Rigorous solution techniques for numerical constraint satisfaction problems

A constraint satisfaction problem (e.g., a system of equations and inequalities) consists of a finite set of constraints specifying which value combinations from given variable domains are admitted. It is called numerical if its variable domains are continuous. Such problems arise in many applications, but form a difficult problem class since they are NP-hard. Solving a constraint satisfaction problem is to find one or more value combinations satisfying all its constraints. Numerical computations on floating-point numbers in computers often suffer from rounding errors. The rigorous control of rounding errors during numerical computations is highly desired in many applications because it would benefit the quality and reliability of the decisions based on the solutions found by the computations. Various aspects of rigorous numerical computations in solving constraint satisfaction problems are addressed in this thesis: search, constraint propagation, combination of inclusion techniques, and post-processing. The solution of a constraint satisfaction problem is essentially performed by a search. In this thesis, we propose a new complete search technique (i.e., it can find all solutions within a predetermined tolerance) for numerical constraint satisfaction problems. This technique is general and can be used in place of branching steps in most branch-and-prune methods. Moreover, this new technique speeds up the most recent general search strategy (often by an order of magnitude) and provides a concise representation of solutions. To make a constraint satisfaction problem easier to solve, a major approach, called constraint propagation, in the constraint programming1 field is often used to reduce the variable domains (by discarding redundant value combinations from the domains). Basing on directed acyclic graphs, we propose a new constraint propagation technique and a method for coordinating constraint propagation and search. More importantly, we propose a novel generic scheme for combining multiple inclusion techniques2 in numerical constraint propagation. This scheme allows bringing into the constraint propagation framework the strengths of various techniques coming from different fields. To illustrate the flexibility and efficiency of the generic scheme, we base on this scheme and devise several specific combination strategies for rigorous numerical constraint propagation using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming. Our experiments show that the new propagation techniques outperform previously available methods by 1 to 4 orders of magnitude or more in speed. We also propose several post-processing techniques for the representation of continuums of solutions. Based on connectedness, they allow grouping each cluster of connected solution subsets into a larger subset, thus allowing getting additional grouping information. Potentially, these techniques enable interval-based solution techniques to be alternatives to bounding-volume techniques in applications such as collision detection and interactive graphics. __________________________________________________ 1 Constraint programming is an approach to programming that relies on both reasoning and computing. 2 An inclusion technique is to include a set of interest into enclosures. It is also called an enclosure technique

Branch-and-Prune Search Strategies for Numerical Constraint Solving

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete solution set, most of these solvers alternate the pruning steps with branching steps, which split each problem into subproblems. This forms the so-called branch-and-prune framework, well known among the approaches for solving numerical constraints. The basic branch-and-prune search strategy that uses domain bisections in place of the branching steps is called the bisection search. In general, the bisection search works well in case (i) the solutions are isolated, but it can be improved further in case (ii) there are continuums of solutions (this often occurs when inequalities are involved). In this paper, we propose a new branch-and-prune search strategy along with several variants, which not only allow yielding better branching decisions in the latter case, but also work as well as the bisection search does in the former case. These new search algorithms enable us to employ various pruning techniques in the construction of inner and outer approximations of the solution set. Our experiments show that these algorithms speed up the solving process often by one order of magnitude or more when solving problems with continuums of solutions, while keeping the same performance as the bisection search when the solutions are isolated.Comment: 43 pages, 11 figure

Enhancing numerical constraint propagation using multiple inclusion representations

Building tight and conservative enclosures of the solution set is of crucial importance in the design of efficient complete solvers for numerical constraint satisfaction problems (NCSPs). This paper proposes a novel generic algorithm enabling the cooperative use, during constraint propagation, of multiple enclosure techniques. The new algorithm brings into the constraint propagation framework the strength of techniques coming from different areas such as interval arithmetic, affine arithmetic, and mathematical programming. It is based on the directed acyclic graph (DAG) representation of NCSPs whose flexibility and expressiveness facilitates the design of fine-grained combination strategies for general factorable systems. The paper presents several possible combination strategies for creating practical instances of the generic algorithm. The experiments reported on a particular instance using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming illustrate the flexibility and efficiency of the approac

Interval propagation and search on directed acyclic graphs for numerical constraint solving

The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed in Schichl and Neumaier (J. Global Optim. 33, 541-562, 2005). For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose directed edges are computational flows. Compared to tree-based representations [Benhamou etal. Proceedings of the International Conference on Logic Programming (ICLP'99), pp. 230-244. Las Cruces, USA (1999)], DAGs offer the essential advantage of more accurately handling the influence of subexpressions shared by several constraints on the overall system during propagation. In this paper we show how interval constraint propagation and search on DAGs can be made practical and efficient by: (1) flexibly choosing the nodes on which propagations must be performed, and (2) working with partial subgraphs of the initial DAG rather than with the entire graph. We propose a new interval constraint propagation technique which exploits the influence of subexpressions on all the constraints together rather than on individual constraints. We then show how the new propagation technique can be integrated into branch-and-prune search to solve numerical constraint satisfaction problems. This algorithm is able to outperform its obvious contenders, as shown by the experiment

Effect of Halothane Genotype, Gender on Carcass Characteristics and Meat Quality of Stress Negative Piétrain Pigs

peer reviewedThis study was carried out at the animal farm of Hanoi University of Agriculture from August 2012 to April 2013 to evaluate effects of halothane genotype (CC and CT) and gender (intact males and gilts) on carcass characteristics and meat quality of Piétrain stress negative pigs. Backfat thickness, depth of longissimus dorsi muscle and lean meat percentage at 7.5 months were collected from 83 pigs (31 females and 52 intact males). Data on carcass performance were collected from 43 pigs (28 females and 15 intact males). The organoleptic quality of longissimus dorsi muscle was determined from 35 samples (19 females and 16 intact males) of longissimus dorsi muscle. For meat chemical compositions, 24 samples (14 females and 10 intact males) were analyzed. Slaughter weight (88.75 kg), carcass weight (58.40 kg), eye muscle area (57.54 cm²), backfat thickness (9.26 mm) and depth of longissimus dorsi muscle (58.01 mm) of gilts were higher than those of intact males (81.29 kg, 52.77 kg, 51.04 cm², 8.01 mm and 52.76 mm). Killing out percentage, carcass percentage and carcass length were similar between gilts and intact males (P>0.05). The pH of longissimus dorsi muscle at 24 hours post mortem between gilts (5.34) and boars (5.50) were significantly different (P<0.001). Gilts had more lipids than intact males (P<0.01). Halothane genotype did not affect carcass characteristics, meat quality and meat chemical composition (P>0.05). The results indicate that Piétrain stress negative pigs had high carcass percentage and good meat quality. Individuals with halothane genotype CC and CT can be choose for the breeding without affecting the carcass performance and meat qualit

Economic Instruments and the Pollution Impact of the 2006-2010 Vietnam Socio-Economic Development Plan

The current study derives optimal growth paths for pollution emission charges, in order to control future water pollution emissions in the Vietnamese manufacturing sector. The study builds on a prior study, which estimated the manufacturing sector pollution impact of the 2006- 2010 SEDP development plan for Vietnam (Jensen et al.; 2008). The current study demonstrates that effective implementation and moderate expansion of optimal emission charges, under certain conditions, could have been used, as part of the 2006-2010 SEDP development plan, to control pollution emissions at 2005 levels. Moreover, such a scenario would have been accompanied by a moderate expansion in fiscal revenues and a relatively minor economy-wide efficiency loss. The current study, therefore, suggests that effective implementation and gradual expansion of pollution emission charges should be incorporated into future SEDP development plans, in order to control pollution emissions as development progresses in Vietnam.Vietnam, manufacturing, CGE

Assessing Student’s Acceptance of Digital Transformation in Business and Management Universities in Vietnam

In recent years, the trend of digital transformation in education has increased significantly. A series of policies to promote the digital transformation of education have been issued, gradually completing the legal corridor such as the regulations on applying information technology, information in management, organization of online training, the use of the entire industry database system. Therefore, this article is the result of a more comprehensive research project and aims to analyze the digital transformation acceptance of college students in Economic - Business Universities in the North of Vietnam. The Unified Theory of Acceptance and Use of Technology (UTAUT) and independent variable Perceived Security (PS) have been combined together in order to support the survey. The data was analyzed using the method of multiple regression. These findings shed the light on the digital transformation acceptance level of students with the positive link of Performance Expectancy (PE), Social Influence (SI), Perceived Security (PS) and Facilitating Conditions (FC) on Behavioral Intention of digital transformation and its Use Behavior. Moreover, the study also has the contribution to provide orientations and solutions that will be proposed to approach the trend encouraging the application of digital transformation into higher education specifically in the business field. Keywords: UTAUT, digital transformation, perceived security, higher education DOI: 10.7176/JESD/12-8-02 Publication date: April 30th 202

A Target Threat Assessment Method for Application in Air Defense Command and Control Systems

Introduction. This paper presents a solution for threat assessment of air targets using the fuzzy logic inference method. The approach is based on the Sugeno fuzzy model, which has multiple inputs representing target trajectory parameters and a single output representing the target threat value. A set of IF–THEN fuzzy inference rules, utilizing the AND operator, is developed to assess the input information.Aim. To develop and test an algorithm model to calculate the threat value of an air target for use in real-time automated command and control systems.Materials and methods. An algorithm model was developed using a fuzzy model to calculate the threat value of a target. The model is presented in the form of a flowchart supported by a detailed stepwise implementation process. The accuracy of the proposed algorithm was evaluated using the available toolkit in MATLAB. Additionally, a BATE software testbed was developed to assess the applicability of the algorithm model in a real-time automated command and control system.Results. The efficiency of the proposed fuzzy model was evaluated by its simulation and testing using MATLAB tools on a set of 10 target trajectories with different parameters. Additionally, the BATE software was utilized to test the model under various air defense scenarios. The proposed fuzzy model was found to be capable of efficiently computing the threat value of each target with respect to the protected object.Conclusion. The proposed fuzzy model can be applied when developing tactical supporting software modules for real-time air defense command and control systems.Introduction. This paper presents a solution for threat assessment of air targets using the fuzzy logic inference method. The approach is based on the Sugeno fuzzy model, which has multiple inputs representing target trajectory parameters and a single output representing the target threat value. A set of IF–THEN fuzzy inference rules, utilizing the AND operator, is developed to assess the input information.Aim. To develop and test an algorithm model to calculate the threat value of an air target for use in real-time automated command and control systems.Materials and methods. An algorithm model was developed using a fuzzy model to calculate the threat value of a target. The model is presented in the form of a flowchart supported by a detailed stepwise implementation process. The accuracy of the proposed algorithm was evaluated using the available toolkit in MATLAB. Additionally, a BATE software testbed was developed to assess the applicability of the algorithm model in a real-time automated command and control system.Results. The efficiency of the proposed fuzzy model was evaluated by its simulation and testing using MATLAB tools on a set of 10 target trajectories with different parameters. Additionally, the BATE software was utilized to test the model under various air defense scenarios. The proposed fuzzy model was found to be capable of efficiently computing the threat value of each target with respect to the protected object.Conclusion. The proposed fuzzy model can be applied when developing tactical supporting software modules for real-time air defense command and control systems

Enhancing numerical constraint propagation using multiple inclusion representations

Building tight and conservative enclosures of the solution set is of crucial importance in the design of efficient complete solvers for numerical constraint satisfaction problems (NCSPs). This paper proposes a novel generic algorithm enabling the cooperative use, during constraint propagation, of multiple enclosure techniques. The new algorithm brings into the constraint propagation framework the strength of techniques coming from different areas such as interval arithmetic, affine arithmetic, and mathematical programming. It is based on the directed acyclic graph (DAG) representation of NCSPs whose flexibility and expressiveness facilitates the design of fine-grained combination strategies for general factorable systems. The paper presents several possible combination strategies for creating practical instances of the generic algorithm. The experiments reported on a particular instance using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming illustrate the flexibility and efficiency of the approach