Algorithms for the fixed linear crossing number problem

METAHEURISTIC ALGORITHMS FOR MINIMUM CROSSING NUMBER PROBLEM

This paper presents the application of metaheuristic methods to the minimum crossing number problem for the first time. These algorithms including particle swarm optimization, improved ray optimization, colliding bodies optimization and enhanced colliding bodies optimization. For each method, a pseudo code is provided. The crossing number problem is NP-hard and has important applications in eng...

Algorithms for the fixed linear crossing number problem

A Parallel Algorithm for Fixed Linear Crossing Number Problem

This paper proposes a gradient ascent learning algorithm of the Hopfield neural networks for solving fixed linear crossing number problem. The fixed linear crossing number problem is an important problem in printed circuit board layout, VLSI circuit routing, and automated graph drawing. The objective of this problem which is shown to be NP-hard is to embed the edges so that the total number of ...

Approximating the fixed linear crossing number

We present a randomized polynomial-time approximation algorithm for the fixed linear crossing number problem (FLCNP). In this problem, the vertices of a graph are placed in a fixed order along a horizontal “node line” in the plane, each edge is drawn as an arc in one of the two half-planes (pages), and the objective is to minimize the number of edge crossings. FLCNP is NP-hard, and no previous ...

Electromagnetism-like Algorithms for The Fuzzy Fixed Charge Transportation Problem

In this paper, we consider the fuzzy fixed-charge transportation problem (FFCTP). Both of fixed and transportation cost are fuzzy numbers. Contrary to previous works, Electromagnetism-like Algorithms (EM) is firstly proposed in this research area to solve the problem. Three types of EM; original EM, revised EM, and hybrid EM are firstly employed for the given problem. The latter is being firstl...