Special Issue "Multi-Criteria Optimization Models and Applications"

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

Deadline for manuscript submissions: closed (31 December 2020).

Special Issue Editor

Prof. Dr. Bartosz Sawik
E-Mail Website
Guest Editor
AGH University of Science and Technology, 30059 Krakow, Poland. University of California at Berkeley, Berkeley, CA 94720, USA
Interests: operations engineering; multicriteria optimization; decision sciences; green vehicle routing problems; portfolio optimization; computer science; conditional value-at-risk

Special Issue Information

Dear Colleagues,

The importance of strategic behavior in the human and social world is increasingly recognized in theory and practice. As a result, multicriteria optimization models and applications have emerged as a fundamental tool in pure and applied research. Multicriteria optimization models and applications strongly support decision-making processes in an interactive environment. They draw on mathematics, economics, statistics, engineering, biology, political science, operations research, and other subjects. A multioptimization occurs when multiple criteria considered by a decision maker are concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. The decision maker considers a set of objectives in a situation in which each objective is possibly conflicting, possibly equally important, or possibly overlapping. The problem is then to determine the trade-off between objectives to support the decision-making process.

The purpose of this Special Issue is to gather a collection of articles reflecting the latest developments in the mathematical programming methods of operations research for multicriteria optimization for different fields of multicriteria optimization approaches, models,  applications and techniques.

Prof. Bartosz Sawik
Guest Editor

Manuscript Submission Information

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Keywords

  • Multicriteria decision making
  • Mathematical programming
  • Mixed integer programming
  • Linear programming
  • Quadratic programming
  • Portfolio optimization
  • Fair decision making
  • Pareto frontier
  • Conditional value-at-risk
  • Value-at-risk
  • Weighting approach
  • Lexicographic approach
  • Reference point method
  • Reference sets
  • Fuzzy sets
  • Exact methods
  • Heuristics

Published Papers (9 papers)

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Research

Article
Decision Support System for Evaluating Suitable Job Applicants
Mathematics 2021, 9(15), 1773; https://doi.org/10.3390/math9151773 - 27 Jul 2021
Viewed by 305
Abstract
This paper describes a novel approach in the area of evaluating suitable job applicants for various job positions, and specifies typical areas of requirement and their usage. Requirements for this decision-support system are defined in order to be used in middle-size companies. Suitable [...] Read more.
This paper describes a novel approach in the area of evaluating suitable job applicants for various job positions, and specifies typical areas of requirement and their usage. Requirements for this decision-support system are defined in order to be used in middle-size companies. Suitable tools chosen were fuzzy expert systems, primarily the inference system Takagi-Sugeno type, which were then supplied with implementation of methods of variant multi-criteria analysis. The resulting system is a variable tool with the possibility to simply set the importance of individual selection criteria so that it can be used in various situations, primarily in repeated selection procedures for similar job positions. A strong emphasis is devoted to the explanatory module, which enables the results of the expert system to be used easily. Verification of the system on real data in cooperation with a collaborating company has proved that the system is easily usable. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
Fuzzy Multicriteria Decision Mapping to Evaluate Implant Design for Maxillofacial Reconstruction
Mathematics 2020, 8(12), 2121; https://doi.org/10.3390/math8122121 - 26 Nov 2020
Viewed by 1247
Abstract
Technological advancements in healthcare influence medical practitioners as much as they impact the routine lives of the patients. The mandible reconstruction, which constitutes an important branch in facioplasty, has been a challenging task for medical professionals. As part of scientific innovation, tailor-made implants [...] Read more.
Technological advancements in healthcare influence medical practitioners as much as they impact the routine lives of the patients. The mandible reconstruction, which constitutes an important branch in facioplasty, has been a challenging task for medical professionals. As part of scientific innovation, tailor-made implants are valuable for sustaining and regenerating facial anatomy, as well as preserving the natural appearance. The challenge of choosing an acceptable implant design is a tedious process due to the growing number of designs with conspicuous effectiveness. The design should be agreeable, easy-to-design, sustainable, cost-effective, and undemanding for manufacturing. The optimal implant design can efficiently and effectively recover the structure and morphology of the flawed region. Evidently, among the many variants, the choice of appropriate design is one of the prevalent implant design problems and is still under consideration in most studies. This work is focused on the multiattribute decision-making (MCDM) approach to choosing the most effective implant design. The prevalence of subjectivity in decision-making and the presence of inconsistency from multiple sources emphasize the strategies that must take ambiguity and vagueness into account. An integrated MCDM methodology, assimilating two modern and popular techniques is adopted in this work. The preferred approach implements the Fuzzy Analytical Hierarchy Process based on the trapezoidal fuzzy number to extract the criteria weights in decision mapping and the Technique for Order of Preference by Similarity to Ideal Solution and VIKOR to assess design choices. A two-stage mechanism is the cornerstone of the established methodology. The first stage analyses the criteria from the point of view of the designer, the context of fabrication, and consumer experience. The second stage identifies the most viable and feasible design. The procedure applied in this analysis can be considered to choose the optimal implant design and to decide on areas of improvement that ensure greater patient experience. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
A Risk-Aversion Approach for the Multiobjective Stochastic Programming Problem
Mathematics 2020, 8(11), 2026; https://doi.org/10.3390/math8112026 - 13 Nov 2020
Viewed by 1406
Abstract
Multiobjective stochastic programming is a field that is well suited to tackling problems that arise in many fields: energy, financial, emergencies, among others; given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in [...] Read more.
Multiobjective stochastic programming is a field that is well suited to tackling problems that arise in many fields: energy, financial, emergencies, among others; given that uncertainty and multiple objectives are usually present in such problems. A new concept of solution is proposed in this work, which is especially designed for risk-averse solutions. The proposed concept combines the notions of conditional value-at-risk and ordered weighted averaging operator to find solutions protected against risks due to uncertainty and under-achievement of criteria. A small example is presented in order to illustrate the concept in small discrete feasible spaces. A linear programming model is also introduced to obtain the solution in continuous spaces. Finally, computational experiments are performed by applying the obtained linear programming model to the multiobjective stochastic knapsack problem, gaining insight into the behaviour of the new solution concept. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
On the Geometric Mean Method for Incomplete Pairwise Comparisons
Mathematics 2020, 8(11), 1873; https://doi.org/10.3390/math8111873 - 29 Oct 2020
Cited by 3 | Viewed by 1658
Abstract
One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same [...] Read more.
One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
An Integrated SWARA-WASPAS Group Decision Making Framework to Evaluate Smart Card Systems for Public Transportation
Mathematics 2020, 8(10), 1723; https://doi.org/10.3390/math8101723 - 07 Oct 2020
Cited by 4 | Viewed by 1712
Abstract
Recent technological developments affect daily life as much as they affect the industries. As part of these developments, automation and smart systems are important part of everyday life. Smart card systems are one of the well-known types of smart automation technology being used [...] Read more.
Recent technological developments affect daily life as much as they affect the industries. As part of these developments, automation and smart systems are important part of everyday life. Smart card systems are one of the well-known types of smart automation technology being used by the majority of the population in public transportation in most developed countries. Even though automated fare payment systems have been widely integrated into public transportation in developed countries, integration of smart card systems is still under consideration in most developing countries. The aim of this study is to propose a framework to evaluate different smart card systems to determine the best one and additionally validate their benefits when compared with the traditional fare payment system. For this purpose, an integrated multi-criteria decision making (MCDM) framework is used that combines two recent and popular methodologies together. The proposed methodology employs Stepwise Weight Assessment Ratio Analysis (SWARA) method for determination of criteria weights in the decision model and the Weighted Additive Sum Product Assessment (WASPAS) method for comparison of alternatives. Research results revealed that all smart card systems show improvements under performance, reliability, and user satisfaction related criteria. However, traditional fare payment systems are found to be safer under consideration of personal data protection. Findings of this study can be used to select the best smart card system and as a guide for deciding on areas of improvement during the implementation phase to ensure higher user satisfaction. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
The Non-Smooth and Bi-Objective Team Orienteering Problem with Soft Constraints
Mathematics 2020, 8(9), 1461; https://doi.org/10.3390/math8091461 - 01 Sep 2020
Cited by 1 | Viewed by 2775
Abstract
In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer [...] Read more.
In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
The Optimal Setting of A/B Exam Papers without Item Pools: A Hybrid Approach of IRT and BGP
Mathematics 2020, 8(8), 1290; https://doi.org/10.3390/math8081290 - 05 Aug 2020
Viewed by 2546
Abstract
The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams ‘fairness’. These are critical [...] Read more.
The administration of A/B exams usually involves the use of items. Issues arise when the pre-establishment of a question bank is necessary and the inconsistency in the knowledge points to be tested (in the two exams) reduces the exams ‘fairness’. These are critical for a large multi-teacher course wherein the teachers are changed such that the course and examination content are altered every few years. However, a fair test with randomly participating students should still be a guaranteed subject with no item pool. Through data-driven decision-making, this study collected data related to a term test for a compulsory general course for empirical assessments, pre-processed the data and used item response theory to statistically estimate the difficulty, discrimination and lower asymptotic for each item in the two exam papers. Binary goal programing was finally used to analyze and balance the fairness of A/B exams without an item pool. As a result, pairs of associated questions in the two exam papers were optimized in terms of their overall balance in three dimensions (as the goals) through the paired exchanges of items. These exam papers guarantee their consistency (in the tested knowledge points) and also ensure the fairness of the term test (a key psychological factor that motivates continued studies). Such an application is novel as the teacher(s) did not have a pre-set question bank and could formulate the fairest strategy for the A/B exam papers. The model can be employed to address similar teaching practice issues. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
A Multi-Criteria Study of Decision-Making Proficiency in Student’s Employability for Multidisciplinary Curriculums
Mathematics 2020, 8(6), 897; https://doi.org/10.3390/math8060897 - 02 Jun 2020
Cited by 4 | Viewed by 4512
Abstract
To effectively increase the employment rate of higher education graduates, higher education institutions are doing their best to provide the most high-quality technologized interdisciplinary curriculum, to educate professional expertise in decision-making and to fortify student employability. Therefore, after executing a series of evaluated [...] Read more.
To effectively increase the employment rate of higher education graduates, higher education institutions are doing their best to provide the most high-quality technologized interdisciplinary curriculum, to educate professional expertise in decision-making and to fortify student employability. Therefore, after executing a series of evaluated measurements, there are four highly valuable and contributive conclusions and findings. First, judgeability was the most critical decision-making employability factor and was directly influenced by the self-efficacy (SE), self-control (SC) and self-regulation (SR) of the autonomy-learning performance of social learning theory (SLT). Second, the SE of autonomy-learning performance of SLT was positively impacted by the behavioral intention to use and actual system use of the technology acceptance model (TAM), and monitor, control and evaluate decision-making, select the best solutions, clarify the objectiveness to be achieved and search for possible solutions of rational decision-making model (RDMM). It is necessary for higher education graduates to possess judgeability to confidently deal with problem-solving issues by actually using diversified technological applications for clarifying, monitoring, controlling and evaluating the decision-making objectiveness, and to comprehensively search the possible solutions, in order to eventually induce the best solutions for the problem. Third, define and diagnose the issues or problems of the RDMM model affected by the self-control (SC) of autonomy-learning performance of the SLT theory, because higher education graduates have to possess justifiability to define and diagnose the problem-solving issues in-depth, by exercising the introspective self-correcting capacities cultivated from an interdisciplinary curriculum. Lastly, actual system use of the TAM indeed impacted the SR of the autonomy-learning performance of SLT, because higher education graduates have to assess, revise and justify their self-actions in thinking, motivation, feeling, cognition and behaviors, by self-observing and accumulating experience from an interdisciplinary curriculum. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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Article
Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method
Mathematics 2020, 8(3), 356; https://doi.org/10.3390/math8030356 - 05 Mar 2020
Viewed by 4824
Abstract
An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. [...] Read more.
An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs. Full article
(This article belongs to the Special Issue Multi-Criteria Optimization Models and Applications)
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