests and demands of innovation subjects, potentially leading to conflicting innovation solutions and inefficiencies. Recently, many external parties, such as consumers and supply chain partners, have been involved in innovative work to create a substantial amount of the product interactive innovation knowledge (PIIK). The value of PIIK is hard to evaluate since this knowledge has evolved as a dynamic relationship among external parties. Thus, a novel method that integrates dynamic knowledge evolution and multiple stakeholders should be developed to dynamically evaluate the value of PIIK. Specially, the objectives in this paper are the knowledge evaluation scores of different innovative aspects and the ability of a model to identify the optimal solutions that receive the highest score from the innovative subjects. Then, the dynamic characteristic is captured by the participation of new parties, the departure of original parties, and the new knowledge created by the existing parties. To verify the effectiveness of feasibility of this model, case studies based on the innovation of a cell phone were implemented. The results show the following: (i). When the interactive relationship is not considered, parties prefer to choose the solution that fits well with their benefits, but the solution may conflict with other solutions chosen by their partners; (ii). Although the best solution is not separately selected by all parties when the interactive relationship is considered, the solution combined with the satisfactory result presents a better performance on product innovation; (iii). Dynamic characteristic should be considered in evaluation process, especially when the core parties are changed. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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13 pages, 769 KiB

Open AccessArticle

Solving Optimal Power Flow Problem via Improved Constrained Adaptive Differential Evolution

by Wenchao Yi, Zhilei Lin, Youbin Lin, Shusheng Xiong, Zitao Yu and Yong Chen

Mathematics 2023, 11(5), 1250; https://doi.org/10.3390/math11051250 - 04 Mar 2023

Cited by 3 | Viewed by 1732

Abstract

The optimal power flow problem is one of the most widely used problems in power system optimizations, which are multi-modal, non-linear, and constrained optimization problems. Effective constrained optimization methods can be considered in tackling the optimal power flow problems. In this paper, an [...] Read more.

The optimal power flow problem is one of the most widely used problems in power system optimizations, which are multi-modal, non-linear, and constrained optimization problems. Effective constrained optimization methods can be considered in tackling the optimal power flow problems. In this paper, an

ϵ

-constrained method-based adaptive differential evolution is proposed to solve the optimal power flow problems. The

ϵ

-constrained method is improved to tackle the constraints, and a p-best selection method based on the constraint violation is implemented in the adaptive differential evolution. The single and multi-objective optimal power flow problems on the IEEE 30-bus test system are used to verify the effectiveness of the proposed and improved

ε

adaptive differential evolution algorithm. The comparison between state-of-the-art algorithms illustrate the effectiveness of the proposed and improved

ε

adaptive differential evolution algorithm. The proposed algorithm demonstrates improvements in nine out of ten cases. Full article

(This article belongs to the Special Issue Optimization in Scheduling and Control Problems)

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