A branch-and-bound algorithm for fitting anti-robinson structures to symmetric dissimilarity matrices

The seriation of proximity matrices is an important problem in combinatorial data analysis and can be conducted using a variety of objective criteria. Some of the most popular criteria for evaluating an ordering of objects are based on (anti-) Robinson forms, which reflect the pattern of elements within each row and/or column of the reordered matrix when moving away from the main diagonal. This paper presents a branch-and-bound algorithm that can be used to seriate a symmetric dissimilarity matrix by identifying a reordering of rows and columns of the matrix optimizing an anti-Robinson criterion. Computational results are provided for several proximity matrices from the literature using four different anti-Robinson criteria. The results suggest that with respect to computational efficiency, the branch-and-bound algorithm is generally competitive with dynamic programming. Further, because it requires much less storage than dynamic programming, the branch-and-bound algorithm can provide guaranteed optimal solutions for matrices that are too large for dynamic programming implementations.     

Riemannian Newton and trust-region algorithms for analytic rotation in exploratory factor analysis

In exploratory factor analysis, latent factors and factor loadings are seldom interpretable until analytic rotation is performed. Typically, the rotation problem is solved by numerically searching for an element in the manifold of orthogonal or oblique rotation matrices such that the rotated factor loadings minimize a pre-specified complexity function. The widely used gradient projection (GP) algorithm, although simple to program and able to deal with both orthogonal and oblique rotation, is found to suffer from slow convergence when the number of manifest variables and/or the number of latent factors is large. The present work examines the effectiveness of two Riemannian second-order algorithms, which respectively generalize the well-established truncated Newton and trust-region strategies for unconstrained optimization in Euclidean spaces, in solving the rotation problem. When approaching a local minimum, the second-order algorithms usually converge superlinearly or even quadratically, better than first-order algorithms that only converge linearly. It is further observed in Monte Carlo studies that, compared to the GP algorithm, the Riemannian truncated Newton and trust-region algorithms require not only much fewer iterations but also much less processing time to meet the same convergence criterion, especially in the case of oblique rotation.     

On the advancement and software support of decision‐making in focused ultrasound therapy

Focused ultrasound therapy (FUS) is a modern and promising way for minimally invasive cancer treatment. Recent advances in treatment technology, bio‐physical models, and numerical simulation methods have given rise to a significant curative potential. However, clinical routine of FUS still features classical planning approaches, which widely fail in exploiting this potential. The structure of FUS planning problems strongly suggests interactive multi‐criteria decision‐making concepts in order to improve treatment quality. This research work introduces an multi‐criteria decision‐making approach to FUS planning and explains how to bridge the conceptual gap between the clinical state of the art and this new planning paradigm.     

A bare bones bacterial foraging optimization algorithm

Bacterial foraging optimization (BFO), based on the social foraging behaviors of bacteria, is a new intelligent optimizer. It has been widely accepted as an optimization algorithm of current interest for a variety of fields. However, compared with other optimizers, the BFO possesses a poor convergence performance over complex optimization problems. To improve the optimization capability of the BFO, in this paper a bare bones bacterial foraging optimization (BBBFO) algorithm is developed. First, a chemotactic strategy based on Gaussian distribution is incorporated into this method through making use of both the historical information of individual and the share information of group. Then the swarm diversity is introduced in the reproduction strategy to promote the exploration ability of the algorithm. The performance of BBBFO is verified on various benchmark functions, the comparative results reveal that the proposed approach is more superior to its counterparts.     

A goal programming model for crew duties generation

An Erratum has been published for this article in Journal of Multi‐Criteria Decision Analysis 10(5) 2001, 285. This paper proposes a model for the generation of daily work duties of airside crew (being bus drivers) at the Hong Kong International Airport. The results can be adopted as a good crew schedule, in the sense that it is both feasible, satisfying requirements of various work conditions, and ‘optimal’ in minimizing overtime shifts. It is formulated as a goal programme, specifically designed to cater for the manpower planning issues to handle frequent changes of flight schedules by flexibility in work patterns of driver duties. Illustrative results from an actual case study are given. Copyright © 2001 John Wiley & Sons, Ltd.     

A Bibliographic Survey of the Activities and International Nature of Multiple Criteria Decision Making

One of the fascinating things about multiple criteria decision making (MCDM) is the degree to which the contributions that have built the field have come from all over the world. In this paper the international nature of the authorships of the 1216 refereed journal articles published on MCDM between 1987 and 1992, and the journals in which they have appeared, is examined. Also, an analysis of the 217 books and 31 journal special issues that have been published on MCDM, and 143 conferences that have been held on MCDM since the inception of the field, is similarly conducted. The paper concludes with a conference organizer, author and special issue guest editor index.     

Combining diversity and dispersion criteria for anticlustering: A bicriterion approach

Most partitioning methods used in psychological research seek to produce homogeneous groups (i.e., groups with low intra-group dissimilarity). However, there are also applications where the goal is to provide heterogeneous groups (i.e., groups with high intra-group dissimilarity). Examples of these anticlustering contexts include construction of stimulus sets, formation of student groups, assignment of employees to project work teams, and assembly of test forms from a bank of items. Unfortunately, most commercial software packages are not equipped to accommodate the objective criteria and constraints that commonly arise for anticlustering problems. Two important objective criteria for anticlustering based on information in a dissimilarity matrix are: a diversity measure based on within-cluster sums of dissimilarities; and a dispersion measure based on the within-cluster minimum dissimilarities. In many instances, it is possible to find a partition that provides a large improvement in one of these two criteria with little (or no) sacrifice in the other criterion. For this reason, it is of significant value to explore the trade-offs that arise between these two criteria. Accordingly, the key contribution of this paper is the formulation of a bicriterion optimization problem for anticlustering based on the diversity and dispersion criteria, along with heuristics to approximate the Pareto efficient set of partitions. A motivating example and computational study are provided within the framework of test assembly.     

A non-linear multi-criteria model for strategic fms selection decisions

The strategic decision of selecting an optimal flexible manufacturing system (FMS) configuration is a complicated question which involves evaluating trade-offs between a number of different, potentially conflicting criteria such as annual production volume, flexibility, production and investment costs and average throughput of the system. Recently, several structured multicriteria approaches have been proposed to aid management in the FMS selection process. While acknowledging the non-linear nature of a number of the relationships in the model, notably between batch size and the number of batches produced of each part, these studies used linear simplifications to illustrate the decision dynamics of the problem. These linear models were shown to offer useful analytical tools in the FMS pre-design process. Owing to the non-linearities of the true relationships, however, the trade-offs between the criteria could not fully be explored within the linear framework. This paper builds on the two-phase decision support framework proposed by Stam and Kuula (1991) and uses a modified non-linear multi-criteria formulation to solve the problem. The software used in the illustration can easily be implemented, is user-interactive and menu-driven. The methodology is applied to real data from a Finnish metal product company and the results are compared with those obtained in previous studies.     

Pairwise agreement of gradient directions in interactive multicriterion optimization

Statistical tests involving mean directions have in the past been limited to two- and three-dimensional settings, perhaps owing to their primary applications to such fields as geology, meteorology and related earth sciences. In the study of interactive multicriterion optimization it becomes necessary to compare gradient directions obtained from decision makers by two or more methods. Typically these direction vectors are in a higher-dimensional space. This paper provides a general procedure based on Householder transformations which is potentially suitable for any finite dimension. An illustration and comparison of the method are provided.     

Multicriteria Optimization Technique for Optimal Design of Orthotropic Bridges

The design improvement of large‐scale structures such as cable stayed and suspension bridges with large spans is one of the major engineering optimization problems faced by design engineers. In many real‐life engineering design problems, it is necessary to carry out large‐scale experimental physical models for only one prototype to construct the feasible solution set that is too expensive and not practical. For these reasons, an experimental search for optimal solutions is often not carried out at all. This paper presents a technique for multicriteria analysis, which involve the finite element analysis of the prototype in the optimization process. The improvement of the Suez Canal Bridge in Egypt is introduced as a real‐life large‐scale case study. The parameter space investigation method, the visual basic for application programming language, and Femap as finite element analysis software provide an implementation tools to construct the feasible and Pareto solution sets for the studied bridge. An efficient combination between the parameter space investigation method and the finite element programme was successfully investigated to obtain the Pareto solution set. This study shows possibility to apply the multicriteria optimization method for more applications on different large‐scale structural systems in the future. Copyright © 2013 John Wiley & Sons, Ltd.