This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time many one reductions It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity It follows that every weakly hard problem has a dense set of such maximally hard instances This extends the theorem ...

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...

Consider a decision problem that cannot be 1 ? approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a fraction of instances. We show that for any such problem there is a speciic \hard-core" set of inputs which is at least a fraction of all inputs and on which no circuit of a slightly smaller size can get even a small advantage ...

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. ...