Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.

Instance generators and test suites for the multiobjective quadratic assignment problem

We describe, and make publicly available, two problem instance generators for a multiobjective version of the well-known quadratic assignment problem (QAP). The generators allow a number of instance parameters to be set, including those controlling epistasis and inter-objective correlations. Based on these generators, several initial test suites are provided and described. For each test instance we measure some global properties and, for the smallest ones, make some initial observations of the Pareto optimal sets/fronts. Our purpose in providing these tools is to facilitate the ongoing study of problem structure in multiobjective (combinatorial) optimization, and its effects on search landscape and algorithm performance.

Environmental behavior of soils and mixtures of soil-whitewash mud

The present study sought to observe the behavior of soils in natural state and in mixtures, in different ratios, with the industrial solid residue called whitewash mud. The work was conducted with samples of typical soils from the region of Alagoinhas, Bahia-Brazil. Wet chemical analysis and atomic absorption spectrophotometry were used in order to obtain the classification of the industrial solid residue. Solubilization and leaching tests were performed and X-ray diffraction and electron microscopy techniques were carried out. The results showed that the whitewash mud was classified as non-inert, but with great capacity of heavy metal retention largely owed to the kaolinite and goethite presence in the clay fraction of the soils, making it difficult to have heavy metals readily available for exchange.

Well-Behavior, Well-Posedness and Nonsmooth Analysis

AMS subject classification: 90C30, 90C33.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Confining solutions of massive spin-0 bosons by a linear nonminimal vector coupling in the Duffin-Kemmer-Petiau theory

The Duffin-Kemmer-Petiau (DKP) equation, in the scalar sector of the theory and with a linear nominimal vector potential, is mapped into the nonrelativistic harmonic oscillator problem. The behavior of the solutions for this sort of vector DKP oscillator is discussed in detail.

Calculating the Best Dual Bound for Problems with Multiple Lagrangian Relaxations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses' preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust. © 2013 Springer Science+Business Media New York.

Estados ligados em mecânica quântica relativística

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reasoning with incomplete and imprecise preferences

Preferences are present in many real life situations but it is often difficult to quantify them giving a precise value. Sometimes preference values may be missing because of privacy reasons or because they are expensive to obtain or to produce. In some other situations the user of an automated system may have a vague idea of whats he wants. In this thesis we considered the general formalism of soft constraints, where preferences play a crucial role and we extended such a framework to handle both incomplete and imprecise preferences. In particular we provided new theoretical frameworks to handle such kinds of preferences. By admitting missing or imprecise preferences, solving a soft constraint problem becomes a different task. In fact, the new goal is to find solutions which are the best ones independently of the precise value the each preference may have. With this in mind we defined two notions of optimality: the possibly optimal solutions and the necessary optimal solutions, which are optimal no matter we assign a precise value to a missing or imprecise preference. We provided several algorithms, bases on both systematic and local search approaches, to find such kind of solutions. Moreover, we also studied the impact of our techniques also in a specific class of problems (the stable marriage problems) where imprecision and incompleteness have a specific meaning and up to now have been tackled with different techniques. In the context of the classical stable marriage problem we developed a fair method to randomly generate stable marriages of a given problem instance. Furthermore, we adapted our techniques to solve stable marriage problems with ties and incomplete lists, which are known to be NP-hard, obtaining good results both in terms of size of the returned marriage and in terms of steps need to find a solution.

The role of drinking restraint in alcohol dependence: validation of the temptation and restraint inventory in an alcohol dependent sample

Objective: The Temptation and Restraint Inventory (TRI) is commonly used to measure drinking restraint in relation to problem drinking behavior. However, as yet the TRI has not been validated in a clinical group with alcohol dependence. Method: Male (n = 111) and female (n = 57) inpatients with DSM-IV diagnosed alcohol dependence completed the TRI and measures of problem drinking severity, including the Alcohol Dependence Scale and the quantity, frequency and week total of alcohol consumed. Results: The factor structure of the TRI was replicated in the alcohol dependent sample. Cognitive Emotional Preoccupation (CEP), one of the two higher order factors of the TRI, demonstrated sound predictive power toward all dependence severity indices. The other higher order factor, Cognitive Behavioral Control (CBC), was related to frequency of drinking. There was limited support for the CEP/CBC interactional model of drinking restraint. Conclusions: Although the construct validity of the TRI was sound, the measure appears more useful in understanding the development, maintenance and severity of alcohol-related problems in nondependent drinkers. The TRI may show promise in detecting either continuous drinking or heavy episodic type dependent drinkers.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Design and evaluation of a consulting system for database design

Database design is a difficult problem for non-expert designers. It is desirable to assist such designers during the problem solving process by means of a knowledge based (KB) system. A number of prototype KB systems have been proposed, however there are many shortcomings. Few have incorporated sufficient expertise in modeling relationships, particularly higher order relationships. There has been no empirical study that experimentally tested the effectiveness of any of these KB tools. Problem solving behavior of non-experts, whom the systems were intended to assist, has not been one of the bases for system design. In this project a consulting system for conceptual database design that addresses the above short comings was developed and empirically validated.^ The system incorporates (a) findings on why non-experts commit errors and (b) heuristics for modeling relationships. Two approaches to knowledge base implementation--system restrictiveness and decisional guidance--were used and compared in this project. The Restrictive approach is proscriptive and limits the designer's choices at various design phases by forcing him/her to follow a specific design path. The Guidance system approach which is less restrictive, provides context specific, informative and suggestive guidance throughout the design process. The main objectives of the study are to evaluate (1) whether the knowledge-based system is more effective than a system without the knowledge-base and (2) which knowledge implementation--restrictive or guidance--strategy is more effective. To evaluate the effectiveness of the knowledge base itself, the two systems were compared with a system that does not incorporate the expertise (Control).^ The experimental procedure involved the student subjects solving a task without using the system (pre-treatment task) and another task using one of the three systems (experimental task). The experimental task scores of those subjects who performed satisfactorily in the pre-treatment task were analyzed. Results are (1) The knowledge based approach to database design support lead to more accurate solutions than the control system; (2) No significant difference between the two KB approaches; (3) Guidance approach led to best performance; and (4) The subjects perceived the Restrictive system easier to use than the Guidance system. ^

Design and evaluation of a consulting system for database design

Database design is a difficult problem for non-expert designers. It is desirable to assist such designers during the problem solving process by means of a knowledge based (KB) system. Although a number of prototype KB systems have been proposed, there are many shortcomings. Firstly, few have incorporated sufficient expertise in modeling relationships, particularly higher order relationships. Secondly, there does not seem to be any published empirical study that experimentally tested the effectiveness of any of these KB tools. Thirdly, problem solving behavior of non-experts, whom the systems were intended to assist, has not been one of the bases for system design. In this project, a consulting system, called CODA, for conceptual database design that addresses the above short comings was developed and empirically validated. More specifically, the CODA system incorporates (a) findings on why non-experts commit errors and (b) heuristics for modeling relationships. Two approaches to knowledge base implementation were used and compared in this project, namely system restrictiveness and decisional guidance (Silver 1990). The Restrictive system uses a proscriptive approach and limits the designer's choices at various design phases by forcing him/her to follow a specific design path. The Guidance system approach, which is less restrictive, involves providing context specific, informative and suggestive guidance throughout the design process. Both the approaches would prevent erroneous design decisions. The main objectives of the study are to evaluate (1) whether the knowledge-based system is more effective than the system without a knowledge-base and (2) which approach to knowledge implementation - whether Restrictive or Guidance - is more effective. To evaluate the effectiveness of the knowledge base itself, the systems were compared with a system that does not incorporate the expertise (Control). An experimental procedure using student subjects was used to test the effectiveness of the systems. The subjects solved a task without using the system (pre-treatment task) and another task using one of the three systems, viz. Control, Guidance or Restrictive (experimental task). Analysis of experimental task scores of those subjects who performed satisfactorily in the pre-treatment task revealed that the knowledge based approach to database design support lead to more accurate solutions than the control system. Among the two KB approaches, Guidance approach was found to lead to better performance when compared to the Control system. It was found that the subjects perceived the Restrictive system easier to use than the Guidance system.

Similarity Measures for Exam Timetabling Problems

A large number of heuristic algorithms have been developed over the years which have been aimed at solving examination timetabling problems. However, many of these algorithms have been developed specifically to solve one particular problem instance or a small subset of instances related to a given real-life problem. Our aim is to develop a more general system which, when given any exam timetabling problem, will produce results which are comparative to those of a specially designed heuristic for that problem. We are investigating a Case based reasoning (CBR) technique to select from a set of algorithms which have been applied successfully to similar problem instances in the past. The assumption in CBR is that similar problems have similar solutions. For our system, the assumption is that an algorithm used to find a good solution to one problem will also produce a good result for a similar problem. The key to the success of the system will be our definition of similarity between two exam timetabling problems. The study will be carried out by running a series of tests using a simple Simulated Annealing Algorithm on a range of problems with differing levels of similarity and examining the data sets in detail. In this paper an initial investigation of the key factors which will be involved in this measure is presented with a discussion of how the definition of good impacts on this.