Stepwise contouring of efficient criterion vectors for large-scale MOLP

In this paper a new method of presenting the overall (focused) structure of the efficient criterion vectors (N) for large-scale MOLP is proposed. The proposed algorithm ASEOV (approximation of the set of efficient objective vectors) determines the representative subset of N and ensures full coverage of N , with corresponding coverage precision indicated. ASEOV works in objective space directly and eliminates unnecessary computational effort at the collapsing extreme points of X , which are transformed to non-extreme points in objective space. The Tchebycheff metric is employed to measure the coverage precision. ASEOV allows a decision maker (DM) to control the determination procedure by assessing the coverage allowance for each criterion. When the DM's preference is available, ASEOV can focus contouring on the subset of N which fits with the extracted preference. Combined with proper interactive methods, this focused contour over N can reduce the DM's burden, inconsistency or cognitive bias in assessing his preference from which to derive the final best-compromise solution. An illustrative example is presented.     

Surrogate‐assisted multicriteria optimization: Complexities,prospective solutions,and business case

Complexity in solving real‐world multicriteria optimization problems often stems from the fact that complex, expensive, and/or time‐consuming simulation tools or physical experiments are used to evaluate solutions to a problem. In such settings, it is common to use efficient computational models, often known as surrogates or metamodels, to approximate the outcome (objective or constraint function value) of a simulation or physical experiment. The presence of multiple objective functions poses an additional layer of complexity for surrogate‐assisted optimization. For example, complexities may relate to the appropriate selection of metamodels for the individual objective functions, extensive training time of surrogate models, or the optimal use of many‐core computers to approximate efficiently multiple objectives simultaneously. Thinking out of the box, complexity can also be shifted from approximating the individual objective functions to approximating the entire Pareto front. This leads to further complexities, namely, how to validate statistically and apply the techniques developed to real‐world problems. In this paper, we discuss emerging complexity‐related topics in surrogate‐assisted multicriteria optimization that may not be prevalent in nonsurrogate‐assisted single‐objective optimization. These complexities are motivated using several real‐world problems in which the authors were involved. We then discuss several promising future research directions and prospective solutions to tackle emerging complexities in surrogate‐assisted multicriteria optimization. Finally, we provide insights from an industrial point of view into how surrogate‐assisted multicriteria optimization techniques can be developed and applied within a collaborative business environment to tackle real‐world problems.     

Using the dual‐criteria methods to supplement visual inspection: An analysis of nonsimulated data

The purpose of our study was to examine the probability of observing false positives in nonsimulated data using the dual‐criteria methods. We extracted data from published studies to produce a series of 16,927 datasets and then assessed the proportion of false positives for various phase lengths. Our results indicate that collecting at least three data points in the first phase (Phase A) and at least five data points in the second phase (Phase B) is generally sufficient to produce acceptable levels of false positives.     

Age of Onset of ADHD in a Sample of Elementary School Students

Examined the age of onset of ADHD symptoms and subtypes using parent ratings of a large sample of elementary school students. Results showed: (1) in children with ADHD-combined type, hyperactive-impulsive symptoms emerged at younger ages than inattention symptoms; (2) about one-fifth of children who met symptom count and impairment criteria for ADHD did not meet the age of onset criterion; (3) Children who did not meet the age of onset criterion consisted primarily of children with inattention problems; and (4) children who did not meet the age of onset criterion had more impaired parent-child relationships, self-esteem, family functioning, and higher overall impairment ratings than children who did meet the criterion. These results raise questions about the validity of the age of onset criterion for ADHD as formulated in DSM-IV.     

A dynamic objective–subjective structure for forest management focusing on environmental issues

In this paper a decision-making process is applied to a Chilean forestry firm that must deal with a host of environmental variables as well as profit making. At the core of this process is a ‘dynamic objective–subjective structure’ founded on the approach that decision making is about comprehending the preferences of the various parties involved and expanding the set of alternatives open to the decision makers. This is in contrast to many models that aim at finding the ‘best alternative’ and to decision analysis approaches that focus on presenting preferences via value functions. The paper describes in chronological order, following the sessions of a decision-making process, how the various components of the structure emerged. In doing so it demonstrates how the process led to an understanding of the real effects of dealing with the environment and how comprehending the preferences led to the introduction of new decision variables. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi‐criteria minisum facility location problems

This paper deals with the multi‐criteria Weber (minisum) problem. Several new solution concepts are introduced, related to ideas of equilibrium between the different aspects covered by the objectives. Structural results are presented characterizing the proposed solution sets and showing the relationships existing with the efficient sets in the point objective location problem. Also, algorithms to solve this problem for the polyhedral norm case are developed. The proposed approach is more general than previously studied on multi‐criteria location problems and is particularly applicable in the real world when different scenarios must be compared. Copyright © 1999 John Wiley & Sons, Ltd.     

Evolution of multi‐criteria analysis: a scientometric analysis

The field of multi‐criteria analysis has known very important developments during the last 20 years, if one considers the very large amount of activities that it has generated and continues to generate (papers in journals, a dedicated journal, books, meetings, applications, …). Even if multi‐criteria analysis has reached some maturity, its future is subject to questions and debate among its researchers: what is the evolution of the field? What is its structure? Is it integrating new topics? In order to answer such questions at least partially, we have studied multi‐criteria analysis literature by means of the method of associated words (scientometric analysis) and the software ‘Leximappe’. All the abstracts of the papers which are relative to multi‐criteria analysis and are included in the bibliographic ABI‐INFORM database from 1985 to 1996 have been analysed. In this paper, we will present some results of this study. Copyright © 1999 John Wiley & Sons, Ltd.     

Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi‐criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi‐criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. Copyright © 1999 John Wiley & Sons, Ltd.     

Detecting local convexity on the pareto surface

Recent regain in interest in multi‐criteria optimization approaches to provide a designer with multiple solutions to select from and support decisions has led to various methodologies to generate such solutions and possibly approximate the Pareto set. This paper introduces the notions of H‐ and w‐convexities, and develops a simple method to identify local convexity of Pareto hyper‐surfaces since their shape can dictate the choice of the method to use to obtain Pareto solutions and possibly to build an approximation of that set. The method is based on comparing the results from the weighting method to those of the Tchebycheff method at any point on the Pareto hyper‐surface. If, under some conditions, the points obtained from the two methods are identical or not, a local convexity or its lack can be assumed at that location and in its immediate neighbourhood. A numerical example is included. Copyright © 2002 John Wiley & Sons, Ltd.