Generalized Scalarizing Problems GENS and GENSLex of Multicriteria Optimization

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making".

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Classification-Based Method of Linear Multicriteria Optimization

The paper describes a classification-based learning-oriented interactive method for solving linear multicriteria optimization problems. The method allows the decision makers describe their preferences with greater flexibility, accuracy and reliability. The method is realized in an experimental software system supporting the solution of multicriteria optimization problems.

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

DC Fuzzy Multicriteria Approach to Increase the Probability of Delivering Power in Distribution Networks

This paper proposes a methodology to increase the probability of delivering power to any load point through the identification of new investments. The methodology uses a fuzzy set approach to model the uncertainty of outage parameters, load and generation. A DC fuzzy multicriteria optimization model considering the Pareto front and based on mixed integer non-linear optimization programming is developed in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power to all customers in the distribution network at the minimum possible cost for the system operator, while minimizing the non supplied energy cost. To illustrate the application of the proposed methodology, the paper includes a case study which considers an 33 bus distribution network.

MultiDecision-2: A Multicriteria Decision Support System

The paper presents a multicriteria decision support system, called MultiDecision-2, which consists of two independent parts - MKA-2 subsystem and MKO-2 subsystem. MultiDecision-2 software system supports the decision makers (DMs) in the solving process of different problems of multicriteria analysis and linear (continues and integer) problems of multicriteria optimization. The two subsystems MKA-2 and MKO-2 of of MultiDecision-2 are briefly described in the paper in the terms of the class of the problems being solved, the system structure, the operation with the interface modules for input data entry and the information about DM’s local preferences, as well as the operation with the interface modules for visualization of the current and final solutions.

A Multicriteria Decision Support System MultiDecision-1

* This paper is partially supported by the National Science Fund of Bulgarian Ministry of Education and Science under contract № I–1401\2004 "Interactive Algorithms and Software Systems Supporting Multicriteria Decision Making."

A redistricting problem applied to meter reading in power distribution networks

The capacitated redistricting problem (CRP) has the objective to redefine, under a given criterion, an initial set of districts of an urban area represented by a geographic network. Each node in the network has different types of demands and each district has a limited capacity. Real-world applications consider more than one criteria in the design of the districts, leading to a multicriteria CRP (MCRP). Examples are found in political districting, sales design, street sweeping, garbage collection and mail delivery. This work addresses the MCRP applied to power meter reading and two criteria are considered: compactness and homogeneity of districts. The proposed solution framework is based on a greedy randomized adaptive search procedure and multicriteria scalarization techniques to approximate the Pareto frontier. The computational experiments show the effectiveness of the method for a set of randomly generated networks and for a real-world network extracted from the city of São Paulo. © 2013 Elsevier Ltd.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

Multicriteria Evaluation and Optimization of Hierarchical Systems

It is shown that any multicriteria problem can be represented by a hierarchical system. Separate properties of the object are evaluated at the lower level of the system, using a criteria vector, and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriteria problems of evaluation and optimization. It is based on nested scalar convolutions of vector- valued criteria and allows simple structural and parametrical synthesis of multicriteria hierarchical systems.

Decision making in fuzzy environment and multicriteria power engineering problems

This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multicriteria power engineering problems. The application of the approach conforms to the principle of guaranteed result and provides constructive lines in computationally effective obtaining harmonious solutions on the basis of solving associated maxmin problems. The presented results are universally applicable and are already being used to solve diverse classes of power engineering problems. It is illustrated by considering problems of power and energy shortage allocation, power system operation, optimization of network configuration in distribution systems, and energetically effective voltage control in distribution systems. (c) 2011 Elsevier Ltd. All rights reserved.

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process. The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert`s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index. In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology. (C) 2009 Elsevier Inc. All rights reserved.

Swarm Intelligent Selection and Optimization of Machining System Parameters for Microchannel Fabrication in Medical Devices

Current technology trends in medical device industry calls for fabrication of massive arrays of microfeatures such as microchannels on to nonsilicon material substrates with high accuracy, superior precision, and high throughput. Microchannels are typical features used in medical devices for medication dosing into the human body, analyzing DNA arrays or cell cultures. In this study, the capabilities of machining systems for micro-end milling have been evaluated by conducting experiments, regression modeling, and response surface methodology. In machining experiments by using micromilling, arrays of microchannels are fabricated on aluminium and titanium plates, and the feature size and accuracy (width and depth) and surface roughness are measured. Multicriteria decision making for material and process parameters selection for desired accuracy is investigated by using particle swarm optimization (PSO) method, which is an evolutionary computation method inspired by genetic algorithms (GA). Appropriate regression models are utilized within the PSO and optimum selection of micromilling parameters; microchannel feature accuracy and surface roughness are performed. An analysis for optimal micromachining parameters in decision variable space is also conducted. This study demonstrates the advantages of evolutionary computing algorithms in micromilling decision making and process optimization investigations and can be expanded to other applications

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Systematic Approach for the selection of monitoring technologies in CO2 geological storage projects. Application of multicriteria decision making

Geologic storage of carbon dioxide (CO2) has been proposed as a viable means for reducing anthropogenic CO2 emissions. Once injection begins, a program for measurement, monitoring, and verification (MMV) of CO2 distribution is required in order to: a) research key features, effects and processes needed for risk assessment; b) manage the injection process; c) delineate and identify leakage risk and surface escape; d) provide early warnings of failure near the reservoir; and f) verify storage for accounting and crediting. The selection of the methodology of monitoring (characterization of site and control and verification in the post-injection phase) is influenced by economic and technological variables. Multiple Criteria Decision Making (MCDM) refers to a methodology developed for making decisions in the presence of multiple criteria. MCDM as a discipline has only a relatively short history of 40 years, and it has been closely related to advancements on computer technology. Evaluation methods and multicriteria decisions include the selection of a set of feasible alternatives, the simultaneous optimization of several objective functions, and a decision-making process and evaluation procedures that must be rational and consistent. The application of a mathematical model of decision-making will help to find the best solution, establishing the mechanisms to facilitate the management of information generated by number of disciplines of knowledge. Those problems in which decision alternatives are finite are called Discrete Multicriteria Decision problems. Such problems are most common in reality and this case scenario will be applied in solving the problem of site selection for storing CO2. Discrete MCDM is used to assess and decide on issues that by nature or design support a finite number of alternative solutions. Recently, Multicriteria Decision Analysis has been applied to hierarchy policy incentives for CCS, to assess the role of CCS, and to select potential areas which could be suitable to store. For those reasons, MCDM have been considered in the monitoring phase of CO2 storage, in order to select suitable technologies which could be techno-economical viable. In this paper, we identify techniques of gas measurements in subsurface which are currently applying in the phase of characterization (pre-injection); MCDM will help decision-makers to hierarchy the most suitable technique which fit the purpose to monitor the specific physic-chemical parameter.