On the number of local minima for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) is an NP-hard combinatorial optimization problem occurring in many applications, such as data association, target tracking, and resource planning. As many solution approaches to this problem rely, at least partly, on local neighborhood search algorithms, the number of local minima affects solution difficulty for these algorithms. This paper investigates the expected number of local minima in randomly generated instances of the MAP. Lower and upper bounds are developed for the expected number of local minima, E[M], in an MAP with iid standard normal coefficients. In a special case of the MAP, a closed-form expression for E[M] is obtained when costs are iid continuous random variables. These results imply that the expected number of local minima is exponential in the number of dimensions of the MAP. Our numerical experiments indicate that larger numbers of local minima have a statistically significant negative effect on the quality of solutions produced by several heuristic algorithms that involve local neighborhood search.Partially supported by the NSF grant DMI-0457473.     

Statistical considerations for crowdsourced perceptual ratings of human speech productions

Crowdsourcing has become a major tool for scholarly research since its introduction to the academic sphere in 2008. However, unlike in traditional laboratory settings, it is nearly impossible to control the conditions under which workers on crowdsourcing platforms complete tasks. In the study of communication disorders, crowdsourcing has provided a novel solution to the collection of perceptual ratings of human speech production. Such ratings allow researchers to gauge whether a treatment yields meaningful change in how human listeners' perceive disordered speech. This paper will explore some statistical considerations of crowdsourced data with specific focus on collecting perceptual ratings of human speech productions. Random effects models are applied to crowdsourced perceptual ratings collected in both a continuous and binary fashion. A simulation study is conducted to test the reliability of the proposed models under differing numbers of workers and tasks. Finally, this methodology is applied to a data set from the study of communication disorders.     

Robust multi-sensor scheduling for multi-site surveillance

This paper presents mathematical programming techniques for solving a class of multi-sensor scheduling problems. Robust optimization problems are formulated for both deterministic and stochastic cases using linear 0–1 programming techniques. Equivalent formulations are developed in terms of cardinality constraints. We conducted numerical case studies and analyzed the performance of optimization solvers on the considered problem instances.     

Revised GRASP with path-relinking for the linear ordering problem

The linear ordering problem (LOP) is an NP\mathcal{NP}-hard combinatorial optimization problem with a wide range of applications in economics, archaeology, the social sciences, scheduling, and biology. It has, however, drawn little attention compared to other closely related problems such as the quadratic assignment problem and the traveling salesman problem. Due to its computational complexity, it is essential in practice to develop solution approaches to rapidly search for solution of high-quality. In this paper we propose a new algorithm based on a greedy randomized adaptive search procedure (GRASP) to efficiently solve the LOP. The algorithm is integrated with a Path-Relinking (PR) procedure and a new local search scheme. We tested our implementation on the set of 49 real-world instances of input-output tables (LOLIB instances) proposed in Reinelt (Linear ordering library (LOLIB) 2002). In addition, we tested a set of 30 large randomly-generated instances proposed in Mitchell (Computational experience with an interior point cutting plane algorithm, Tech. rep., Mathematical Sciences, Rensellaer Polytechnic Institute, Troy, NY 12180-3590, USA 1997). Most of the LOLIB instances were solved to optimality within 0.87 seconds on average. The average gap for the randomly-generated instances was 0.0173% with an average running time of 21.98 seconds. The results indicate the efficiency and high-quality of the proposed heuristic procedure.     

On the complexity of path problems in properly colored directed graphs

We address the complexity class of several problems related to finding a path in a properly colored directed graph. A properly colored graph is defined as a graph G whose vertex set is partitioned into $\mathcal{X}(G)$ stable subsets, where $\mathcal{X}(G)$ denotes the chromatic number of G. We show that to find a simple path that meets all the colors in a properly colored directed graph is NP-complete, and so are the problems of finding a shortest and longest of such paths between two specific nodes.     

Attachment and Coping Strategies in Middle Childhood Children whose Mothers Have a Mental Health Problem: Implications for Social Work Practice

Mental health has implications for the quality of relationshipswithin a family, particularly between parents and children,but also between other family and non-family members. Previousresearch has investigated parental reports of attachment infamilies with mental health problems, but relationship representationsas experienced by these children, especially in middle childhood,have not been so frequently investigated. An understanding ofchildren’s representations of attachment relationshipsand the different coping strategies that may result is importantfor social work practice when offering support, not only tothe children, but also other family members. Methods of investigatingattachment, such as the Separation Anxiety Test, have been usedto understand the relationship issues, fears and coping strategiesof other vulnerable children, and this study was designed specificallyto investigate relationship issues in middle childhood childrenwhose mothers had previously been hospitalized with mental healthproblems. We found that these children tended to be less emotionallyopen and secure, and generated fewer adaptive coping strategiesthan children whose mothers had never had mental health problems.Other themes also emerged from the interviews, such as a senseof trust in the parent–child relationship and the ‘containment’of fears. Implications for social work practice are discussed.     

Set and revealed preference axioms for multi-valued choice

Theory and Decision - We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We...