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Mathematics
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Combinatorial Optimization Problems in Planning and Decision Making
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Combinatorial Optimization Problems in Planning and Decision Making

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

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 6345

Special Issue Editors

Dr. Cristian Ramírez Atencia

E-Mail Website
Guest Editor
Department of Computer Systems, Polytechnic University of Madrid, 28031 Madrid, Spain
Interests: multi-objective optimization; constraint programming; bio-inspired algorithms; multi-criteria decision making; planning and scheduling
Special Issues, Collections and Topics in MDPI journals
Dr. Sara Perez-Carabaza

E-Mail Website
Guest Editor
Department of Applied Mathematics and Computer Science, University of Cantabria, 39005 Santander, Spain
Interests: metaheuristics; bio-inspired algorithms; combinatorial optimization problems; statistics; convolutional neural networks

Special Issue Information

Dear Colleagues,

In recent years, combinatorial optimization has taken the attention of research academics and industry because of the several real-life problems that can be modelled. Several optimization methods have been proposed for solving a variety of popular planning problems including the travelling salesman problem, the vehicle routing problem, the job shop scheduling, the timetabling problem, and many more. Most of these problems are NP-hard, which makes it complicated to obtain the optimal solution in a reasonable time. Although classical methods have been widely used, in the last years many authors have also considered stochastic methods and specially metaheuristics for solving these combinatorial problems, due to their ability to reduce the computational time needed for finding a near-optimal solution.

On the other hand, most of the frameworks in the state-of-the-art for solving combinatorial optimization problems usually consider several solutions for the same problem, which makes it hard for decision makers to choose the most appropriate one. For this reason, it is essential to propose decision support systems that alleviate this workload through the use of decision-making methods, especially when there are multiple objectives being considered at the same time.

This Special Issue will focus on recent theoretical and computational studies of combinatorial optimization, with a focus on planning and scheduling problems, as well as decision making methods for the selection of the optimal solution. Topics include, but are not limited to, the following:

  1. Constraint programming techniques for solving planning and scheduling problems
  2. Stochastic algorithms for combinatorial optimization
  3. Metaheuristics for combinatorial optimization
  4. Decision support systems for planning and scheduling
  5. Multi-objective combinatorial optimization
  6. Multi-criteria decision making in planning and scheduling

Dr. Cristian Ramírez Atencia
Dr. Sara Perez-Carabaza
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 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

  • Combinatorial optimization
  • Constraint programming
  • Stochastic algorithms
  • Metaheuristics
  • Planning problems
  • Scheduling problems
  • Decision making methods

Published Papers (3 papers)

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Research

22 pages, 1334 KiB  
Article
A Genetic Hyper-Heuristic for an Order Scheduling Problem with Two Scenario-Dependent Parameters in a Parallel-Machine Environment
by Lung-Yu Li, Jian-You Xu, Shuenn-Ren Cheng, Xingong Zhang, Win-Chin Lin, Jia-Cheng Lin, Zong-Lin Wu and Chin-Chia Wu
Mathematics 2022, 10(21), 4146; https://0-doi-org.brum.beds.ac.uk/10.3390/math10214146 - 06 Nov 2022
Cited by 1 | Viewed by 1287
Abstract
Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these [...] Read more.
Studies on the customer order scheduling problem have been attracting increasing attention. Most current approaches consider that either component processing times for customer orders on each machine are constant or all customer orders are available at the outset of production planning. However, these assumptions do not hold in real-world applications. Uncertainty may be caused by multiple issues including a machine breakdown, the working environment changing, and workers’ instability. On the basis of these factors, we introduced a parallel-machine customer order scheduling problem with two scenario-dependent component processing times, due dates, and ready times. The objective was to identify an appropriate and robust schedule for minimizing the maximum of the sum of weighted numbers of tardy orders among the considered scenarios. To solve this difficult problem, we derived a few dominant properties and a lower bound for determining an optimal solution. Subsequently, we considered three variants of Moore’s algorithm, a genetic algorithm, and a genetic-algorithm-based hyper-heuristic that incorporated the proposed seven low-level heuristics to solve this problem. Finally, the performances of all proposed algorithms were evaluated. Full article
(This article belongs to the Special Issue Combinatorial Optimization Problems in Planning and Decision Making)
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23 pages, 2743 KiB  
Article
Optimal Emergency Evacuation Route Planning Model Based on Fire Prediction Data
by Kunxiang Deng, Qingyong Zhang, Hang Zhang, Peng Xiao and Jiahua Chen
Mathematics 2022, 10(17), 3146; https://0-doi-org.brum.beds.ac.uk/10.3390/math10173146 - 01 Sep 2022
Cited by 8 | Viewed by 2368
Abstract
For the emergency evacuation of cruise ships in case of sudden fire, this research proposes a dynamic route optimization method based on the improved A∗ algorithm for real-time information, in order to obtain the real-time optimal evacuation route. Initially, a basic network [...] Read more.
For the emergency evacuation of cruise ships in case of sudden fire, this research proposes a dynamic route optimization method based on the improved A∗ algorithm for real-time information, in order to obtain the real-time optimal evacuation route. Initially, a basic network topology diagram is established according to the internal structure of the cruise ship. Before the occurrence of the accident, the A∗ algorithm can be applied to obtain an a priori evacuation network consisting of all the optimal routes from each node to the exit. At the time of the accident, the dynamic diffusion of fire can be simulated using Fire Dynamics Simulator (FDS) based on the preliminary information of the fire, so as to estimate the impact of the fire domain on each node of the network. Then, according to the fire dynamic diffusion data, the evacuation route planning is carried out by the improved A∗ algorithm applying the breadth-first search strategy, so as to determine the optimal route from the current node to the safety exit and to reduce the possibility of casualties due to the uncertainty of the fire during the evacuation. This model allows for both people’s safety and evacuation time to dynamically avoid fire-affected nodes and helps people to reach the safe area as soon as possible. Finally, the evacuation model is established according to the open-source cruise ship structure, and the evacuation process of people under the dynamic spread of cruise ship fire is simulated. The results show that the route planning method proposed in this research works out well in evacuating mass people, which can effectively reduce the evacuation time and improve the safety of the evacuation process. Full article
(This article belongs to the Special Issue Combinatorial Optimization Problems in Planning and Decision Making)
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24 pages, 2539 KiB  
Article
Artificial Bee Colony Algorithm with Nelder–Mead Method to Solve Nurse Scheduling Problem
by Rajeswari Muniyan, Rajakumar Ramalingam, Sultan S. Alshamrani, Durgaprasad Gangodkar, Ankur Dumka, Rajesh Singh, Anita Gehlot and Mamoon Rashid
Mathematics 2022, 10(15), 2576; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152576 - 25 Jul 2022
Cited by 2 | Viewed by 1619
Abstract
The nurse scheduling problem (NSP) is an NP-Hard combinatorial optimization scheduling problem that allocates a set of shifts to the group of nurses concerning the schedule period subject to the constraints. The objective of the NSP is to create a schedule that satisfies [...] Read more.
The nurse scheduling problem (NSP) is an NP-Hard combinatorial optimization scheduling problem that allocates a set of shifts to the group of nurses concerning the schedule period subject to the constraints. The objective of the NSP is to create a schedule that satisfies both hard and soft constraints suggested by the healthcare management. This work explores the meta-heuristic approach to an artificial bee colony algorithm with the Nelder–Mead method (NM-ABC) to perform efficient nurse scheduling. Nelder–Mead (NM) method is used as a local search in the onlooker bee phase of ABC to enhance the intensification process of ABC. Thus, the author proposed an improvised solution strategy at the onlooker bee phase with the benefits of the NM method. The proposed algorithm NM-ABC is evaluated using the standard dataset NSPLib, and the experiments are performed on various-sized NSP instances. The performance of the NM-ABC is measured using eight performance metrics: best time, standard deviation, least error rate, success percentage, cost reduction, gap, and feasibility analysis. The results of our experiment reveal that the proposed NM-ABC algorithm attains highly significant achievements compared to other existing algorithms. The cost of our algorithm is reduced by 0.66%, and the gap percentage to move towards the optimum value is 94.30%. Instances have been successfully solved to obtain the best deal with the known optimal value recorded in NSPLib. Full article
(This article belongs to the Special Issue Combinatorial Optimization Problems in Planning and Decision Making)
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