Ryuichi Hirabayashi

A generalized utility for parallel branch and bound algorithms

Branch and bound algorithms are general methods applied to various combinatorial optimization problems. Recently, parallelizations of these algorithms have been proposed. In spite of the generality of these methods, many of the parallelizations have been set up for a specific problem and a specific parallel computer. A generalized utility PUBB (Parallelization Utility for Branch and Bound algorithms) is presented. It can be used on a network of workstations and enables us to easily apply parallelized branch and bound algorithms on any specific combinatorial optimization problem. A new selection rule (hybrid selection rule) was implemented during this study. Several branch and bound algorithms were experimentally parallelized with PUBB, using up to 111 networked workstations. The results of these experiments show that superlinear speedup in solving time may be achieved when the number of processing elements is increased and also indicate that the hybrid selection rule has an advantage over other selection rules.

A robust technique for sound source localization in consideration of room capacity

This paper proposes a robust technique for a sound source localization based on the time difference of arrival in noisy or reverberant environments. A nonlinear minimization problem for estimating source positions is formulated as a constrained optimization problem in consideration of room capacity. Then, a penalty function for a feasible region of this problem is used as the objective function. As a result, only estimation results within the room can be obtained. It is shown by several experiments that, by using the technique, estimation accuracy can be improved more than 25%.

Solving the maximum clique problem using PUBB

Given an (undirected) graph G=(V, E), a clique of G is a subset of vertices in which every pair is connected by an edge. The problem of finding a clique of maximum size is a classical NP-hard problem, and many algorithms, both heuristic and exact, have been proposed. While the philosophy behind the heuristic algorithms varies greatly, almost all of the exact algorithms are designed in the branch-and-bound framework. As is well known, branch-and-bound is well suited to parallelization, and PUBB is a software utility which implements a generic version of it. The authors show effectiveness of parallelization of branch-and-bound for the maximum clique problem. Especially, by using PUBB with good heuristics and branching techniques, they were able to solve five previously unsolved DIMACS benchmark problems to optimality.

Optimal design of FIR filter with discrete coefficients based on integer semi-infinite linear programs

The purpose of the paper is to propose, a new design method of FIR filters with discrete coefficients considering optimality. In the proposed method, the design problem of FIR filters is formulated as a Mixed Integer Semi-Infinite Linear Programming problem (MISILP), which can be solved by a branch and bound technique. Then, it is possible to obtain the optimal discrete coefficients, and the optimality of the obtained solution can be guaranteed. It was confirmed that optimal coefficients of linear phase FIR filter with discrete coefficients could be designed in reasonable computational time with sufficient precision based on the results of computational experiments.

A new heuristic signed-power of two term allocation approach for designing of FIR filters

In this paper, we consider design problems of linear phase FIR filters with CSD (or SP2) coefficients. When the total number of non-zero SP2 terms is given for the design problem, we have to determine the number of non-zero SP2 terms allocated for each filter coefficient respectively, while maintaining the total number. However, this is considered to be an NP-hard problem. Hence, Lim et al. (1998) developed an heuristic method for this allocation problem. In this paper, we propose a new heuristic method for the problem and compare it with Lims method through numerical experiments.

An Interface Design for General Parallel Branch-and-Bound Algorithms

Branch-and-Bound algorithms are general methods applicable to various combinatorial optimization problems. There are two hopeful methods to improve the algorithms. One is development of the algorithms which exploit the structure of each problem. The other is parallelization of the algorithms. These two methods have been studied by different research communities independently. If a well-designed interface separating the two kinds of implementation of the methods clearly could be constructed, it would enable us to adapt latest algorithms or technology easily. In this paper, we propose a small and simple interface design of a generalized system for parallel branch-and-bound algorithms.

Manifold Structure of the Karush–Kuhn–Tucker Stationary Solution Set with Two Parameters

This paper deals with a 2-dimensional parameter family of nonlinear programs: minimize

New design methods of FIR filters with signed power of two coefficients based on a new linear programming relaxation with triangle inequalities

h_0 ( x,t )

Optimal design method for FIR filter with discrete coefficients based on integer semi-infinite linear programs

subject to the equality constraints

Optimal design of fir filters in complex Chebyshev sense using semi-infinite programming method

h_i (x,t) = 0\, (i = 1,\ldots ,l)