A visual basic tool for Multiple Criteria Optimization (original) (raw)
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A visual interactive method for solving the multiple criteria problem
European Journal of Operational Research, 1986
This paper proposes a new method for solving multiple criteria mathematical programming problems. The method does not rely on explicit knowledge of the properties of the utility function. However, if the utility function is assumed to be pseudoconcave and differentiable when the procedure terminates, sufficient conditions for optimality can be established.
A Software System for Multicriteria Analysis and Optimization
2007
The multicriteria analysis (MA) and multicriteria optimization (MO) problems are multicriteria decision making problems. In MA and MO problems several criteria are simultaneously optimized. In the general case there does not exist one alternative(solution), which optimizes all the criteria. The solution of MA or MO problem is a set of alternatives, called a set of the non-dominating or of the Pareto optimal alternatives. Each alternative in this set could be a solution of the multicriteria problem. In order to select one alternative, it is necessary to have additional information set by the so-called decision maker (DM). The information that the DM provides reflects his/ her global preferences with respect to the quality of the alternative sought. The methods developed to solve MA problems, can be grouped in three separate classes: weighting methods, outranking methods and interactive methods. The main element in the weighting methods is the way of determining the criteria weights, ...
A multiple objective linear programming decision support system
Decision Support Systems, 1990
in this paper we describe the principles of VIG (Visual Interactive Goal Programming), a Multiple Criteria Decision Support System, recently developed by Korhonen. PARETO RACE is a cornerstone of the system, which is designed to support both the modelling and solving of a multiple objective linear programming problem. A menu, spreadsheets, and interactive computer graphics play a key role.
Development of Software for Multiple Criteria Evaluation
Informatica, 2003
This paper considers the main positions of one-sided and two-sided problems. For onesided problems only the method of solution "the distance to the ideal point" is discussed in the actual version. For two-sided problems a distinction is made between games with rational behaviour and games against nature. The main strategic principles are as follows: simple min-max principle, extended min-max principle, Wald's rule, Savage criterion, Hurwicz's rule, Laplace's rule, Bayes's rule, Hodges-Lehmann rule. Questions of transforming the decision-making matrix are considered. The article gives the description of a software as well as an example of an investment variant estimation.
Multiple Criteria Decision Making
The process of multiple criteria decision-making (MCDM) has gained wide popularity in different sciences and applications. As the MCDM methods are much expanded most multiobjective optimization (MOO) problems in different disciplines can be classified on the basis of them. Real-life engineering optimization problems need MOO tools. These problems are highly non-linear. Thus MCDM Meanwhile the increasing number of involved components, variables, parameters, constraints and objectives in the process, has made the process very complicated. However the new generation of MOO tools has made the optimization process more automated, but still initializing the process and setting the initial value of simulation tools and also identifying the effective input variables and objectives in order to reach the smaller design space are still complicated. In this situation adding a preprocessing step into the MCDM procedure could make a huge difference in terms of organizing the input variables according to their effects on the optimization objectives of the system. The aim of this paper is to introduce the classification task of data mining as an effective option for identifying the most effective variables of the MCDM systems. To evaluate the effectiveness of the proposed method an example has been given for 3D wing design.
A Brief Look at Multi-Criteria Problems: Multi-Threshold Optimization versus Pareto-Optimization
IntechOpen
Multi-objective optimization problems are important as they arise in many practical circumstances. In such problems, there is no general notion of optimality, as there are different objective criteria which can be contradictory. In practice, often there is no unique optimality criterion for measuring the solution quality. The latter is rather determined by the value of the solution for each objective criterion. In fact, a practitioner seeks for a solution that has an acceptable value of each of the objective functions and, in practice, there may be different tolerances to the quality of the delivered solution for different objective functions: for some objective criteria, solutions that are far away from an optimal one can be acceptable. Traditional Pareto-optimality approach aims to create all non-dominated feasible solutions in respect to all the optimality criteria. This often requires an inadmissible time. Besides, it is not evident how to choose an appropriate solution from the...
Quality and Reliability Engineering International, 2013
When choosing a best solution based on simultaneously balancing multiple objectives, the Pareto front approach allows promising solutions across the spectrum of user preferences for the weightings of the objectives to be identified and compared quantitatively. The shape of the complete Pareto front provides useful information about the amount of tradeoff between the different criteria and how much compromise is needed from some criterion to improve the others. Visualizing the Pareto front in higher (3 or more) dimensions becomes difficult, so a numerical measure of this relationship helps capture the degree of trade-off. The traditional hypervolume quality indicator based on subjective scaling for multiple criteria optimization method comparison provides an arbitrary value that lacks direct interpretability. This paper proposes an interpretable summary for quantifying the nature of the relationship between criteria with a standardized hypervolume under the Pareto front (HVUPF) for a flexible number of optimization criteria, and demonstrates how this single number summary can be used to evaluate and compare the efficiency of different search methods as well as tracking the search progress in populating the complete Pareto front. A new HVUPF growth plot is developed for quantifying the performance of a search method on completeness, efficiency, as well as variability associated with the use of random starts, and offers an effective approach for method assessment and comparison. Two new enhancements for the algorithm to populate the Pareto front are described and compared with the HVUPF growth plot. The methodology is illustrated with an optimal screening design example, where new Pareto search methods are proposed to improve computational efficiency, but is broadly applicable to other multiple criteria optimization problems.
Journal of Automation, Mobile Robotics & Intelligent Systems, 2015
The paper presents the method of facilitating joint decision making in a competitive environment. We deal with a joint decision when the group of people with different preferences are to make one single decision. The joint decision selection process is modelled with the use of multi-criteria optimization task. It is solved with the use of reference point method. This method is an interactive method in which every person specifies its requirements in the form of a reference point, expressing the desired values for its evaluation function. On the basis of the provided reference point, a scalar achievement function is built. Maximization of this function generates a solution of the multi-criteria task. This solution is presented to every person for acceptance or as a basis for the modification of the reference point. The paper gives an example of applying the proposed decision making while competing by three persons of different preferences.
Pareto multi-criteria decision making q
The paper concerns design governed by multiple objective criteria, which are conflicting in the sense of competing for common resources to achieve variously different performance objectives (financial, functional, environmental, esthetical, etc.). A multi-criteria decision making (MCDM) strategy is proposed that employs a tradeoff-analysis technique to identify compromise designs for which the competing criteria are mutually satisfied in a Pareto-optimal sense. The MCDM strategy is initially developed for the case of design governed by n = 2 objective criteria. It is then extended to design governed by n > 2 objective criteria, by introducing the concept of primary and aggregate criteria. It is proved that, from among the theoretically infinite number of feasible designs forming the Pareto front for a design problem governed by n independent objective criteria, there exists a unique Pareto-compromise design that represents a mutually agreeable tradeoff between all n criteria. This remarkable result is illustrated for a flexural plate design governed by n = 2 criteria, a bridge maintenance-intervention protocol design governed by n = 3 criteria, and a media centre envelop design governed by n = 11 criteria.
A robust multi-criteria optimization approach
Mechanism and Machine Theory, 1997
The overall value of a product is typically determined by its performance with respect to multiple measures. As such, the product design task will be simplified if all these performance measures were optimized simultaneously. Another significant factor that ...