Iterative classical superadiabatic algorithm for combinatorial optimization

Iterative Methods in Combinatorial Optimization

In these lectures, I will describe a simple iterative method that supplies new proofs of integrality of linear characterizations of various basic problems in combinatorial optimization, and also allows adaptations to design approximation algorithms for NP-hard variants of these problems involving extra “degree-like” budget constraints. It is inspired by Jain’s iterative rounding method for desi...

Combinatorial Optimization Problems for Which Almostevery Algorithm

Consider a class of optimization problems for which the cardinality of the set of feasible solutions is m and the size of every feasible solution is N. We prove in a general probabilistic framework that the value of the optimal solution and the value of the worst solution are asymptotically almost surely (a.s.) the same provided log m = o(N) as N and m become large. This result implies that for...

A New Optimization Algorithm For Combinatorial Problems

Combinatorial optimization problems are those problems that have a finite set of possible solutions. The best way to solve a combinatorial optimization problem is to check all the feasible solutions in the search space. However, checking all the feasible solutions is not always possible, especially when the search space is large. Thus, many meta-heuristic algorithms have been devised and modifi...

Graph Algorithm and Combinatorial Optimization

Flying Ant Colony Optimization Algorithm for Combinatorial Optimization

In this paper is introduce "flying" ants in Ant Colony Optimization (ACO). In traditional ACO algorithms the ants construct their solution regarding one step forward. In proposed ACO algorithm, the ants make their decision, regarding more than one step forward, but they include only one new element in their solutions.