the multiple traveling salesman problem (mtsp) is a generalization of the famous traveling salesman problem (tsp), where more than one salesman is used in the solution. although the mtsp is a typical kind of computationally complex combinatorial optimization problem, it can be extended to a wide variety of routing problems. this paper presents an efficient and evolutionary optimization algorith...

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

A generally-accepted minimum requirement for an algorithm to be considered ‘efficient’ is that its running time is polynomial: O(nc) for some constant c, where n is the size of the input.1 Researchers recognized early on that not all problems can be solved this quickly, but we had a hard time figuring out exactly which ones could and which ones couldn’t. there are several so-called NP-hard prob...

the vehicle routing problem with simultaneous pickup and delivery (vrpspd) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. the objective is to minimize the distance traveled. the vrpspd is an np-hard combinatorial optimization problem. therefore, practical large-scale instances of vrpspd...