Special Issue "Recent Advances of Disсrete Optimization and Scheduling"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 28 February 2023 | Viewed by 4153

Special Issue Editors

Dr. Alexander A Lazarev
E-Mail Website
Guest Editor
Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia
Interests: scheduling theory; discrete optimization; NP hardness; combinatorics; train scheduling; polynomial algorithms
Prof. Dr. Frank Werner
E-Mail Website
Guest Editor
Faculty of Mathematics, Otto-von-Guericke-University, P.O. Box 4120, D-39016 Magdeburg, Germany
Interests: scheduling, in particular development of exact and approximate algorithms; stability investigations is discrete optimization; scheduling with interval processing times; complexity investigations for scheduling problems; train scheduling; graph theory; logistics; supply chains; packing; simulation and applications
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Bertrand M.T. Lin
E-Mail Website
Guest Editor
Institute of Information Management, National Chiao Tung University, Taipei 100-116, Taiwan
Interests: scheduling theory; operations management; discrete optimization

Special Issue Information

Dear colleagues,

The development of software products that enable effective planning and optimization of production processes is necessary to improve the quality of the industrial sector. This Special Issue is devoted to modern approaches to solving discrete optimization problems and scheduling problems. Special attention is paid to problems with practical applications. First of all, this concerns the tasks that were updated as a result of the pandemic crisis of 2020–2021: the tasks of managing medical institutions, the tasks of cargo transportation, the tasks of production planning, and so on. NP-hard problems are the most difficult since they require significant computational resources to find a solution in general cases. Various models are studied, and their effectiveness is compared based on the study of special (pseudo-)polynomial solvable cases of problems, the measure of (pseudo-)polynomial unsolvability, the radius of stability, and the efficiency of algorithms. 

Dr. Alexander A Lazarev
Prof. Dr. Frank Werner
Prof. Dr. Bertrand M.T. Lin
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • scheduling theory
  • discrete optimization
  • NP hardness
  • combinatorics
  • train scheduling
  • plane graph
  • polynomial algorithm
  • routing
  • multi-agent technology
  • resource management

Published Papers (6 papers)

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Research

Article
Autonomous Digital Twin of Enterprise: Method and Toolset for Knowledge-Based Multi-Agent Adaptive Management of Tasks and Resources in Real Time
Mathematics 2022, 10(10), 1662; https://doi.org/10.3390/math10101662 - 12 May 2022
Viewed by 626
Abstract
Digital twins of complex technical objects are widely applied for various domains, rapidly becoming smart, cognitive and autonomous. However, the problem of digital twins for autonomous management of enterprise resources is still not fully researched. In this paper, an autonomous digital twin of [...] Read more.
Digital twins of complex technical objects are widely applied for various domains, rapidly becoming smart, cognitive and autonomous. However, the problem of digital twins for autonomous management of enterprise resources is still not fully researched. In this paper, an autonomous digital twin of enterprise is introduced to provide knowledge-based multi-agent adaptive allocation, scheduling, optimization, monitoring and control of tasks and resources in real time, synchronized with employees’ plans, preferences and competencies via mobile devices. The main requirements for adaptive resource management are analyzed. The authors propose formalized ontological and multi-agent models for developing the autonomous digital twin of enterprise. A method and software toolset for designing the autonomous digital twin of enterprise, applicable for both operational management of tasks and resources and what-if simulations, are developed. The validation of developed methods and toolsets for IT service desk has proved increase in efficiency, as well as savings in time and costs of deliveries for various applications. The paper also outlines a plan for future research, as well as a number of new potential business applications. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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Article
Complexity of Solutions Combination for the Three-Index Axial Assignment Problem
Mathematics 2022, 10(7), 1062; https://doi.org/10.3390/math10071062 - 25 Mar 2022
Viewed by 511
Abstract
In this work we consider the NP-hard three-index axial assignment problem. We formulate and investigate a problem of combining feasible solutions. Such combination can be applied in a wide range of heuristic and approximate algorithms for solving the assignment problem, instead of the [...] Read more.
In this work we consider the NP-hard three-index axial assignment problem. We formulate and investigate a problem of combining feasible solutions. Such combination can be applied in a wide range of heuristic and approximate algorithms for solving the assignment problem, instead of the commonly used strategy of selecting the best solution among the found feasible solutions. We discuss approaches to a solution of the combination problem and prove that it becomes NP-hard already in the case of combining four solutions. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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Article
Special Type Routing Problems in Plane Graphs
Mathematics 2022, 10(5), 795; https://doi.org/10.3390/math10050795 - 02 Mar 2022
Viewed by 562
Abstract
We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G. We determine the appropriate type of route [...] Read more.
We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G. We determine the appropriate type of route for the given graph: OE-route represents an ordered sequence of chains satisfying the requirement that the part of the route that is not passed does not intersect the interior of its passed part, AOE-chain represents OE-chain consecutive edges which are incident to vertex v and they are neighbours in the cyclic order O±(v), NOE-route represents the non-intersecting OE-route, PPOE-route represents the Pierce Point NOE-route with allowable pierce points that are start points of OE-chains forming this route. We analyse the solvability of the listed routing problems in graph G. We developed the polynomial algorithms for obtaining listed routes with the minimum number of covering paths and the minimum length of transitions between the ending of the current path and the beginning of the next path. The solutions proposed in the article can improve the quality of technological preparation of cutting processes in CAD/CAM systems. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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Article
Decomposition of the Knapsack Problem for Increasing the Capacity of Operating Rooms
Mathematics 2022, 10(5), 784; https://doi.org/10.3390/math10050784 - 01 Mar 2022
Viewed by 585
Abstract
This paper is aimed at the problem of scheduling surgeries in operating rooms. To solve this problem, we suggest using some variation of the bin packing problem. The model is based on the actual operation of 10 operating rooms, each of which belongs [...] Read more.
This paper is aimed at the problem of scheduling surgeries in operating rooms. To solve this problem, we suggest using some variation of the bin packing problem. The model is based on the actual operation of 10 operating rooms, each of which belongs to a specific department of the hospital. Departments are unevenly loaded, so operations can be moved to operating rooms in other departments. The main goal is to increase patient throughput. It is also necessary to measure how many operations take place in other departments with the proposed solution. The preferred solution is a solution with fewer such operations, all other things being equal. Due to the fact that the mixed-integer linear programming model turned out to be computationally complex, two approximation algorithms were also proposed. They are based on decomposition. The complexity of the proposed algorithms is estimated, and arguments are made regarding their accuracy from a theoretical point of view. To assess the practical accuracy of the algorithms, the Gurobi solver is used. Experiments were conducted on real historical data on surgeries obtained from the Burdenko Neurosurgical Center. Two decomposition algorithms were constructed and a comparative analysis was performed for 10 operating rooms based on real data. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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Article
JMA: Nature-Inspired Java Macaque Algorithm for Optimization Problem
Mathematics 2022, 10(5), 688; https://doi.org/10.3390/math10050688 - 23 Feb 2022
Viewed by 480
Abstract
In recent years, optimization problems have been intriguing in the field of computation and engineering due to various conflicting objectives. The complexity of the optimization problem also dramatically increases with respect to a complex search space. Nature-Inspired Optimization Algorithms (NIOAs) are becoming dominant [...] Read more.
In recent years, optimization problems have been intriguing in the field of computation and engineering due to various conflicting objectives. The complexity of the optimization problem also dramatically increases with respect to a complex search space. Nature-Inspired Optimization Algorithms (NIOAs) are becoming dominant algorithms because of their flexibility and simplicity in solving the different kinds of optimization problems. Hence, the NIOAs may be struck with local optima due to an imbalance in selection strategy, and which is difficult when stabilizing exploration and exploitation in the search space. To tackle this problem, we propose a novel Java macaque algorithm that mimics the natural behavior of the Java macaque monkeys. The Java macaque algorithm uses a promising social hierarchy-based selection process and also achieves well-balanced exploration and exploitation by using multiple search agents with a multi-group population, male replacement, and learning processes. Then, the proposed algorithm extensively experimented with the benchmark function, including unimodal, multimodal, and fixed-dimension multimodal functions for the continuous optimization problem, and the Travelling Salesman Problem (TSP) was utilized for the discrete optimization problem. The experimental outcome depicts the efficiency of the proposed Java macaque algorithm over the existing dominant optimization algorithms. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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Article
A Three-Stage ACO-Based Algorithm for Parallel Batch Loading and Scheduling Problem with Batch Deterioration and Rate-Modifying Activities
Mathematics 2022, 10(4), 657; https://doi.org/10.3390/math10040657 - 20 Feb 2022
Viewed by 398
Abstract
This paper addresses a batch loading and scheduling problem of minimizing the makespan on parallel batch processing machines. For batch loading, jobs with compatible families can be assigned to the same batch process even if they differ in size; however, batches can only [...] Read more.
This paper addresses a batch loading and scheduling problem of minimizing the makespan on parallel batch processing machines. For batch loading, jobs with compatible families can be assigned to the same batch process even if they differ in size; however, batches can only be formed from jobs within the same family, and the batch production time is determined by the family. During the batch scheduling, the deterioration effects are continuously added to batches processed in each parallel machine so that the batch production times become deteriorated. The deteriorated processing time of batches can be recovered to the original processing times of batches by a maintenance or cleaning process of machines. In this problem, we sequentially determine the batching of jobs and the scheduling of batches. Due to the complexity of the problem, we proposed a three-stage ant colony optimization algorithm. The proposed algorithm found an optimal solution for small-sized problems and achieved near-optimal solutions and better performance than a genetic algorithm or a particle swarm optimization for large-sized problems. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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