New Complexity Results and Algorithms for the Minimum Tollbooth Problem

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) problem, which seeks social optimum inducing tolls with minimum support. We prove for single commodity networks with linear latencies that the problem is NP-hard to approximate within a factor of $1.1377$ through a reduction from the minimum vertex cover problem. Insights from network design motivate us to formulate a new variation of the problem where, in addition to placing tolls, it is allowed to remove unused edges by the social optimum. We prove that this new problem remains NP-hard even for single commodity networks with linear latencies, using a reduction from the partition problem. On the positive side, we give the first exact polynomial solution to the MINTB problem in an important class of graphs---series-parallel graphs. Our algorithm solves MINTB by first tabulating the candidate solutions for subgraphs of the series-parallel network and then combining them optimally

Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: (i) Optimal recombination problem is solved within crossover operator. (ii) A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. (iii) Greedy constructive heuristic of W.Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.Comment: Proc. of The 11th International Conference on Large-Scale Scientific Computations (LSSC-17), June 5 - 9, 2017, Sozopol, Bulgari

Genetic algorithms for the no-wait flowshop sequencing problem with time restrictions

This article deals with the no- wait. owshop problem with sequence dependent set-ups and ready times solved by an evolutionary approach. The hybrid genetic algorithm presented here addresses a new hierarchically organized complete ternary tree to represent the population that put together with a recombination plan resembles a parallel processing scheme for solving combinatorial optimization problems. Embedded in the hybrid approach, a novel recursive local search scheme, recursive arc insertion (RAI), is also proposed. The effectiveness of the local search phase is crucial given that it is responsible for about 90% of the total processing time of the algorithm. Instances with known optimal solution are used to test the new algorithm and compare it to a previously proposed heuristic approach.44593995

Intra-domain traffic engineering with shortest path routing protocols

Throughout the last decade, extensive deployment of popular intra-domain routing protocols such as open shortest path first and intermediate system–intermediate system, has drawn an ever increasing attention to Internet traffic engineering. This paper reviews optimization techniques that have been deployed for managing intra-domain routing in networks operated with shortest path routing protocols, and the state-of-the-art research that has been carried out in this direction.SCOPUS: ar.jinfo:eu-repo/semantics/publishe