This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19 matrix, M, in the following way: We obtain the remainders modulo 100 of each of the smallest 342 odd primes. we obtain the remainders modulo 100 of each of the primes. They are placed in M according to the original value of each prime. Thus their...

the travelling salesmen problem (tsp) is one of the most important and famous combinational optimization problems that aim to find the shortest tour. in this problem, the salesman starts to move from an arbitrary place called depot and after visiting all nodes, finally comes back to depot. solving this problem seems hard because program statement is simple and leads this problem belonging to np...

In this paper we evaluate the usefulness of seeding genetic algorithms (GAs) from a case-base. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. We evaluate this case-based seeding on popular GA solutions to the Travelling Salesman Problem (TSP) and the Job-Shop Scheduling Problem (JSSP). We find that seed...

Definition The traveling salesman problem (TSP) is the following optimization problem. Given a complete graph G with edge costs, find a Hamiltonian cycle of minimum cost in G. Definition The metric traveling salesman problem (∆-TSP) is the TSP restricted to instances satisfying the triangle inequality Definition The traveling salesman problem (TSP) is the following optimization problem. Given a...

<p><span>Travelling salesman problem is a well researched in computer science and has many practical applications. It classified as NP-hard its exact solution can only be obtained exponential time unless P = NP. There are different variants of the travelling (TSP) this paper, asymmetric addressed since variant quite often observed real world scenarios. number heuristic approaches to...

The Resource-Constrained Traveling Salesman Problem (RCTSP) is formulated as follows. A set of n cities is given (denoted by V ); travelling from city i to city j incurs cost cij as well as resource consumption rij . The objective is to find a minimum cost Hamilton cycle (or tour) that consumes not more than Rmax units of the resource, where Rmax is some constant. The cost (resource consumption...