Multicriteria Optimization

The main attention is paid to optimization issues, as well as mathematical modeling of systems that are important for the initial stages of the design of communication networks. Examples of solving scalar and vector optimization problems are given taking into account mathematical models of various types of communication networks. Information is given about standard software packages that can be used for optimization and computer simulation of communication networks.

A route alignment planning has various stages. At different stages, multi-criteria decision analysis (MCDA) is required. This paper integrates geographical information system (GIS) and MCDA for designing the optimum route alignment. A GIS-based model using the multi-criteria decision analysis for finding the optimum route alignment to design major road from a source to a destination within two locations is proposed. Three different levels of analysis were performed in this study such as criteria map analysis, surface cost analysis , and least-cost path analysis. The optimum route has the least cost and satisfies other environmental, technical, social, and economic criteria. The proposed model is implemented to design optimum route alignment between two locations in the outer area of Allahabad City, India. Four route alignments are created, and one of the best routes is chosen.

Intersections are critical places which experience high levels of accidents due to the availability of vehicle movements from different directions. Therefore, there is a need to understand the factors that significantly contribute to injuries at such places. These factors can fall under different dimensions in traffic safety such as environmental conditions, road user behavior, traffic police enforcement, road design and crash characteristics. The paper will analyze the factors related to crash characteristics and traffic signal operation that affect the likelihood of accident severity located at intersections. The data for intersection accidents in Abu Dhabi from 2013 to 2016 were used in this analysis. Ordinal logistic model was considered for the analysis to account for the ordinal nature of severity levels. Several diagnostics tests of the model were preformed such as parameters evaluation, overall model evaluation and prediction accuracy. For parameter evaluation, out of 11 independent variables, 6 were non-significant and dropped from the model. Most of the non-significant variables were related to the driver-at-fault details. The results of the final model showed an overall good fit based on a p-value of less than 0.05, as well as a good accuracy of prediction 84.8%. Finally, odds ratios were estimated to interpret the final results of the model.

Multicriterion Decision-Making (MCDM) can be perceived as a process of evaluating real-world situations based on various qualitative/quantitative criteria in certain/uncertain/risky environments in order to find a suitable course of action/choice/strategy/policy among the several available options.

This book concentrates on the basic principles of multicriterion analysis and acquaints the reader with the recent trends in MCDM analysis. It explains the basics of Structured Decision-Making (SDM) and describes the various features of traditional optimization methods such as linear and non-linear programming, and dynamic programming, as well as non-traditional optimization methods such as genetic algorithms, differential evolution, and simulated annealing and quenching.

The text elaborates the normalization methods, weight estimation methods and multiobjective optimization methods both in traditional and non-traditional environments. Classification approaches with cluster validation indices, discrete MCDM methods both in deterministic and fuzzy approach and group decision-making methods are discussed in detail. Advanced topics in decision-making such as data envelopment analysis, Taguchi methodology, ant colony optimization, and particle swarm optimization are also covered.

In addition, the book includes many case studies for better comprehension of the procedures involved in the methods.

KEY FEATURES :

Introduces relevant software to keep the students updated and aware of its potentiality and applicability in multicriterion analysis.

Includes a summary at the end of each chapter to facilitate quick revision of the key learning points.

Provides a number of solved problems to enable students to acquire a clear understanding of the concepts and methods discussed.

Offers several problems at the end of each chapter with answers to help students develop problem-solving skills.

PowerPoint presentations for each chapter are available for instructors.

This book is designed for undergraduate and postgraduate courses in operations research, optimization, soft computing, fuzzy logic and other related courses in engineering and management programmes. It will also be useful to researchers and professionals working in the fields of operations research and management studies.

Complex problems in practice are generally multi-criteria. The criteria may be more or less conflicting and of lesser or greater significance. The possibility of applying multi-criteria decision making is shown through mathematical modeling, adapting known models, or developing new models of selected processes, such as: (a) a range of core activities from operational and annual production plans, transportation plans, contractor selection and management projects to mid-term development plans, and (b) business in various fields economy (metal and chemical industry, glass industry, agriculture, construction, etc.). More important methods have been elaborated or new methods have been developed for pre-defined multi-criteria models and the available software is analyzed and when necessary, appropriate algorithms and software have been developed. Exposed to solving the select specific problems in the above areas, a comparison of those methods was made which enable the same problem to be solved and appropriate conclusions are formulated. In order to facilitate the application of the considered procedures of preparation of elements for decision making in the dissertation, the process of forming multi-criteria models, solving methods and multi-attribute analysis for one complex concrete problem (multiphase production in the chemical industry) was integrated into an appropriate decision support system..

Složeni problemi u praksi su po pravilu sa više kriterijuma. Kriterijumi mogu biti u manjoj ili većoj meri konfliktni i manjeg ili većeg stepena značajnosti.
Mogućnost primene višekriterijumskog odlučivanja pokazuje se kroz
matematičko modeliranje, prilagodjavanjem poznatih modela, odnosno razvojem novih modela odabranih procesa, kao što su: (a) niz osnovnih aktivnosti od operativnih i godišnjih planova proizvodnje, planova transporta, izbora izvodjača i upravljanja
projektima do srednjoročnih planova razvoja, i (b) poslovanje u raznim oblastima
privredjivanja (metalna i hemijska industrija, industrija stakla, poljoprivreda,
gradjevinarstvo i sl.). Obradjene su bitnije metode ili su razvijene nove metode za
napred definisane višekriterijumske modele i analiziran je raspoloživi softver, a kada je
potrebno, razvijeni su odgovarajući algoritmi i softver. Izloženo je rešavanje odabranih
konkretnih problema iz napred navedenih oblasti, izvršena je komparacija onih metoda
koje omogućavaju rešavanje istog problema i formulisani su odgovarajući zaključci. U
cilju da se korisnicima olakša primena u disertaciji razmatranih postupaka pripremanja elemenata za donošenje odluka izvršeno je objedinjavanje procesa formiranja višekriterijumskih modela, metoda rešavanja i višeatributne analize za jedan složeni konkretni problem (višefazne proizvodnje u hemijskoj industriji) u odgovarajući sistem za podršku odlučivanju.

According to the European Railway Agency in the European Union every year on railway level crossings (RLC) occurs over 1200 traffic accident in which life loses more than 400 people. In addition to the tunnel and specific locations that are identified as black spots on the roads, RLC have been identified as potential weak points in road infrastructure that significantly jeopardize traffic safety. In Serbia exists about 2350 RLC, one of which is part the secured by systems of active and passive safety (traffic signs, light signals, sound signals, barriers, etc..). Insurance RLC is a material expenditure. The RLC selection process for installation of security equipment accompanied by a greater or lesser degree of criteria vagueness that are necessary for making the relevant decisions. For exploitation these uncertainties and vagueness in this paper was used fuzzy logic. This paper presents the application of a new method of multi-criteria decision-making (Multi-Atributive Real-Ideal Comparative Analysis - MARICA), which represents support in the selection process for RLC to invest in safety equipment. Identified are eight criteria that influence the investment decision. MARICA method was tested on the example of choice of eight RLC for investing in safety equipment.
Keywords: mathematical decision making model, Multicriteria decision making, MARICA, DEMATEL

The theory of the INDEPENDENT planning of one or more projects and the concurrent planning of multiple projects competing for joint resources are presented.

CA-SuperProject is the only software that supports:

1. Planning of unspent resources (type of workers and mechanization - reducing daily use to the available class of lessons)
2. PLANNING RESOURCES (type of materials and money - procurement, spending, reduction of inventory, stock of materials or liquidity on the project from the point of view of money, new procurement / new inflow or postponement of works until procurement / inflow).
*) Multiple tasks for planning CONSUMER RESOURCES are presented.

**) Cannot be used on computers with newer operating systems !!!

Izložena je teorija o NEZAVISNOM planiranju jednog ili više prjekata i ISTOVREMENOM planiranju više projekata koji konkurišu za zajedničke resurse.
CA-SuperProject je jedini softver koji podržava:
1. Planiranje NEPOTROŠIVIH RESURSA (tipa radnika i mehanizacije - svođenje dnevnog korišćenja u raspoloživi fond časova)
2. Planiranje POTRŠIVIH RESURSA (tipa materijala i novca - nabavke, trošenje, smanjivanje zaliha, stanje zaliha materijala odnosno likvidnost na projektu sa stanovišta novca, nove nabavke /priliv nova ili odlaganje radova do nabbavki / priliva).
*)  Izloženo je više zadataka za planiranje POTROŠIVIH RESURSA.
**) Ne može da se koristi na računarima sa novijim operativnim sistemima !!!

The complex nature of construction projects and the involvement of a large number of unpredictable correlated factors make them susceptible to disputes. Although a wide range of dispute resolution mechanisms exists, experts in the construction industry favor arbitration over litigation when legally binding dispute resolution mechanisms are concerned. Because initiating a litigation or arbitration case against a business partner often severs the business relationship between them, predicting the arbitrator’s decision becomes valuable to the arbitrating parties. Because arbitration has been extensively treated as a game, and because the proposed approach relies on the wealth maximization concept, which is in turn dependent on the sum of utility sources of a firm, modeling arbitration is best achieved as a game with disputing parties’ utility profiles that would have an agreement zone. A construction-specific utility framework for the disputing parties arbitrating before a single arbitrator is proposed based on the additive expected utility theory. The proposed additive utility framework preserves the industry practicality and, most importantly, considers direct short-term factors and indirect long-term factors that would address factual disputes related to claim entitlement and quantification. It is expected that such a framework could then be used to identify utility equilibrium points between the disputing parties, which would serve the purpose of predicting the arbitration outcome.

The paper considers a model of linear linear programming (CLP, GLP) in the problem of the standard cost-based transport task when deviation variables are introduced for the source offers. If the solution requires unacceptable deviations from the starting quotes of certain starting points, then the limits for the corresponding deviation variables are introduced. Illustrative examples are solved with WinQSB (Quantitative Systems for Bussines) Version 1.0 software.

U radu se razmatra model ciljnog linearnog programiranja (CLP, GLP) u problemu standardnog zadatka transporta po troškovima kada se za ponude ishodišta uvode devijacione promenljive. Ako rešenje zahteva neprihvatljiva odstupanja od polaznih ponuda određenih ishodišta, uvode se granice za odgovarajuće devijacione promenljive. Ilustrativni primeri rešavani su softverom WinQSB (Quantitative Systems for Bussines) Version 1.0.

ÖZET Karar verme hayatın her alanında kullanılan bir davranış şeklidir. Bireyler için günlük yaşamı kolaylaştırmak, işletmeler için varlıklarını devam ettirip en çok karı sağlamak, ülkeler için de diğer ülkelerle kıyaslanmasını sağlayacak kararlar almak gibi durumlar mevcuttur. Tüm bu durumlar için alınan kararlara yardımcı olan kriterler mevcuttur. Özellikle işletmelerde yöneticiler kararlarını alırken mevcut alternatifler arasından en uygun olanın seçilmesi ile karşı karşıya kalırlar. Yöneticiler için her konuda olduğu gibi, insan kaynakları açısından tercihlerde bulunurken en ideal çözüme ulaşma konusunda karmaşık değerlendirmelerin ve belirsizliklerin ortada olması, karar süreçlerinin önündeki en önemli problem olarak ortaya çıkmaktadır. Bu nedenle Çok Kriterli Karar Verme yöntemlerinin uygulanmasıyla karmaşıklıklar ve belirsizlikler minimize edilerek optimum tercihin yapılması sağlanır. Bu çalışmada, Avrupa Birliği Katılım Öncesi Yardım Aracı kapsamında Orta Anadolu Kalkınma Ajansı tarafından proje olarak yürütülen Sivas İş Geliştirme Merkezi'nde istihdam edilecek genel müdür pozisyonu için, adaylar arasından en uygun olanın seçimi amaçlanmıştır. Değerlendirmelerde, birbiri ile çelişen kriterlerin bulunduğu durumlarda alternatifler arasında sıralama ve seçim yapılmasına imkân veren VIKOR yöntemi ve alternatiflerin ideal çözüme yakınlık ve uzaklıklarının kıyaslanmasına imkân veren TOPSIS yöntemi kullanılmıştır. VIKOR yöntemi işlem adımlarına göre GM005 ve GM103 kısaltmaları ile verilen alternatifler eş değerli olarak değerlendirilip sıralamada ilk sıralarda yer almışlardır. TOPSIS yöntemine göre GM103 ilk sırada yer alan genel müdür adayıdır. Uygulanan yöntemler sonucunda sıralama referans alınarak, en uygun genel müdür adayları belirlenerek şirketin yönetim kuruluna öneri olarak sunulmuştur. ABSTRACT Decision making is a form of behavior used in all areas of life. There are situations such as facilitating daily life for individuals, maintaining their existence and providing the most profit for businesses, and making decisions for countries to compare with other countries. There are criteria that help the decisions taken for all these situations. Especially in the enterprises, while making their decisions, they are faced with choosing the most suitable one among the alternatives available.

La recherche opérationnelle a traditionnellement pour objectif de minimiser les coûts ou de maximiser les profits. Cet article présente un modèle d’aide à la décision basé sur l’optimisation multicritère qui intègre l’analyse de cycle de vie conséquentielle. Les options considérées sont d’ordre stratégique, car il est question des flux de matière entre les différents produits, les investissements permettant l'intégration de nouvelles technologies et leurs interactions. Grâce à une approche a priori, toutes les solutions ont été explorées, en faisant varier les pondérations de chacun des critères. Il est ainsi possible de générer des fronts de Pareto qui représentent les compromis entre les critères. Ce qui permet à l’industriel de faire une sélection des solutions les plus pertinentes. Le modèle est développé à partir de données spécifiques à une entreprise forestière, couvrant les activités de récolte en forêt et de transformation des produits du bois. Les résultats proposés sont donc propres au contexte de l’entreprise. Malgré cela, dans la partie discussion est présentée une courbe d’abattement des coûts marginaux. Il s’agit d’une représentation qui montre explicitement le coût de la réduction d’émissions de gaz à effet de serre par l’implantation d’une nouvelle technologie. Ce qui pourrait aider la gouvernance publique à fixer le prix de la tonne de carbone.

Personal financial planning is the preparation of target-oriented decisions con-cerning personal assets, incomes, and expenses. Important part of personal financial planning is personal financial scheduling that is about choosing timepoints for real-ization of extraordinary expenses and incomes. As people have different preferences for different financial goals, and the goals are flexible, personal financial planning may be formulated as a multicriteria decision making problem that is usually ad-dressed by trial calculations under different scenarios. We describe a mathematical programming approach for optimal decision making provided that the weights are prescribed to different objectives. To simplify the multiriteria decision making we examine a sum of the weighted goals as an objective function to be maximized via a mathematical program. Solving the mathematical program problem gives an optimal financial schedule concerning personal financial goals and preferences.

International Book Series" Information Science and Computing" 17 A GENERAL PURPOSE SOFTWARE SYSTEM FOR LINEAR OPTIMIZATION AND DECISION SUPPORT “OPTIMA-PLUS” Vassil Vassilev, Mariyana Vassileva, Krassimira Genova, Boris Staykov Abstract: The paper ...

The problem of computing a good approximation set of the Pareto front of a multiobjective optimization problem can be recasted as the maximization of its S-metric value, which measures the dominated hypervolume. In this way, the S-metric has recently been applied in a variety of metaheuristics. In this work, a novel high-precision method for computing approximation sets of a Pareto front with maximal S-Metric is proposed as a high-level relay hybrid of an evolutionary algorithm and a gradient method, both guided by the S-metric. First, an evolutionary multiobjective optimizer moves the initial population close to the Pareto front. The gradient-based method takes this population as its starting point for computing a local maximal approximation set with respect to the S-metric. Thereby, the population is moved according to the gradient of the S-metric. This paper introduces expressions for computing the gradient of a set of points with respect to its S-metric on basis of the gradients of the objective functions. It discusses singularities where the gradient is vanishing or differentiability is one sided. To circumvent the problem of vanishing gradient components of the S-metric for dominated points in the population a penalty approach is introduced. In order to test the new hybrid algorithm, we compute the precise maximizer of the S-metric for a generalized Schaffer problem and show, empirically, that the relay hybrid strategy linearly converges to the precise optimum. In addition we provide first case studies of the hybrid method on complicated benchmark problems.

The issue of electric power grid mode of optimization is one of the basic
directions in power engineering research. Currently, methods other than
classical optimization methods based on various bio-heuristic algorithms are applied. The problems of reactive power optimization in a power grid using bio-heuristic algorithms are considered. These algorithms allow obtaining more efficient solutions as well as taking into account several criteria. The Firefly algorithm is adapted to optimize the placement of reactive power sources as well as to select their values. A key feature of the proposed modification of the Firefly algorithm is the solution for the multi-objective optimization problem. Algorithms based on a bio-heuristic process can find a neighborhood of global extreme, so a local gradient descent in the neighborhood is applied for a more accurate solution of the problem. Comparison of gradient descent, Firefly algorithm and Firefly algorithm with gradient descent is carried out.

This paper introduces a new solution concept for games with incomplete preferences. The concept is based on rationalizability and it is more general than the existing ones based on Nash equilibrium. In rationalizable strategies, we assume that the players choose nondominated strategies given their beliefs of what strategies the other players may choose. Our solution concept can also be used, e.g., in ordinal games where the standard notion of rationalizability cannot be applied. We show that the sets of rationalizable strategies are the maximal mutually nondominated sets. We also show that no new rationalizable strategies appear when the preferences are refined, i.e., when the information gets more precise. Moreover, noncooperative multicriteria games are suitable applications of incomplete preferences. We apply our framework to such games, where the outcomes are evaluated according to several criteria and the payoffs are vector-valued. We use the sets of feasible weights to represent the relative importance of the criteria. We demonstrate the applicability of the new solution concept with an ordinal game and a bicriteria Cournot game.

РЕЙТИНГ В АНАЛИЗЕ ФИНАНСОВО-ХОЗЯЙСТВЕННОЙ ДЕЯТЕЛЬНОСТИ ПРЕДПРИЯТИЯ Клевец Н.И., кандидат технических наук, доцент, Академия биоресурсов и природопользования ФГАОУ ВО «КФУ имени В.И. Вернадского» Многокритериальное ранжирование альтернатив является надежным инструментом анализа эффективности финансово-хозяйственной деятельности предприятия и может быть применено для оценки уровня конкурентоспособности, экономической устойчивости, динамики роста, диагностики кризисных явлений и во многих других случаях. Ключевые слова: рейтинг, многокритериальное ранжирование, финансово-хозяйственная деятельность, уровень конкурентоспособности, диагностика кризисных явлений
Multicriteria ranging of alternatives is an efficient evaluating tool of the enterprise financial and economic efficiency and it can be used to an assessment of a competitiveness level, an economic stability, growth dynamics, the crisis phenomena diagnostics and in many other cases.