We prove that, up to homeomorphism, any graph subject natural necessary conditions on orientation and the number of cycles can be realized as Reeb a Morse function given closed manifold $M$. Along way, we show that $\mathcal{R}(M)$, i.e. maximal among all graphs functions $M$, is equal corank fundamental group $\pi_1(M)$, thus extending previous result Gelbukh non-orientable case.

multiple traveling salesman problem (mtsp) is one of the most popular operation research problem and is known as combinatorial optimization problems. mtsp is an extension version of the famous and widely used problem named traveling salesman problem (tsp). because of its benefices in various domains, many researchers have tried to solve that, and many methods have proposed so far. mtsp is a np-...

the traveling salesman problem (tsp) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. the tsp is probably the most famous and extensively studied problem in the field of combinatorial optimization. because this problem is an np-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

The p-median problem is one of the discrete optimization problem in location theory which aims to satisfy total demand with minimum cost. A high-level algorithmic approach can be specialized to solve optimization problem. In recent years, meta-heuristic methods have been applied to support the solution of Combinatorial Optimization Problems (COP). Collision Bodies Optimization algorithm (CBO) a...