Murat Köksalan

Fuzzy versus statistical linear regression

Abstract Statistical linear regression and fuzzy linear regression have been developed from different perspectives, and thus there exist several conceptual and methodological differences between the two approaches. The characteristics of both methods, in terms of basic assumptions, parameter estimation, and application are described and contrasted. Their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other. It turns out that statistical linear regression is superior to fuzzy linear regression in terms of predictive capability, whereas their comparative descriptive performance depends on various factors associated with the data set (size, quality) and proper specificity of the model (aptness of the model, heteroscedasticity, autocorrelation, nonrandomness of error terms). Specifically, fuzzy linear regression performance becomes relatively better, vis-a-vis statistical linear regression, as the size of the data set diminishes and the aptness of the regression model deteriorates. Fuzzy linear regression may thus be used as a viable alternative to statistical linear regression in estimating regression parameters when the data set is insufficient to support statistical regression analysis and/or the aptness of the regression model is poor (e.g., due to vague relationship among variables and poor model specification).

Multiple Criteria Decision Making:From Early History to the 21st Century

Multiple Criteria Decision Making (MCDM) is all about making choices in the presence of multiple conflicting criteria. MCDM has become one of the most important and fastest growing subfields of Operations Research/Management Science. As modern MCDM started to emerge about 50 years ago, it is now a good time to take stock of developments. This book aims to present an informal, nontechnical history of MCDM, supplemented with many pictures. It covers the major developments in MCDM, from early history until now. It also covers fascinating discoveries by Nobel Laureates and other prominent scholars. The book begins with the early history of MCDM, which covers the roots of MCDM through the 1960s. It proceeds to give a decade-by-decade account of major developments in the field starting from the 1970s until now. Written in a simple and accessible manner, this book will be of interest to students, academics, and professionals in the field of decision sciences.

An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization

We propose an evolutionary metaheuristic for multiobjective combinatorial optimization problems that interacts with the decision maker (DM) to guide the search effort toward his or her preferred solutions. Solutions are presented to the DM, whose pairwise comparisons are then used to estimate the desirability or fitness of newly generated solutions. The evolutionary algorithm comprising the skeleton of the metaheuristic makes use of selection strategies specifically designed to address the multiobjective nature of the problem. Interactions with the DM are triggered by a probabilistic evaluation of estimated fitnesses, while memory structures with indifference thresholds restrict the presentation of solutions resembling those that have already been rejected. The algorithm has been tested on a number of random instances of the Multiobjective Knapsack Problem (MOKP) and the Multiobjective Spanning Tree Problem (MOST). Simulation results indicate that the algorithm requires only a small number of comparisons to be made for satisfactory solutions to be found.

An interactive approach for placing alternatives in preference classes

Abstract In this paper, we consider the multiple criteria decision making problem of partitioning alternatives into preference classes. We develop an interactive procedure based on the assumption that the decision maker (DM) has a linear utility function. The approach requires the DM to place an alternative in a preference class from time to time. Based on the preference information derived from the DM’s placement as well as from dominance and linearity, we try to place other alternatives. We present results on the performance of the algorithm applied to four different sets of alternatives.

Optimization of printed circuit board manufacturing: Integrated modeling and algorithms

This paper focuses on an integrated optimization problem that is designed to improve productivity in printed circuit board (PCB) manufacturing. We examine the problems of allocating the components to feeders and sequencing the placement of these components on the PCBs, populated by a rotary head machine with surface mount technology. While previous research focuses on sequencing the placement and only considers this subproblem as part of an interrelated set of problems, we provide an integrated approach which tackles all subproblems simultaneously as a single problem. Given an e-approximation algorithm for the vehicle routing problem we present a solution with an e-error gap for the PCB problem. ” 2000 Elsevier Science B.V. All rights reserved.

Locating Disaster Response Facilities in Istanbul

We study the problem of locating disaster response and relief facilities in the city of Istanbul, where a massively destructive earthquake is expected to occur in the near future. The Metropolitan Municipality of Istanbul decided to establish facilities to preposition relief aid and execute post-disaster response operations. We propose a two-tier distribution system that utilizes existing public facilities locally in addition to the new facilities that will act as regional supply points. We develop mathematical models to decide on the locations of the new facilities with the objectives of minimizing the average-weighted distance between casualty locations and closest facilities, and opening a small number of facilities, subject to distance limits and backup requirements under regional vulnerability considerations. We analyze the trade-offs between these two objectives under various disaster scenarios and investigate the solutions for several modelling extensions. The results demonstrate that a small number of facilities will be sufficient and their locations are robust to various parameter and modelling changes.

A Territory Defining Multiobjective Evolutionary Algorithms and Preference Incorporation

We have developed a steady-state elitist evolutionary algorithm to approximate the Pareto-optimal frontiers of multiobjective decision making problems. The algorithms define a territory around each individual to prevent crowding in any region. This maintains diversity while facilitating the fast execution of the algorithm. We conducted extensive experiments on a variety of test problems and demonstrated that our algorithm performs well against the leading multiobjective evolutionary algorithms. We also developed a mechanism to incorporate preference information in order to focus on the regions that are appealing to the decision maker. Our experiments show that the algorithm approximates the Pareto-optimal solutions in the desired region very well when we incorporate the preference information.

Using genetic algorithms for single-machine bicriteria scheduling problems

Abstract We consider two bicriteria scheduling problems on a single machine: minimizing flowtime and number of tardy jobs, and minimizing flowtime and maximum earliness. Both problems are known to be NP-hard. For the first problem, we developed a heuristic that produces an approximately efficient solution (AES) for each possible value the number of tardy jobs can take over the set of efficient solutions. We developed a genetic algorithm (GA) that further improves the AESs. We then adapted the GA for the second problem by exploiting its special structure. We present computational experiments that show that the GAs perform well. Many aspects of the developed GAs are quite general and can be adapted to other multiple criteria scheduling problems.

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.

An interactive sorting method for additive utility functions

In this paper, we consider the problem of placing alternatives that are defined by multiple criteria into preference-ordered categories. We consider a method that estimates an additive utility function and demonstrate that it may misclassify many alternatives even when substantial preference information is obtained from the decision maker (DM) to estimate the function. To resolve this difficulty, we develop an interactive approach. Our approach occasionally requires the DM to place some reference alternatives into categories during the solution process and uses this information to categorize other alternatives. The approach guarantees to place all alternatives correctly for a DM whose preferences are consistent with any additive utility function. We demonstrate that the approach works well using data derived from ranking global MBA programs as well as on several randomly generated problems.