Monaldo Mastrolilli

Effective Neighborhood Functions for the Flexible Job Shop Problem

The flexible job shop problem is an extension of the classical job shop scheduling problem which allows an operation to be performed by one machine out of a set of machines. The problem is to assign each operation to a machine (routing problem) and to order the operations on the machines (sequencing problem), such that the maximal completion time (makespan) of all operations is minimized. To solve the flexible job shop problem approximately, we use local search techniques and present two neighbourhood functions (Nopt1, Nopt2). Nopt2 is proved to be optimum connected. Nopt1 does not distinguish between routing or sequencing an operation. In both cases, a neighbour of a solution is obtained by moving an operation which affects the makespan. Our main contribution is a reduction of the set of possible neighbours to a subset for which can be proved that it always contains the neighbour with the lowest makespan. An efficient approach to compute such a subset of feasible neighbours is presented. A tabu search procedure is proposed and an extensive computational study is provided. We show that our procedure outperforms previous approaches. Copyright

Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands

This article analyzes the performance of metaheuristics on the vehicle routing problem with stochastic demands (VRPSD). The problem is known to have a computationally demanding objective function, which could turn to be infeasible when large instances are considered. Fast approximations of the objective function are therefore appealing because they would allow for an extended exploration of the search space. We explore the hybridization of the metaheuristic by means of two objective functions which are surrogate measures of the exact solution quality. Particularly helpful for some metaheuristics is the objective function derived from the traveling salesman problem (TSP), a closely related problem. In the light of this observation, we analyze possible extensions of the metaheuristics which take the hybridized solution approach VRPSD-TSP even further and report about experimental results on different types of instances. We show that, for the instances tested, two hybridized versions of iterated local search and evolutionary algorithm attain better solutions than state-of-the-art algorithms.

An optimization methodology for intermodal terminal management

A solution to the problems of resource allocation and scheduling of loading and unloading operations in a container terminal is presented. The two problems are formulated and solved hierarchically. First, the solution of the resource allocation problem returns, over a number of work shifts, a set of quay cranes used to load and unload containers from the moored ships and the set of yard cranes to store those containers on the yard. Then, a scheduling problem is formulated to compute the loading and unloading lists of containers for each allocated crane. The feasibility of the solution is verified against a detailed, discrete-event based, simulation model of the terminal. The simulation results show that the optimized resource allocation, which reduces the costs by [frac13], can be effectively adopted in combination with the optimized loading and unloading list. Moreover, the simulation shows that the optimized lists reduce the number of crane conflicts on the yard and the average length of the truck queues in the terminal.

Metaheuristics for the Vehicle Routing Problem with Stochastic Demands

In the vehicle routing problem with stochastic demands a vehicle has to serve a set of customers whose exact demand is known only upon arrival at the customer’s location. The objective is to find a permutation of the customers (an a priori tour) that minimizes the expected distance traveled by the vehicle. Since the objective function is computationally demanding, effective approximations of it could improve the algorithms’ performance. We show that a good choice is using the length of the a priori tour as a fast approximation of the objective, to be used in the local search of the several metaheuristics analyzed. We also show that for the instances tested, our metaheuristics find better solutions with respect to a known effective heuristic and with respect to solving the problem as two related deterministic problems.

Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut

We consider the Minimum Linear Arrangement problem and the (Uniform) Sparsest Cut problem. So far, these two notorious NP-hard graph problems have resisted all attempts to prove inapproximability results. We show that they have no polynomial time approximation scheme, unless NP-complete problems can be solved in randomized subexponential time. Furthermore, we show that the same techniques can be used for the Maximum Edge Biclique problem, for which we obtain a hardness factor similar to previous results but under a more standard assumption.

Approximation schemes for job shop scheduling problems with controllable processing times

In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. The fact that the jobs have controllable processing times means that it is possible to reduce the processing time of the jobs by paying a certain cost. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are fixed.

Minimizing the sum of weighted completion times in a concurrent open shop

We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal-dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than 6/5 if P NP, or strictly less than 4/3 if the Unique Games Conjecture also holds.

Approximation schemes for parallel machine scheduling problems with controllable processing times

We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job has a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. We present the first known polynomial time approximation schemes for the nonpreemptive case of several identical parallel machines scheduling problems with controllable processing times. Moreover, we study the problem when preemption is allowed and describe efficient exact and approximation algorithms.

Efficient Approximation Schemes for Scheduling Problems with Release Dates and Delivery Times

We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job must be processed without interruption for a given amount of time on any one of the m machines. In addition, each job has a release date, when it becomes available for processing, and, after completing its processing, requires an additional delivery time. The objective is to minimize the time by which all jobs are delivered. In the notation of Graham et al. (1979), this problem is noted P|rj|Lmax. We develop a polynomial time approximation scheme whose running time depends only linearly on n. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound (Hall and Shmoys, 1989). Finally, we discuss the special case of this problem in which there is a single machine and present an improved approximation scheme.

Single Machine Precedence Constrained Scheduling Is a Vertex Cover Problem

In this paper we study the single machine precedence constrained scheduling problem of minimizing the sum of weighted completion time. Specifically, we settle an open problem first raised by Chudak and Hochbaum and whose answer was subsequently conjectured by Correa and Schulz. As shown by Correa and Schulz, the proof of this conjecture implies that the addressed scheduling problem is a special case of the vertex cover problem. This means that previous results for the scheduling problem can be explained, and in some cases improved, by means of vertex cover theory. For example, the conjecture implies the existence of a polynomial time algorithm for the special case of two-dimensional partial orders. This considerably extends Lawler’s result from 1978 for series-parallel orders.