Abstract. In this paper, the time-optimal velocity planning problem for five axis CNC machining along a given parametric tool path under chord error, acceleration, and jerk constraints is studied. The velocity planning problem under confined chord error and acceleration is reduced to an equivalent linear programming problem by discretizing the tool path and other quantities. As a consequence, a...

ÐWe consider the problem of scheduling n identical jobs with unequal ready times on m parallel uniform machines to minimize the maximum lateness. This paper develops a branch-and-bound procedure that optimally solves the problem and introduces six simple single-pass heuristic procedures that approximate the optimal solution. The branch-and-bound procedure uses the heuristics to establish an ini...

The paper investigates the application of a simple nonlinear structure to the problem of adaptive channel equalisation. Based on the Bayes decision rule, it is shown that the optimal equalisation solution is an inherently nonlinear problem and, therefore, it is desired to incorporate some degree of nonlinearity in the design of equaliser structure. The approximate realisation of the optimal equ...

In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...

In this paper, we consider sparse optimization problems with L0 norm penalty or constraint. We prove that it is strongly NP-hard to find an approximate optimal solution within certain error bound, unless P = NP. This provides a lower bound for the approximation error of any deterministic polynomialtime algorithm. Applying the complexity result to sparse linear regression reveals a gap between c...

THE THREE DIMENSIONAL FLOW PAST A STRETCHING SHEET BY EXTENDED OPTIMAL HOMOTOPY ASYMPTOTIC METHOD H. Ullah, S. Islam, M. Idrees, M. Fiza, A. Zaman Abdul Wali Khan University Mardan, 23200, Khyber Pakhtunkhwa, Pakistan ABSTRACT: In this paper Extended Optimal Homotopy Asymptotic Method (EOHAM), a new analytic approximate technique has been used to three dimensional flow past a stretching sheet. ...

The paper introduces a smoothing method to the lower order penalty function for constrained optimization problems. It is shown that, under some mild conditions, an optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, an algorithm is presented and its convergence is proved under some mild assumptions....

An incompressible Newtonian fluid is forced through the porous of a circular slider which is moving laterally on a horizontal plan. In this paper, we introduce and apply the one step Optimal HomotopyAnalysisMethod one step OHAM to the problem of the circular porous slider where a fluid is injected through the porous bottom. The effects of mass injection and lateral velocity on the heat generate...

Approximation algorithms are used when we know a problem is hard. It is a way to consider optimization versions of function problems. For instance, given a 3-CNF formula, finding a maximal truth assignment is essentialy a MAX3SAT. Approximation algorithms return solutions that are close to the optimal in some way. So, if OPT (x) is the optimal solution for problem x, and A(x) is our approximate...