Candido F. X. Mendonça

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.

Modeling the kinetics of the coalescence of water droplets in crude oil emulsions subject to an electric field, with the cellular automata technique

In this study, the concept of cellular automata is applied in an innovative way to simulate the separation of phases in a water/oil emulsion. The velocity of the water droplets is calculated by the balance of forces acting on a pair of droplets in a group, and cellular automata is used to simulate the whole group of droplets. Thus, it is possible to solve the problem stochastically and to show the sequence of collisions of droplets and coalescence phenomena. This methodology enables the calculation of the amount of water that can be separated from the emulsion under different operating conditions, thus enabling the process to be optimized. Comparisons between the results obtained from the developed model and the operational performance of an actual desalting unit are carried out. The accuracy observed shows that the developed model is a good representation of the actual process.

Nonplanar vertex deletion: maximum degree thresholds for NP/Max SNP-hardness and a 34-approximation for finding maximum planar induced subgraphs☆

Abstract The non planar vertex deletion v d ( G ) , of a graph G is the smallest positive integer k, such that the removal of k vertices from G produces a planar graph. We solve a problem proposed by Yannakakis: find the threshold for the maximum degree of a graph G such that, given a graph G and a positive integer k, to decide whether v d ( G ) ≤ k is NP-complete. We prove that it is NP-complete to decide whether a maximum degree 3 graph G and a positive integer k satisfy v d ( G ) ≤ k . We prove that to compute v d ( G ) is Max SNP-hard when restricted to a cubic input G. We exhibit a polynomial 3 4 -approximation algorithm for finding a maximum planar induced subgraph of a maximum degree 3 graph.

Hamiltonian Cycles in Kneser Graphs for n=2k+2

Abstract The Kneser graph K ( n , k ) has all k-subsets of an n-set as its vertices and two subsets are adjacent if they are disjoint. Lovasz conjectured that every connected vertex-transitive graph has a hamiltonian path. For n ⩾ 2 k + 1 , the Kneser graphs form a well-studied family of connected, regular, vertex-transitive graphs. A direct computation of hamiltonian cycles in K ( n , k ) is not feasible for large values of k, because K ( n , k ) has ( n k ) vertices. We give a sufficient condition for K ( 2 k + 2 , k ) to be hamiltonian for odd k: the existence of a particular hamiltonian path in a reduced graph over K ( 2 k + 2 , k ) . Also, we extend this result to the bipartite Kneser graphs B ( 2 k + 2 , k ) for odd k.

Modeling of Kinetics of Water Droplets Coalescence in Crude Oil Emulsion Subjected to an Electrical Field.

Abstract Water is used in petroleum desalting units to dilute and remove the salted water droplets that the crude oil contains. The basic processes promote the coalescence of small droplets of conducting water dispersed in a crude oil emulsion. In order to make separation easier, the emulsion is distributed horizontally between two electrodes and subjected to an electrical field, which generates an attractive force among the droplets, promoting coalescence phenomena and further sedimentation. The main purpose of this study is to reduce the demand of fresh water and the liquid effluent generation in refineries. This paper presents a new model developed in order to calculate the droplets velocity by using the balance of the acting forces. The model is able to determine the droplets trajectory in order to define if they can be separated from the continuous phase. Besides the deterministic approaches based on traditional equations, the model uses also the concept of cellular automata. Thus it is possible to solve the problem in a stochastic way and to show visually the sequence of droplets collisions and coalescence phenomena. This methodology enables to calculate the amount of water that can be separated of the emulsion for a number of different operating conditions and then to optimize the process. Comparisons between the obtained results by the developed model and the operational performance of a real desalting unit are carried out. A good accuracy is observed, which shows that the real process is very well represented by the developed model.

Fast holographic-like stereogram display using shell rendering and a holographic screen

Display systems relying on computer graphics techniques usually create 2.5D image display on a 2D screen. To obtain 3D image display, most system uses auxiliary devices or viewing tricks, such as polarized glasses, virtual reality helmet, detection of observers location, divergent viewing, etc. We call these systems stereoscopic. A system that can display 3D images in a natural way is called a self- stereoscopic system. We know that stereoscopic system do not have horizontal parallax such as seen in holograms, which display continuum parallax. In this paper, we introduce a new technique based on shell rendering to discretize horizontal parallax by coding several views of the object forming a holographic-like stereogram and a new self- stereoscopic 3D display system to visualize holographic stereograms on a holographic screen. We also demonstrate the new system using medical image data.

Combining Heuristic and Utility Function for Fair Train Crew Rostering

In this paper we address the problem of defining a work assignment for train drivers within a monthly planning horizon with even distribution of satisfaction based on a real-would problem. We propose an utility function, in order to measure the individual satisfaction, and a heuristic approach to construct and assign the rosters. In the first phase we apply stated preference methods to devise a utility function. The second phase we apply a heuristic algorithm which constructs and assigns the rosters based on the previous utility function. The heuristic algorithm constructs a cyclic roster in order to find out a minimum number of train drivers required for the job. The cyclic roster generated is divided into different truncated rosters and assigned to each driver in such way the satisfactions should be evenly distributed among all drivers as much as possible. Computational tests are carried out using real data instance of a Brazilian railway company. Our experiments indicated that the proposed method is feasible to reusing the discrepancies between the individual rosters.

An Evolutionary Algorithm for Graph Planarisation by Vertex Deletion

A non-planar graph can only be planarized if it is structurally modified. This work presents a new heuristic algorithm that uses vertices deletion to modify a non-planar graph in order to obtain a planar subgraph. The proposed algorithm aims to delete a minimum number of vertices to achieve its goal. The vertex deletion number of a graph G = (V, E) is the smallest integer k � 0 such that there is an induced planar subgraph of G obtained by the removal of k vertices of G. Considering that the corresponding decision problem is NP-complete and an approximation algorithm for graph planarization by vertices deletion does not exist, this work proposes an evolutionary algorithm that uses a constructive heuristic algorithm to planarize a graph. This constructive heuristic has time complexity of O(n + m), where m = |V| and n = |E|, and is based on the PQ-trees data structure and on the vertex deletion operation. The algorithm performance is verified by means of case studies.