Heuristics for cartographic label placement problems

The cartographic label placement problem is an important task in automated cartography and Geographical Information Systems. Positioning the texts requires that overlap among texts should be avoided, that cartographic conventions and preference should be obeyed. This paper examines the point-feature cartographic label placement problem (PFCLP) as an optimization problem. We formulate the PFCLP considering the minimization of existing overlaps and labeling of all points on a map. This objective improves legibility when all points must be placed even if overlaps are inevitable. A new mathematical formulation of binary integer linear programming that allows labeling of all points is presented, followed by some Lagrangean relaxation heuristics. The computational tests considered instances proposed in the literature up to 1000 points, and the relaxations provided good lower and upper bounds.     

Dispersion for the point-feature cartographic label placement problem

The point-feature cartographic label placement problem (PFCLP) is a NP-Hard problem arising in design of maps and other graphic objects. For the sake of a better map legibility it is important to avoid overlaps in the process of labeling. This paper examines the PFCLP in the legibility context and proposes a dispersion approach for the problem. It is considered that when all points must to be labeled and overlaps are inevitable, the map can be more readable if overlapping labels are placed more distant from each other. The PFCLP is modeled as a dispersion problem on two mathematical formulations based on binary integer linear programming. Computational tests have provided good results on several generated instances.     

Lagrangean relaxation with clusters for point-feature cartographic label placement problems

This paper presents two new mathematical formulations for the point-feature cartographic label placement problem (PFCLP) and a new Lagrangean relaxation with clusters (LagClus) to provide bounds to these formulations. The PFCLP can be represented by a conflict graph and the relaxation divides the graph in small subproblems (clusters) that are easily solved. The edges connecting clusters are relaxed in a Lagrangean way and a subgradient algorithm improves the bounds. The LagClus was successfully applied to a set of instances up to 1000 points providing the best results of those reported in 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.     

Improving the Clustering Search heuristic: An application to cartographic labeling

The use of hybrid metaheuristics is a good approach to improve the quality and efficiency of metaheuristics. This paper presents a hybrid method based on Clustering Search (CS). CS seeks to combine metaheuristics and heuristics for local search, intensifying the search on regions of the search space which are considered promising. We propose a more efficient way to detect promising regions, based on the clustering techniques of Density-based spatial clustering of applications with noise (DBSCAN), Label-propagation (LP), and Natural Group Identification (NGI) algorithms. This proposal is called Density Clustering Search (DCS). To analyze this new approach, we propose to solve a combinatorial optimization problem with many practical applications, the Point Feature Cartographic Label Placement (PFCLP). The PFCLP attempts to locate identifiers (labels) of regions on a map without damaging legibility. The computational tests used instances taken from the literature. The results were satisfactory for clusters made with LP and NGI, presenting better results than the classic CS, which indicates these methods are a good alternative for the improvement of this method.     

A hybrid data mining heuristic to solve the point‐feature cartographic label placement problem

A clean map visualization requires the fewest possible overlaps and depends on how labels are attached to point features. In this paper, we address the cartographic label placement variant problem whose objective is to label a set of points maximizing the number of conflict‐free points. Thus, we propose a hybrid data mining heuristic to solve the point‐feature cartographic label placement problem based on a clustering search (CS) heuristic, a state‐of‐the‐art method for this problem. Although several works have investigated the combination of data mining and multistart metaheuristics, this is the first time data mining has been used to improve CS and simulated annealing based heuristics. Computational experiments showed that the proposed hybrid heuristic was able to reach better cost solutions than the original strategy, with the same time effort. The proposed heuristic also could find almost all known optimal solutions and improved most of the best results for the set of large instances reported so far in the literature.     

Topological reorganization of inconsistent geographical databases: A step towards their certification

Due to the excessive price of digitizing, many geographical databases are not well captured and structured: even if the maps look good, in reality, the database is likely to consist of a set of lines of various lengths with no sets of cartographic objects. Some experts claim that 80% of actual geographical databases are sets of disordered texts and spaghetti lines instead of well-constructed geographical objects.

So, the topological reorganization of those databases represents a challenge to be faced. In this paper, the general problem is described and some solutions are offered, especially regarding the topological reorganization of utility networks and cadasters.

The main characteristics of those methods are to combine computational geometry and relational algebra.     

The fixed set search applied to the power dominating set problem

In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.     

Ant colony optimization algorithm for the Euclidean location-allocation problem with unknown number of facilities

This paper addresses the Euclidean location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. This is a NP-hard problem and in this paper, a three-stage ant colony optimization (ACO) algorithm is introduced and its performance is evaluated by comparing its solutions to the solutions of genetic algorithms (GA). The results show that ACO outperformed GA and reached better solutions in a faster computational time. Furthermore, ACO was tested on the relaxed version of the problem where the number of facilities is known, and compared to existing methods in the literature. The results again confirmed the superiority of the proposed algorithm.     

Bicriteria scheduling problem for unrelated parallel machines with release dates

This research proposes a heuristic and a tabu search algorithm (TSA) to find non-dominated solutions to bicriteria unrelated parallel machine scheduling problems with release dates. The two objective functions considered in this problem are to minimize both makespan and total weighted tardiness. The computational results show that the proposed heuristic is computationally efficient and provides solutions of reasonable quality. The proposed TSA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.     

Real-time map labelling for mobile applications

It is essential to label roads, landmarks, and other important features on maps for mobile applications to help users to understand their location and the environment. This paper aims to examine real-time map labelling methods suitable for the small screen on mobile devices. A slider method with a continuous search space was proposed to sequentially label both line and point features. The method starts with defining a range box for possible locations of the label. Then a search is performed, and the range box is reduced, if there are any cartographic objects that overlap the range box. Finally, the label is placed, at the best possible position in the reduced range box according to normal cartographic preferences, where it does not obscure any cartographic object. We implemented this method in a Java environment using the open source library JTS Topology Suite. A case study showed sound cartographic results of the labelling and acceptable computational efficiency.     

A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimise total flowtime

This paper focuses on the blocking flow shop scheduling problem with the objective of total flowtime minimisation. This problem assumes that there are no buffers between machines and, due to its application to many manufacturing sectors, it is receiving a growing attention by researchers during the last years. Since the problem is NP-hard, a large number of heuristics have been proposed to provide good solutions with reasonable computational times. In this paper, we conduct a comprehensive evaluation of the available heuristics for the problem and for related problems, resulting in the implementation and testing of a total of 35 heuristics. Furthermore, we propose an efficient constructive heuristic which successfully combines a pool of partial sequences in parallel, using a beam-search-based approach. The computational experiments show the excellent performance of the proposed heuristic as compared to the best-so-far algorithms for the problem, both in terms of quality of the solutions and of computational requirements. In fact, despite being a relative fast constructive heuristic, new best upper bounds have been found for more than 27% of Taillard’s instances.     

A constraint-guided method with evolutionary algorithms for economic problems

This paper presents an evolutionary algorithms based constrain-guided method (CGM) that is capable of handling both hard and soft constraints in optimization problems. While searching for constraint-satisfied solutions, the method differentiates candidate solutions by assigning them with different fitness values, enabling favorite solutions to be distinguished more likely and more effectively from unfavored ones.We illustrate the use of CGM in solving two economic problems with optimization involved: (1) searching equilibriums for bargaining problems; (2) reducing the rate of failure in financial prediction problems. The efficacy of the proposed CGM is analyzed and compared with some other computational techniques, including a repair method and a penalty method for the problem (1), a linear classifier and three neural networks for the problem (2), respectively. Our studies here suggest that the evolutionary algorithms based CGM compares favorably against those computational approaches.     

Solving the team orienteering problem using effective multi-start simulated annealing

The team orienteering problem (TOP) is known as an NP-complete problem. A set of locations is provided and a score is collected from the visit to each location. The objective is to maximize the total score given a fixed time limit for each available tour. Given the computational complexity of this problem, a multi-start simulated annealing (MSA) algorithm which combines a simulated annealing (SA) based meta-heuristic with a multi-start hill climbing strategy is proposed to solve TOP. To verify the developed MSA algorithm, computational experiments are performed on well-known benchmark problems involving numbers of locations ranging between 42 and 102. The experimental results demonstrate that the multi-start hill climbing strategy can significantly improve the performance of the traditional single-start SA. Meanwhile, the proposed MSA algorithm is highly effective compared to the state-of-the-art meta-heuristics on the same benchmark instances. The proposed MSA algorithm obtained 135 best solutions to the 157 benchmark problems, including five new best solutions. In terms of both solution quality and computational expense, this study successfully constructs a high-performance method for solving this challenging problem.     

Multiple representations for cartographic objects in a multi-scale tree—An intelligent graphical zoom

In Geographic Information Systems, a function to draw cartographic sketches quickly and in arbitrary scales is needed. This calls for cartographic generalization, a notoriously difficult problem. Efforts to achieve automatic cartographic generalization were successful for specific aspects, but no complete solution is known, nor are there any expected within the immediate future. In practical applications, a base map is stored and its scale is changed. Without major distortions, only changes to twice or half the original scale are feasible by simple numeric scale change. Everything beyond this requires adaptation of symbols, selection of objects, placements of labels, etc.

Extending ideas of hierarchies or pyramids, where representations of the same objects at different scales are stored, a multi-scale, hierarchial spatial model is proposed. Objects with increasing detail are stored in levels and can be used to compose a map at a particular scale. Applied to the particular problem of cartographic mapping, this results in a multi-scale cartographic tree. The same concept can be used equally well for other applications, which require rendering of objects at different levels of detail.

The structure of the multi-scale tree is explained. It is based on a trade-off between storage and computation, replacing all steps which are difficult to automate by essentially redundant storage. The dominant operation is ‘zoom,’ which moves towards a more detailed level, intelligently replacing the current graphical representation with the more detailed one, appropriate for the selected new scale. Methods to select objects for rendering are based on the principle of equal information density. Principles of possible implementations are presented.     

The usable leftover one‐dimensional cutting stock problem—a priority‐in‐use heuristic

We consider a one‐dimensional cutting stock problem in which the material not used in the cutting patterns, if large enough, is kept for use in the future. Moreover, it is assumed that leftovers should not remain in stock for a long time, hence, such leftovers have priority‐in‐use compared to standard objects (objects bought by the industry) in stock. A heuristic procedure is proposed for this problem, and its performance is analyzed by solving randomly generated dynamic instances where successive problems are solved in a time horizon. For each period, new demands arise and a new problem is solved on the basis of the information about the stock of the previous periods (remaining standard objects in the stock) and usable leftovers generated during those previous periods. The computational experiments show that the solutions presented by the proposed heuristic are better than the solutions obtained by other heuristics from the literature.     

Computing all efficient solutions of the biobjective minimum spanning tree problem

A common way of computing all efficient (Pareto optimal) solutions for a biobjective combinatorial optimisation problem is to compute first the extreme efficient solutions and then the remaining, non-extreme solutions. The second phase, the computation of non-extreme solutions, can be based on a “k-best” algorithm for the single-objective version of the problem or on the branch-and-bound method. A k-best algorithm computes the k-best solutions in order of their objective values. We compare the performance of these two approaches applied to the biobjective minimum spanning tree problem. Our extensive computational experiments indicate the overwhelming superiority of the k-best approach. We propose heuristic enhancements to this approach which further improve its performance.     

A knowledge-based approach for task allocation in heterogeneous distributed computer systems

Abstract: This paper presents a knowledge-based system for task allocation in a network of processors. Since the problem is NP-complete, optimisation techniques are computationally prohibitive and impractical. Our approach reduces computational burden by using (1) a two-level hierarchical scheduling model to alleviate the problem complexity, and (2) a search strategy that uses knowledge from the knowledge base to limit the search space to a manageable size. The major goal of our approach is to generate good but not necessarily optimal solutions quickly. The system is implemented on a Sun SPARCstation 1 + using Common Lisp. Our computational experience in using this system for task allocation indicates that the two-level hierarchical approach generates better schedules in shorter computational time than a non-hierarchical approach.     

A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

This paper proposes a 0-1 integer linear programming model for the point-feature cartographic label placement problem based on labeling of the largest number of free labels. In addition, one non-trivial valid inequality is presented to strengthen this proposed model. Even with the strengthened model, a commercial solver was not able to solve a representative sample of known instances presented in the literature. Thus, we also present a Lagrangean decomposition technique based on graph partitioning. Our added approaches established optimal solutions for practically all the used instances and the results significantly improved the ones presented in recent studies concerning the problem.