Hybrid Constraint Research Articles

Constraint Programming and Hybrid Formulations for Three Life Designs

Conway's game of Life provides an interesting testbed for exploring issues in formulation, symmetry, and optimization with constraint programming and hybrid constraint programming/integer programming methods. We consider three Life pattern-creation problems: finding maximum density still-Lifes, finding smallest immediate predecessor patterns, and finding period-2 oscillators. For the first two problems, integrating integer programming and constraint programming approaches provides a much better solution procedure than either individually. For the final problem, the constraint programming formulation provides the better approach.

Solving Fixed-Charge Network Flow Problems with a Hybrid Optimization and Constraint Programming Approach

We apply to fixed charge network flow (FCNF) problems a general hybrid solution method that combines constraint programming and linear programming. FCNF problems test the hybrid approach on problems that are already rather well suited for a classical 0–1 model. They are solved by means of a global constraint that generates specialized constraint propagation algorithms and a projected relaxation that can be rapidly solved as a minimum cost network flow problem. The hybrid approach ran about twice as fast as a commercial mixed integer programming code on fixed charge transportation problems with its advantage increasing with problem size. For general fixed charge transshipment problems, however, it has no effect because the implemented propagation methods are weak.

Hybrid Constraints in Automated Model Synthesis and Model Processing

Abstract Both parametric design tasks and analysis tasks of technical systems have a similar problem setting: The structure of the system to be configured or analyzed is defined already. Within the parametric design task unknown values for component geometries have to be determined, while within the analysis task the system has to be completed with respect to missing physical quantities. The tasks mentioned form hybrid constraint satisfaction problems, which may be solved by a generic procedure. However, if the no-function-in-structure principle holds, i.e., if the behavior of the entire system can be derived from the behavior of its parts, engineering semantics of model synthesis and simulation apply. As a result, not only domain knowledge can be exploited to solve the constraint satisfaction problem efficiently, but also instances of both types of problems can be tackled by the same problem solving approach: a sequence of intertwined model synthesis and simulation steps. The paper in hand introduces this problem solving approach as a cycle comprising five generic steps and presents case studies of real life problems from the field of hydraulics, which illustrate its successful application.

The hybrid constraint equation for motion extraction

A new derivation of the constraint equation for motion extraction in the image flow is presented. The derivation was obtained by applying the constraint equation to the Fourier transform of the 2D images. It resulted in a hybrid equation joining time-space and frequency notations. The hybrid equation was numerically solved for the 1D case and tested with many image sequences representing coherent, rigid and incoherent motion patterns. Outlines of the 2D case are also presented with some solved examples. The algorithm seems superior to former derivations of the constraint equation for its ability to extract the movement parameters (magnitude and direction) in non-homogeneous movement fields for displacements greater than pixel size. The relevance of the present procedures to machine and organic motion detection is discussed.

Space frame optimization subject to frequency constraints

An efficient structural optimization methodology is presented for the design of minimum weight space frames subject to multiple natural frequency constraints. A powerful class of generalized hybrid c onstraint approximations which require o nly the first order constraint function d erivatives have been developed to overcome inherent nonlinearity of the frequency constraint. The generalized hybrid constraint functions are shown to be relatively conservative, separable and convex in the region bounded by the move limits based on the formula described in this paper. The optimization methodology is implemented in an automated structural optimization system which has been applied to solve a variety of space frame optimization problems. N umerical results obtained for three example problems indicate that the o ptimization methodology requires fewer than 10 complete normal modes analyses to generate a near optimum solution.