the capacitated clustering problem (ccp) is one of the most importantcombinational optimization problems that nowadays has many real applications inindustrial and service problems. in the ccp, a given n nodes with known demandsmust be partitioned into k distinct clusters in which each cluster is detailed by anode acting as a cluster center of this cluster. the objective is to minimize the sumof...

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...

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...

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. ...

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...