Placing Text Labels an Maps and Diagrams using Genetic Algorithms with Masking

Cartographic label placement is one of the most time consuming tasks in the production of high quality maps and other high quality graphical displays It is essential that text labels used to identify various features and objects be placed in a clear and unobscured manner In this paper we are concerned with the placement of labels for point features Speci cally the point feature label placement PFLP problem is the problem of placing text labels to point features on a map graph or diagram in such a manner so as to maximize legibility The PFLP problem has been shown to be NP hard We propose a heuristic method for the PFLP problem based on genetic algorithms GA an adaptive robust search and optimization technique based on the principles of natural genetics and survival of the ttest In particular we emphasize the notion of masking to preserve optimal subsequences in chromosomes and prevent their disruption during crossover and mutation We ran our algorithms on randomly placed point features in a region and on datasets from various regions of the USA map with great success Our GA implementation with masking solved each of the test cases extremely well and proved to be an excellent heuristic for solving the PFLP problem Furthermore our GA with masking performed signi cantly better than other PFLP algorithms from the literature Text labels used to identify various features and objects are a fundamental part of producing good graphs and maps It is essential that text labels be placed in a clear and unobscured manner Typically in maps there are three types of features that need to be labeled point features such as cities linear features such as boundaries rivers roads and area features such as lakes airports parks states and counties Cook and Jones claim that the placement of labels by cartographers typically takes up to one half of the total time required for generating high quality maps In this paper we are only concerned with the placement of labels for point features Labeling point features is the essential part of producing quality maps Speci cally the point feature label placement PFLP problem is the problem of placing text labels to point features on a map graph or diagram in such a manner so as to maximize legibility There are three issues to consider when placing text on point features The rst issue is the number and extent in which labels overlap each other The second concern is the number of times a label may overlap another point feature on the map but perhaps not the label for that point The third issue concerns a preference assignment to the placement of a label for a point as long as no other labels and points are obscured The third issue is less signi cant than the rst two The notion of labeling quality has been studied by many researchers Figure shows the traditional set of eight standard label positions for a point feature Each rectangle indicates a region in which a label may be placed The value inside each rectangle indicates the traditional accepted order of preference for placing a label Lower values indicate more desirable or more aesthetically pleasing positions A continuous label placement model is possible if one is allowed to place the label anywhere in a much larger rectangle around the point It is also possible to specify a circle around the point feature such that the label must be placed entirely within the circle In all instances labels are placed in a horizontal position In our research we allow for varying length labels around a point feature depending on the length of the labeled text for that point In many applications it may be impossible to place text labels on all points such that there are no overlapping labels This may be the case in highly congested areas of a map A variation of the PFLP problem allows for the deletion of points and their associated labels in order to produce unobscured label placement This variation is called the PFLP point selection problem Of course the object is to minimize the number of deleted points and associated labels and still produce an unobscured label placement for the remaining points Marks and Shieber provide an excellent proof that the PFLP problem is NP hard Clearly from Figure the number of possible label placements for n point features is n which is exponential not polynomial in n A wide variety of techniques have been developed over the years for automating the PFLP problem as best as possible Yoeli developed a simple deterministic greedy algorithm in the early s for the PFLP problem Jones developed a nondeterministic algorithm based on recursive backtracking Zoraster developed an algorithm based on integer programming Other algorithms for the PFLP problem are presented by Hirsch and Ahn and Freeman Christensen et al developed a simulated annealing algorithm for the PFLP problem Their research will be discussed later in the paper A comprehensive bibliography of the PFLP problem along with a more extensive review of previous research on the PFLP problem is given by Christensen et al and Marks and Shieber In this paper we present a genetic algorithm GA for solving the PFLP problem The authors are not aware of any other GA implementation for the PFLP problem The rest of the paper is described as follows In Section an overview of genetic algorithms is presented along with our GA implementation for the PFLP problem A discussion of masking in genetic algorithms is also presented in this section Results of our experiments and our conclusions are presented in Section