Competitive Sorter-based Encoding of PB-Constraints into SAT

A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean variables. A popular idea to solve PB-constraints is to transform them to CNFs (via BDDs, adders and sorting networks [5, 11]) and process them using – increasingly improving – state-of-the-art SAT-solvers. Recent research have favored the approach that uses Binary Decision Diagrams (BDDs), which is evidenced by several new constructions and optimizations [2, 21]. We show that encodings based on comparator networks can still be very competitive. We present a system description of a PB-solver based on MiniSat+ [11] which we extended by adding a new construction of selection network called 4-Way Merge Selection Network, with a few optimizations based on other solvers. Experiments show that on many instances of popular benchmarks our technique outperforms other state-of-the-art PB-solvers.

Shaping the vibro-isolation properties of horizontal seat suspension

In this paper, an effective procedure of shaping the vibro-isolation properties of seat suspension system is presented. The simulation model is created to determine the dependence of evaluation criteria to the design parameters by means of which the system characteristics are formed. The developed optimisation procedure allows to find Pareto-optimal system configuration for the conflicted vibro-isolating criteria, i.e. the frequency weighted transmissibility factor used to evaluate dynamic seat comfort based on acceleration signals and the suspension travel. In order to optimise both the conflicted vibro-isolation criteria, a minimising of the transmissibility factor (primary criterion) is proposed taking into account the suspension travel that is transferred to a non-linear inequality constraint. The correctness of proposed procedure is evaluated using experimental research of the best solution of horizontal seat suspension. This research is performed using the passive system with optimal visco-elastic characteristics, which are selected especially for the well-defined input vibration. The satisfactory agreement of experimental and numerical results is obtained for the analysed vibration reduction system.

Convex separable minimization problems with a linear constraint and bounded variables

Consider the minimization problem with a convex separable objective function over a feasible region defined by linear equality constraint(s)/linear inequality constraint of the form “greater than or equal to” and bounds on the variables. A necessary and sufficient condition and a sufficient condition are proved for a feasible solution to be an optimal solution to these two problems, respectively. Iterative algorithms of polynomial complexity for solving such problems are suggested and convergence of these algorithms is proved. Some convex functions, important for problems under consideration, as well as computational results are presented.