Duality for nonlinear multiple-criteria optimization problems

1981 ◽  
Vol 35 (3) ◽  
pp. 367-401 ◽  
Author(s):  
G. R. Bitran
Keyword(s):  
Optimization Problems ◽  
Multiple Criteria ◽  
Multiple Criteria Optimization

DIFFERENT APPROACHES IN MULTIPLE-CRITERIA OPTIMIZATION USING THE TAGUCHI METHOD: A CASE STUDY IN A COLD HEADING PROCESS

2004 ◽  
Vol 03 (01) ◽  
pp. 53-68 ◽  
Author(s):  
A. S. MILANI ◽  
C. EL-LAHHAM ◽  
J. A. NEMES
Keyword(s):  
Taguchi Method ◽  
Optimization Problems ◽  
Real Life ◽  
Multiple Attribute Decision Making ◽  
Multiple Criteria ◽  
Multiple Criteria Optimization ◽  
Multiple Attribute ◽  
Overall Evaluation ◽  
Decision Making Model

Real life engineering problems usually require the satisfaction of different, potentially conflicting criteria. Design optimization, on the other hand, based on the conventional Taguchi method cannot accommodate more than one response. However, by the use of the overall evaluation criterion approach, the method can be applied to multiple-criteria optimization problems. This paper presents the use of different utility function methods as well as a multiple attribute decision-making model in the multiple-criteria optimization of a cold heading process. Different aspects of each method are discussed and compared.

Multiple Criteria Optimization in Data Mining

2011 ◽  
pp. 1386-1389 ◽  
Author(s):  
Gang Kou ◽  
Yi Peng ◽  
Yong Shi
Keyword(s):  
Data Mining ◽  
Financial Management ◽  
Large Scale ◽  
Optimization Problems ◽  
Aircraft Design ◽  
Multiple Criteria ◽  
Design Data ◽  
Multiple Criteria Optimization ◽  
Database Technology ◽  
Classification Prediction

Multiple criteria optimization seeks to simultaneously optimize two or more objective functions under a set of constraints. It has a great variety of applications, ranging from financial management, energy planning, sustainable development, to aircraft design. Data mining is aim at extracting hidden and useful knowledge from large databases. Major contributors of data mining include machine learning, statistics, pattern recognition, algorithms, and database technology (Fayyad, Piatetsky-Shapiro, & Smyth, 1996). In recent years, the multiple criteria optimization research community has actively involved in the field of data mining (See, for example: Yu 1985; Bhattacharyya 2000; Francisci & Collard, 2003; Kou, Liu, Peng, Shi, Wise, & Xu, 2003; Freitas 2004; Shi, Peng, Kou, & Chen, 2005; Kou, Peng, Shi, Wise, & Xu, 2005; Kou, Peng, Shi, & Chen, 2006; Shi, Peng, Kou, & Chen, 2007). Many data mining tasks, such as classification, prediction, clustering, and model selection, can be formulated as multi-criteria optimization problems. Depending upon the nature of problems and the characteristics of datasets, different multi-criteria models can be built. Utilizing methodologies and approaches from mathematical programming, multiple criteria optimization is able to provide effective solutions to large-scale data mining problems. An additional advantage of multi-criteria programming is that it assumes no deterministic relationships between variables (Hand & Henley, 1997).

scholarly journals Multiple-Criteria Fuzzy Optimization of the Heat Treatment Processes for Two Steel Rolled Products

2021 ◽  
Vol 11 (5) ◽  
pp. 2324
Author(s):  
Ludmila Dymova ◽  
Krzysztof Kaczmarek ◽  
Pavel Sevastjanov
Keyword(s):  
Heat Treatment ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Quality Parameters ◽  
Process Quality ◽  
Multiple Criteria ◽  
Technological Parameters ◽  
Multiple Criteria Optimization ◽  
Treatment Processes ◽  
Input Variables

This paper presents a developed method for fuzzy multiple-criteria optimization of the rolled-steel heat treatment processes in the modern metallurgical plant. At the first stage of the study, by means of passive industrial experiments or a mathematical simulation of heat transfer processes, and using statistical methods, the regression dependencies of the output parameters of process quality on the input variables that are technological parameters are established. Then, based on the quality parameters, membership functions are formed that represent local criteria of the process quality, and their ranks are calculated using the matrix of pairwise comparisons. The practically useful methodology of the fuzzy multiple-criteria optimization of technological processes is proposed. To illustrate this methodology’s practical efficiency, the solutions of two optimization problems are found by maximizing the global criterion that aggregates local criteria using their ranks. It is shown that the efficiency of the obtained optimal heat treatment modes significantly exceeds the efficiency of the technology used earlier in the plant.

scholarly journals Weights balancing method using entropy values in solving MCDM problem

2016 ◽  
Vol 57 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Natalja Kosareva
Keyword(s):  
Optimization Problems ◽  
Multiple Criteria ◽  
Multiple Criteria Optimization ◽  
Optimization Task ◽  
Local Extrema ◽  
Criteria Weights

The article shows how multiple criteria optimization problems could be solved by application of modified KEMIRA method, when there are three groups of criteria. Criteria priorities are determined by the entropy, criteria weights are calculated by solving optimization task. The proposed method allows to find one of several possible local extrema.

INVESTIGATION OF HUMAN FACTORS WHILE SOLVING MULTIPLE CRITERIA OPTIMIZATION PROBLEMS IN COMPUTER NETWORK

2009 ◽  
Vol 15 (3) ◽  
pp. 464-479 ◽  
Author(s):  
Tomas Petkus ◽  
Ernestas Filatovas ◽  
Olga Kurasova
Keyword(s):  
Human Factors ◽  
Optimization Problem ◽  
Computer Network ◽  
Optimization Problems ◽  
Multiple Criteria ◽  
Experimental Investigations ◽  
Multiple Criteria Optimization ◽  
Parallel Solution ◽  
Solution Strategies ◽  
Weight Coefficients

The aim of this investigation is to analyze a class of multiple criteria optimization problems that are solved by human‐computer interaction, using a computer network. A multiple criteria problem is iterated by interactively selecting different weight coefficients of the criteria. Several parallel solution strategies for solving this optimization problem have been developed and analyzed. The experiments have shown the importance of human assistance in solving this multiple criteria problem. New experimental investigations have been carried out with a different number of computers and different strategies where the human factors are analyzed. We have investigated the time necessary for human's training to solve this multiple criteria optimization problem, the dependence of human factors on the strategy of parallel solution and on the number of computers in a computer network. Santrauka Tyrimo tikslas – ištirti daugiakriterinių optimizavimo uždavinių klasę, kai uždaviniai sprendžiami kompiuterio ir žmogaus sąveikai naudojant kompiuterių tinklą. Daugiakriterinio optimizavimo uždavinys sprendžiamas interaktyviai, kiekvienam kriterijui parenkami skirtingi svoriniai koeficientai. Šiam uždaviniui spręsti buvo sukurtos ir ištirtos kelios lygiagretaus sprendimo strategijos. Eksperimentai parodė žmogaus, dalyvaujančio sprendžiant šį uždavinį, svarbą. Tiriant žmogiškąjį faktorių buvo atlikti eksperimentiniai tyrimai naudojant skirtingą kompiuterių skaičių pagal skirtingas strategijas. Ištirtas laikas, reikalingas žmogui išmokti spręsti šį daugiakriterinį optimizavimo uždavinį, nustatyta žmogiškojo faktoriaus priklausomybė nuo pasirinktos lygiagretaus sprendimo strategijos ir kompiuterių skaičiaus kompiuterių tinkle.

scholarly journals A Compact Representation of Preferences in Multiple Criteria Optimization Problems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1092
Author(s):  
Francisco Salas-Molina ◽  
David Pla-Santamaria ◽  
Ana Garcia-Bernabeu ◽  
Javier Reig-Mullor
Keyword(s):  
Analytic Hierarchy Process ◽  
Optimization Problems ◽  
Multiple Criteria ◽  
Compact Representation ◽  
Relative Priority ◽  
Analytic Hierarchy ◽  
Multiple Criteria Optimization ◽  
Hierarchy Process ◽  
Strict Priority ◽  
Priority Levels

A critical step in multiple criteria optimization is setting the preferences for all the criteria under consideration. Several methodologies have been proposed to compute the relative priority of criteria when preference relations can be expressed either by ordinal or by cardinal information. The analytic hierarchy process introduces relative priority levels and cardinal preferences. Lexicographical orders combine both ordinal and cardinal preferences and present the additional difficulty of establishing strict priority levels. To enhance the process of setting preferences, we propose a compact representation that subsumes the most common preference schemes in a single algebraic object. We use this representation to discuss the main properties of preferences within the context of multiple criteria optimization.

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