A framework for analyzing sub-optimal performance of local search algorithms

This paper presents a framework for analyzing and comparing sub-optimal performance of local search algorithms for hard discrete optimization problems. The β-acceptable solution probability is introduced that captures how effectively an algorithm has performed to date and how effectively an algorithm can be expected to perform in the future. Using this probability, the necessary conditions for a local search algorithm to converge in probability to β-acceptable solutions are derived. To evaluate and compare the effectiveness of local search algorithms, two estimators for the expected number of iterations to visit a β-acceptable solution are obtained. Computational experiments are reported with simulated annealing and tabu search applied to four small traveling salesman problem instances, and the Lin-Kernighan-Helsgaun algorithm applied to eight medium to large traveling salesman problem instances (all with known optimal solutions), to illustrate the application of these estimators.     

Dynamic boundary value problems of the second-order: Bernstein–Nagumo conditions and solvability

This article analyzes the solvability of second-order, nonlinear dynamic boundary value problems (BVPs) on time scales. New Bernstein–Nagumo conditions are developed that guarantee an a priori bound on the delta derivative of potential solutions to the BVPs under consideration. Topological methods are then employed to gain solvability.     

Impulsive neutral functional differential equations in banach spaces

In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for first and second order impulsive neutral functional differential equations in Banach spaces.     

Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.