Mauro Dell’Amico

Optimal Scheduling of Tasks on Identical Parallel Processors

We consider the classical problem of scheduling n tasks with given processing time on m identical parallel processors so as to minimize the maximum completion time of a task. We introduce lower bounds, approximation algorithms and a branch-and-bound procedure for the exact solution of the problem. Extensive computational results show that, in many cases, large-size instances of the problem can be solved exactly. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Solution of the Cumulative Assignment Problem With a Well-Structured TabuSearch Method

The Cumulative Assignment Problem is an NP-complete problem obtained by substituting the linear objective function of the classic Linear Assignment Problem, with a non-linear cumulative function. In this paper we present a first attempt to solve the Cumulative Assignment Problem with metaheuristic techniques. In particular we consider two standard techniques, namely the Simulated Annealing and the Multi-Start methods, and we describe the eXploring Tabu Search: a new structured Tabu Search algorithm which uses an iterative multi-level approach to improve the search. The new method is analyzed through extensive computational experiments and proves to be more effective than the standard methods.

A note on exact algorithms for the identical parallel machine scheduling problem

Abstract A recently published paper by Mokotoff presents an exact algorithm for the classical P ∥ C max scheduling problem, evaluating its average performance through computational experiments on a series of randomly generated test problems. It is shown that, on the same types of instances, an exact algorithm proposed 10 years ago by the authors of the present note outperforms the new algorithm by some orders of magnitude.

A New Tabu Search Approach to the 0–1 Equicut Problem

Given an undirected graph, the 0–1 equicut problem consists of finding a partition of the vertex set into two subsets of equal size, such that the number of edges going from one subset to the other is minimized. A classical heuristics for this problem was presented 25 years ago, whereas simulated annealing, genetic algorithms, tabu search and a greedy randomized procedure have been developed in the last 5 years. In this paper we present a new tabu search algorithm and show, thorough extensive computational experiments, that in most cases it beats the other methods.

Lower bounds and heuristic algorithms for the ki-partitioning problem

We consider the problem of partitioning a set of positive integers values into a given number of subsets, each having an associated cardinality limit, so that the maximum sum of values in a subset is minimized, and the number of values in each subset does not exceed the corresponding limit. The problem is related to scheduling and bin packing problems. We give combinatorial lower bounds, reduction criteria, constructive heuristics, a scatter search approach, and a lower bound based on column generation. The outcome of extensive computational experiments is presented.

New bounds for optimum traffic assignment in satellite communication

Abstract The use of satellites to exchange information between distant places on the earth is a well assessed technique, but each satellite has high cost, so it is important to utilize it efficiently. A satellite receives requests of transmission between pairs of earth stations, which can be represented by a traffic matrix. One of the methods used for managing these communications is the satellite switched time-division-multiple-access system which requires to partition the traffic matrix in submatrices and transmits the information of each submatrix in a single time slot. Therefore a crucial decision for an efficient use of the satellite is how to partition the given traffic matrix so that the total time required to transmit the information is minimized. In the literature this problem has been addressed mainly in the special case in which the number of possible contemporary transmissions is equal to the number of rows and columns in the traffic matrix. In this paper we consider the general case in which the size of the matrix is larger than the number of contemporary transmissions. Our scope is to provide effective heuristic algorithms for finding good approximating solutions and to give tight lower bounds on the optimal solution value, in order to evaluate the quality of the heuristics. In this paper we assume that a satellite has l receiving and transmitting antennas, and we are given a traffic matrix D to be transmitted by interconnecting pairs of receiving–transmitting antennas, through an on board switch. We also assume that l is strictly smaller than the number of rows and columns of D, that no preemption of the communications is allowed, and that changing the configuration of the switch requires a negligible time. We ask for a set of switch configurations that minimizes the total time occurring for transmitting the entire traffic matrix. We present some new lower bounds on the optimum solution value and a new technique to combine bounds which obtains a dominating value. We then present five heuristics: the first two are obtained modifying algorithms from the literature; two others are obtained with standard techniques; the last algorithm is an implementation of a new and promising tabu search method which is called exploring tabu search. Extensive computational experiments compare the performances of the heuristics and that of the lower bound, on randomly generated instances.

An Adaptive Iterated Local Search for the Mixed Capacitated General Routing Problem

We study the mixed capacitated general routing problem (MCGRP) in which a fleet of capacitated vehicles has to serve a set of requests by traversing a mixed weighted graph. The requests may be located on nodes, edges, and arcs. The problem has theoretical interest because it is a generalization of the capacitated vehicle routing problem (CVRP), the capacitated arc routing problem (CARP), and the general routing problem. It is also of great practical interest since it is often a more accurate model for real-world cases than its widely studied specializations, particularly for so-called street routing applications. Examples are urban waste collection, snow removal, and newspaper delivery. We propose a new iterated local search metaheuristic for the problem that also includes vital mechanisms from adaptive large neighborhood search combined with further intensification through local search. The method utilizes selected, tailored, and novel local search and large neighborhood search operators, as well as a new local search strategy. Computational experiments show that the proposed metaheuristic is highly effective on five published benchmarks for the MCGRP. The metaheuristic yields excellent results also on seven standard CARP data sets, and good results on four well-known CVRP benchmarks, including improvement of the best known upper bound for one instance.

Exact algorithms for the bin packing problem with fragile objects

We are given a set of objects, each characterized by a weight and a fragility, and a large number of uncapacitated bins. Our aim is to find the minimum number of bins needed to pack all objects, in such a way that in each bin the sum of the object weights is less than or equal to the smallest fragility of an object in the bin. The problem is known in the literature as the Bin Packing Problem with Fragile Objects, and appears in the telecommunication field, when one has to assign cellular calls to available channels by ensuring that the total noise in a channel does not exceed the noise acceptance limit of a call. We propose a branch-and-bound and several branch-and-price algorithms for the exact solution of the problem, and improve their performance by the use of lower bounds and tailored optimization techniques. In addition we also develop algorithms for the optimal solution of the related knapsack problem with fragile objects. We conduct an extensive computational evaluation on the benchmark set of instances, and show that the proposed algorithms perform very well.

Two-Phase Earthwork Optimization Model for Highway Construction

AbstractOne of the main activities in highway construction is earthwork, which is a complex process involving excavation, transportation, and filling of large quantities of different earth material types. Earthwork operations are costly and undergo several constraints because of the fact that they have large environmental and social effects on the areas surrounding the construction site. Using mathematical models to produce a minimum-cost earthwork plan that satisfies all constraints is thus of great significance for enhancing the productivity of the overall construction project. This paper presents an earthwork optimization system on the basis of the use of linear programming that operates in a novel two-phase approach. In the first phase, an aggregate model determines the feasibility of the overall project, whereas in the second phase, disaggregate models determine the actual flows of each material. The two-phase quantitative method for earthwork optimization developed in this paper includes all feature...

A batching-move iterated local search algorithm for the bin packing problem with generalized precedence constraints

Abstract In this paper, we propose a generalisation of the bin packing problem, obtained by adding precedences between items that can assume heterogeneous non-negative integer values. Such generalisation also models the well-known Simple Assembly Line Balancing Problem of type I. To solve the problem, we propose a simple and effective iterated local search algorithm that integrates in an innovative way of constructive procedures and neighbourhood structures to guide the search to local optimal solutions. Moreover, we apply some preprocessing procedures and adapt classical lower bounds from the literature. Extensive computational experiments on benchmark instances suggest that the developed algorithm is able to generate good quality solutions in a reasonable computational time.