Luiz Antonio Nogueira Lorena

Relaxation heuristics for a generalized assignment problem

Abstract We propose relaxation heuristics for the problem of maximum profit assignment of n tasks to m agents ( n > m ), such that each task is assigned to only one agent subject to capacity constraints on the agents. Using Lagrangian or surrogate relaxation, the heuristics perform a subgradient search obtaining feasible solutions. Relaxation considers a vector of multipliers for the capacity constraints. The resolution of the Lagrangian is then immediate. For the surrogate, the resulting problem is a multiple choice knapsack that is again relaxed for continuous values of the variables, and solved in polynomial time. Relaxation multipliers are used with an improved heuristic of Martello and Toth or a new constructive heuristic to find good feasible solutions. Six heuristics are tested with problems of the literature and random generated problems. Best results are less than 0.5% from the optimal, with reasonable computational times for an AT/386 computer. It seems promising even for problems with correlated coefficients.

A surrogate heuristic for set covering problems

Abstract The purpose of this paper is to present a new heuristic for set covering problems, based upon continuous surrogate relaxations and subgradient optimization. The algorithm combines problem reduction tests, an adequate step size control, and avoid preliminary sorting in solving the continuous surrogate relaxations. Computational tests for large scale set covering problems (up to 1 000 rows and 12 000 columns) indicate better-quality results than algorithms based on Lagrangian relaxations in terms of final solutions and mainly in computer times. Although the solving of a single surrogate optimization problem is slower than a corresponding Lagrangian optimization, the overall performance is almost twice as fast. This is due to the smaller number of iterations which is a result of faster convergence and less oscillation.

Lagrangean/Surrogate Heuristics for p-Median Problems

The p-median problem is the problem of locating p facilities (medians) on a network so as to minimize the sum of all the distances from each demand point to its nearest facility. A successful approach to approximately solve this problem is the use of Lagrangean heuristics, based upon Lagrangean relaxation and subgradient optimization. The Lagrangean/surrogate is an alternative relaxation proposed recently to correct the erratic behavior of subgradient like methods employed to solve the Lagrangean dual. We propose in this paper Lagrangean/surrogate heuristics to p-median problems. Lagrangean and surrogate relaxations are combined relaxing in the surrogate way the assignment constraints in the p-median formulation. Then, the Lagrangean relaxation of the surrogate constraint is obtained and approximately optimized (one-dimensional dual). Lagrangean/surrogate relaxations are very stable (low oscillating) and reach the same good results of Lagrangean (alone) heuristics in less computational times. Two primal heuristics was tested, an interchange heuristic and a location-allocation based heuristic. The paper presents several computational tests which have been conducted with problems from the literature, a set of instances presenting large duality gaps, a set of time consuming instances and a large scale instance.

Constructive Genetic Algorithm for Clustering Problems

Genetic algorithms (GAs) have recently been accepted as powerful approaches to solving optimization problems. It is also well-accepted that building block construction (schemata formation and conservation) has a positive influence on GA behavior. Schemata are usually indirectly evaluated through a derived structure. We introduce a new approach called the Constructive Genetic Algorithm (CGA), which allows for schemata evaluation and the provision of other new features to the GA. Problems are modeled as bi-objective optimization problems that consider the evaluation of two fitness functions. This double fitness process, called fg-fitness, evaluates schemata and structures in a common basis. Evolution is conducted considering an adaptive rejection threshold that contemplates both objectives and attributes a rank to each individual in population. The population is dynamic in size and composed of schemata and structures. Recombination preserves good schemata, and mutation is applied to structures to get population diversification. The CGA is applied to two clustering problems in graphs. Representation of schemata and structures use a binary digit alphabet and are based on assignment (greedy) heuristics that provide a clearly distinguished representation for the problems. The clustering problems studied are the classical p-median and the capacitated p-median. Good results are shown for problem instances taken from the literature.

Tabu Search Heuristic for Point-Feature Cartographic Label Placement

The generation of better label placement configurations in maps is a problem that comes up in automated cartographic production. The objective of a good label placement is to display the geographic position of the features with their corresponding label in a clear and harmonious fashion, following accepted cartographic conventions. In this work, we have approached this problem from a combinatorial optimization point of view, and our research consisted of the evaluation of the tabu search (TS) heuristic applied to cartographic label placement. When compared, in real and random test cases, with techniques such as simulated annealing and genetic algorithm (GA), TS has proven to be an efficient choice, with the best performance in quality. We concluded that TS is a recommended method to solve cartographic label placement problem of point features, due to its simplicity, practicality, efficiency and good performance along with its ability to generate quality solutions in acceptable computational time.

Clustering Search for the Berth Allocation Problem

This work presents a new approach to the Berth Allocation Problem (BAP) for ships in ports. Due to the increasing demand for ships carrying containers, the BAP can be considered as a major optimization problem in marine terminals. In this paper, the BAP is considered as dynamic and modeled in discrete case and we propose a new alternative to solve it. The proposed alternative is based on applying the Clustering Search (CS) method using the Simulated Annealing (SA) for solutions generation. The CS is an iterative method which divides the search space in clusters and it is composed of a metaheuristic for solutions generation, a grouping process and a local search heuristic. The computational results are compared against recent methods found in the literature.

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances.

Clustering search algorithm for the capacitated centered clustering problem

The capacitated centered clustering problem (CCCP) consists in partitioning a set of n points into p disjoint clusters with a known capacity. Each cluster is specified by a centroid. The objective is to minimize the total dissimilarity within each cluster, such that a given capacity limit of the cluster is not exceeded. This paper presents a solution procedure for the CCCP, using the hybrid metaheuristic clustering search (CS), whose main idea is to identify promising areas of the search space by generating solutions through a metaheuristic and clustering them into groups that are then further explored with local search heuristics. Computational results in test problems of the literature show that the CS found a significant number of new best-known solutions in reasonable computational times.

A Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on m machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillards well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling problems.

A new evolutionary clustering search for a no-wait flow shop problem with set-up times

This paper addresses the m-machine no-wait flow shop problem where the set-up time of a job is separated from its processing time. The performance measure considered is the total flowtime. A new hybrid metaheuristic Genetic Algorithm-Cluster Search is proposed to solve the scheduling problem. The performance of the proposed method is evaluated and the results are compared with the best method reported in the literature. Experimental tests show superiority of the new method for the test problems set, regarding the solution quality.