Spatial Change Optimization: Integrating GA with Visualization for 3D ...

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Spatial Change Optimization: Integrating GA with V isualization for 3D Scenario Generation Magesh Chandramouli, Bo Huang, and Lulu Xue

Abstract

Urban spatial analysis is becoming an increasingly complex problem due to the overwhelming demands imposed by the population and several other factors. Consequently, tools are needed to solve complex urban spatial problems that are multiobjective in nature. This study presents a multiobjective optimization approach to generating alternative land use scenarios and offers a visual evaluation tool for assessing the Pareto solutions. Typically, with genetic algorithms (GA), decision makers are finally left with alternative solutions in the form of the Pareto set, from which one or a few more will be chosen. Hence, a visualization tool is employed in this study, whereby the decision makers can better evaluate the alternative solutions from the Pareto set. Modeling futuristic land uses is devised as an optimization problem wherein spatial configurations are created through the use of evolutionary algorithms. With the goal of sustainable urban land use planning, the evolutionary algorithm is designed for multiple objectives, such as maximization of per capita green space, maximization of urban housing density, maximization of public service space, and conflict resolution among neighboring land uses. The results evince the validity of the GA framework and also corroborate the utility of the virtual scenarios.

Introduction

A vast majority of today’s planning problems entail synchronized optimization of multiple objectives, e.g., accommodating maximum population versus providing maximum green space. The key to the problem lies in the efficient trade off among the different objectives thus making a judicious compromise (Huang et al., 2008). Over the last several decades, a good deal of work has been accomplished in the field of land-use planning that aims to channel the change to right zones, e.g., spatial allocation for given resources and constraints and various forms of site selection and suitability studies. Nevertheless, present urban land-uses reveal unsuitable patterns that do not aid sustainable development. Multiobjective optimization genetic algorithm techniques have been used in the recent past to obtain a Pareto set that contains plans that are judicious trade-off among the numerous solutions (Seixas et al., 2005, Stewart et al., 2004).

Magesh Chandramouli is at Purdue University, West Lafayette, IN 47907, ([email protected]). Bo Huang is at the Chinese University of Hong Kong, Shatin N.T., HK. Lulu Xue is at Peking University, Beijing, P.R. China. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

However, during urban planning, authorities cannot implement all the conflicting solutions in the Pareto set, as only one optimal Pareto solution can finally be executed. Matthews et al. (2000) point out the importance of scrutinizing the variations among the range of candidate solutions and comparing and contrasting them to obtain a superior understanding of the fundamental processes and locations. Osyczka (1985) mentions that the process of choosing one single solution over others involves in-depth problem knowledge and various other problem related factors. Seixas et al. (2005) opine that choice of the solution is based on some “higher level information.” In this study, we believe that a tool that can help compare and contrast the various solutions in the Pareto set, and thus evaluate them before making a decision would make the whole exercise of multiobjective optimization extremely fruitful. Hence, we propose to integrate multiobjective genetic algorithms (MOGAs) with a visual evaluation tool to aid help decision makers in comparing various solutions and perform informed decision-making based on concrete visual representations, rather than relying on abstract factors or designating weights subjectively. Conflicting aspects that need to be considered in landuse planning include, but are not limited to, the number of high-rise structures that can be permitted or needed, their impact on the population density or housing capacity, availability of green space for recreational and public amenities, livable environment, aesthetic concerns, etc. A ook at the land-use models developed so far, such as cellular automata models (Clarke and Gaydos, 1998) or statistical models (Huang et al., 2009), have evinced that they cannot provide satisfying solutions to the conflicting demands by urban planners and stakeholders. Therefore, the proposed model integrates the GA-based multiobjective optimization method with a visualization tool that can provide interactive 3D rendering, whereby planners and decision makers will have a directly visual way to compare the alternatives derived from the multiobjective method in terms of both land-use planning and urban design. The aim of this study is to employ genetic algorithms (Goldberg, 1989) as a tool to solve a land-use multiobjective optimization problem (MOP), and subsequently use a visual evaluation tool to aid land managers in selecting appropriate plans. The GA in this study accommodates a carefully selected set of objectives: maximization of urban housing

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density, maximization of per capita green space, maximization of public service space, and maximization the compatibility among adjacent land uses. The outline for the other sections is as follows. The next section discusses about the process of multiobjective optimization and the various approaches for multiobjective land-use optimization followed by a delineation of the GA methodology employed in this study and explicates the research framework and the components. The next section elucidates the implementation of the GA and its outcomes, followed by an explanation of the implementation of the VRbased visualization and presents the results and discussion. The final section provides the conclusions of the study.

Overview of Multiobjective Optimization

A typical MOP consists of a specific number of decision variables and particular number, say n number of objective functions, which need to be attained under a given set of constraints. The aim of the optimization process can be expressed as follows: Maximize (or) minimize f(x) ⫽ y ⫽ (f1(x), f2(x) . . . fn(x)) Conditional on C(x) ⫽ (C1(x), C2(x), . . . , Cm(x)) where n is the number of objective functions, and m is the number of constraints. In the above expression the decision vector x is equal to (x1, x2, . . . xn), and the objective vector y is equal to (y1,y2, . . . ,yn). The set of values (x1,x2, . . . xn) ⑀ X signifies the decision space and the set of values (y1,y2, . . . yn) ⑀ Y represents the objective space. The feasible set of solutions is determined by the set of constraints, i.e., C(x) ⭐ 0. In order for a plan to be considered part of the Pareto set, no other plan, which is superior in all objectives, should be found. In other words, a plan may outdo the Pareto plan in one objective and a different plan may be better in another objective; however, a “single plan” does not outperform a Pareto plan in all the objectives. Balling et al. (2004) correctly point out that the “Pareto set is independent of the relative importance of the objectives.” From the above discussion it can be seen that plans that do not belong to the Pareto set (non-Pareto plans) are “dominated” because a Pareto plan that is better (or that which dominates) already exists. One well-known method employed in multiobjective land-use optimization to model land-use planning problems is multiobjective integer programming. Early attempts in this direction include Bammi and Bammi (1975), Wright et al. (1983), and Gilber et al. (1985). In these works, scalarization techniques are widely adopted, which cumulatively combine all the objectives of multiobjective optimization into a single one. Since it is preferable for decision makers to gain a set of optimal solutions instead of one single “best” solution, the optimization routines are executed numerous times with varied settings of the objective weights. Usually, these weights are subjectively predetermined; nonetheless, it is difficult to achieve a unanimous agreement among different stakeholders (Bennett et al., 2004). Thus, given the complex urban milieu, greater number of stakeholders, and the demand for informed decision-making, the use of more advanced tools is necessitated, which can better handle multiobjective problems. In addition to the aforementioned reasons, the advancement in spatial data procurement and processing techniques and the use of Geographic Information Systems (GIS) have imposed greater demands on the accuracy and reliability of the results. Following the above discussion, multiobjective genetic algorithm (MOGA), a family of heuristic methods, have been 1016 A u g u s t 2 0 0 9

found suitable to tackle the aforementioned problems (Aerts et al., 2005): first, traditional multiobjective land-use allocation confronts the problem of deriving a set of Pareto optimal solutions, whereas MOGA can generate a set of relatively diverse solutions without subjective intervention; second, since multiobjective land-use optimization in the fine-grain scale always involves a large solution space, MOGA provides a sound way to balance between computation costs and solutions approximated, as opposed to the exact methods’ computational intractability; third, provided the inherent complex nature of urban systems, the definitions of many objectives are not always non-linear or additive (Stewart et al., 2004). MOGA extends the limitations of traditional methods in ways that it is capable of solving these non-linear, non-additive optimization problems without reformulating the problems. With these merits, MOGA has been adopted in a large amount of land-use planning research (Matthews et al., 2000; Stewart et al., 2004; Balling et al., 2004). Because MOGA usually retrieves a large number of optimal land-use plans, new techniques are needed in order to facilitate spatial decision making, among which visualization plays an important role (Huang and Lin, 1999; Huang and Claramunt, 2004). In particular, to plot the candidate solutions of the design space or geographical space (Bennett et al., 2004), among others, is an intuitive way to visualize these optimal alternatives (Armstrong et al., 1992). Albeit, until now most research in land-use optimization field still examine the final land-use plans in 2D map forms, leaving much information inside the land-use plan unexplored, such as information related to urban design. Besides viewing the solutions in the design space, there are several ways in which the results can be presented in the objective space, which, on the other hand, involves higher dimensionality with reference to the objective numbers. To name a few, scatterplot matrices and parallel coordinates are often used (Buja and Cook, 1996). Moreover, Chandramouli (2008) developed a set of tools to link the design and objective space together to visualize the Pareto optimal solutions for land-use planning problems.

Methodology

A study area is usually divided into zones (with restrictions), and these zones are allowed to assume different landuses. The genetic framework for the region is represented by a gene each for every changeable zone. In this study, we use an integer based genetic representation, i.e., each gene is an integer that can assume any value from among the various land-uses considered in the study. Here, the land-uses are coded as follows: Agricultural area is assigned a LU_CODE of 0, commercial is 1, Direct Control is 2, Industrial is 3, Green space is 4, Public Service zones is 5, Residential High Density is 6, Residential Low Density is 7, Residential Medium Density is 8, and Urban Reserves is 9. Therefore, each zone is plotted or mapped to an integer within the range of 0 to 9 as specified above and the integer values of all such zones are linked together finally resulting in a integer string. In the beginning (first generation), a random value is assigned by the GA to each gene. Here, the generation size is chosen as 100, corresponding to 100 land-use plans. Then, each plan is scrutinized with respect to the four objectives and three constraints. Plans that meet the constraints are deemed as practicable ones. The goal is to produce a landuse map that will ensure maximum values of urban housing density, per capita green space, per capita space for public service, as well as land-use neighborhood compatibility. As the land-use variables can assume one among 10 values, the PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

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total set of possible plans is as big as 10n, where n is the number of land-use polygons. This signifies an enormously discrete search space. Probably only a tool like GA that is robust and efficient is fit for performing multiobjective optimization in such a large search space. Objective Functions and Constraints GAs typically consist of objective functions that they try to maximize or minimize during the process of optimization. “Sustainability” is the keyword that influenced the selection of objectives for this study. Sustainable development seeks to reconcile the conflicts among economic development, environmental preservation, and equity (Godschalk, 2004). Although there is no doubt with respect to the abstract definition of sustainable development, to spatial explicitly quantify such construct has not yet reached any consensus. In the work done by Ligmann-Zielinska et al. (2005), to gain an operational measurement of sustainability, the concept has been scaled down to urban forms’ compactness. In contrast, this study attempts to preserve the original three dimensions of sustainability, when modeling the spatial explicit land-use allocation problems. Therefore, the economic development and environmental preservation dimensions of sustainability were measured respectively through housing units and green space, while the equity dimension was calibrated by public amenities and neighborhood landuse compatibility. In other words, without loss of generality, four objectives were considered, which ensure that: 1. 2. 3. 4.

The The The The

city can accommodate more residents. urban dwellers get more green spaces. residents get more space for public amenities. plan contains compatible land use neighborhood(s).

The first objective was meant to increase the housing capacity by increasing the number of housing units in the urban milieu. Housing problems seriously deter the progress of a city. This was particularly so in the City of Calgary where serious housing problems were experienced during the year 2006/2007, and the problem was expected to continue. Based on the housing density, the land-use was classified into one of the following three categories: Low Density Residential zone (0 to 25 housing units/hectare), Medium Density Residential zone (26 to 50), High Density Residential zone (51 to 185). The total number of housing units of plan i (denoted by NumHUi) was calculated as follows: NumHUi ⫽ round(ArearesLi ⫻ 50 ⫹ ArearesMi ⫻ 100 ⫹ ArearesHi ⫻ 185) where ArearesLi, ArearesMi, ArearesHi, respectively, refer to the total area of low density residential zones, medium density residential zones, and high density residential zones of plan i. The second objective was the maximization of per capita green space (PCGS). Green spaces are inevitable to reduce environmental pollution and to ensure healthy surroundings for the people. Many authors and land-use planners consider green space as inevitable for attaining sustainable urban environments. The PCGS (Per Capita Green Space) of each land-use plan i was calculated by dividing the total available green space within the study area by the number of residents in the study area: PCGSi ⫽ (AreaGSi)/Pop where PCGSi represents the per capita green space of plan i, AreaGSi represents the total green space area of plan i, and Pop represents the population of study area. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

The third objective was the maximization of per capita space for public service (PCPS). Public service includes all amenities needed for the daily life of the residents in a city, including transportation facilities such as roads, transit stations, rail road network, and various other public amenities under the category of public service. Consequently, the third objective of this study was chosen as maximization of per capita space for public service. Similar to PCGS, the PCPS (Per Capita Public Space) of a land-use plan i was calculated by dividing the total available space for public service within the study area by the population. The fourth and final objective was to resolve conflicts of neighboring land-uses. Through maximizing the compatibility between zone m and its neighborhoods, the final plan can promote mixed land-use (by assigning equal compatibility to different land-uses, like residential-commercial) as well as avoid severe environmental deterioration (e.g., residential-industrial has compatibility of 0). LigmannZielinska et al. (2005) proposed a method to quantify conflicting adjacent land-uses based on raster representation. Here, a similar approach was adopted to solve the very problem in the vector representation. First, an algorithm was used to search all topologically connected zones to each zone m. The level of incompatibility was then estimated by summing up all the compatible evaluation values between the candidate land-use l m of zone m and each land-use within its neighborhood: CmpADi ⫽

zonenum adn(m)

a

m⫽1

a compatibility(plani,m, plani,j) j

where plani,m and plani,j respectively denote the particular land-uses of zone m and its neighboring zone j in the plan i; the function compatibility was defined by the authors and some planning experts interviewed; adn(m) refers to an array of indexes of zones that are adjacent to zone m; and zonenum refers to the total number of zones in the study area. Constraints are limitations on the GA to yield results that can meet some basic requirements. In this study, Urban Reserves and Direct Control zones were maintained the same throughout the iterations. There were other constraints that required the per capita green space and per capita public service space to be above a minimum threshold. During each iteration, the plans in the current generation were checked for feasibility based on the constraints. Plans that do not satisfy the constraints were discarded and those that satisfy the constraints were included in the starting generation. Fitness Evaluation The objectives were normalized using a simple and straightforward procedure that involved scaling. Typically, normalization involves finding the maximum as well as the minimum values for each objective k for a set of plans in a generation and then re-scaling using the following formula: objk(plani) ⫽

valik ⫺ valmin,k valmax,k ⫺ valmin,k

, k ⫽ 1,2,3,4, i ⫽ 1,

100

where valik is the value of the objective k when assuming plan i, valmin,k is the least value of objective k among all the plans in the current generation, and valmax,k is the highest value of objective k among all the plans in a generation. The objectives of each plan were compared with other plans in the generation to find the fit ones in the current generation. Hence, when an objective of a plan i is compared A u g u s t 2 0 0 9 1017

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with that of another plan j, plan j is better than plan i if the difference between j and i is positive, as follows: objk (planj ) ⫺ objk (plani) ⫽ ⫽

valjk ⫺ valmin,k rangek valjk ⫺ valik rangek

⫺

valik ⫺ valmin,k rangek

7 0, k ⫽ 1,2,3,4

max(min(NumHUj ⫺ NumHUi, PCGSj ⫺ PCGSi, PCPSj ⫺ PCPSi , jZi

CmpADj ⫺ CmpADi)) 7 0. Therefore, the fitness of the ith plan in a generation was obtained as follows: fi ⫽ a 1 ⫺ max amina jZi

where rangek denotes the difference between the maximum and minimum values of the objective k. For measuring the fitness of each land-use plan, the Maximin fitness function developed by Balling et al. (2004) was used, which yielded a diverse set of non-dominated plans. The fitness of each plan in a generation was calculated with regard to the other plans in the same generation. Considering two plans planj and plani in a particular generation, plani is dominated (here the definition of “dominated” is stronger than that in multiobjective optimization) by planj if PCGSj, PCPSj, and NumHUj are all greater than the corresponding objective values, namely PCGSi, PCPSi, and NumHUi. This can be restated as follows: min (NumHUj ⫺ NumHUi, PCGSj ⫺ PCGSi, CmpADj ⫺ CmpADi) ⬎ 0.

PCPSj ⫺ PCPSi,

Each plan in a generation must be compared with all other plans within the same generation. Plani in a particular generation is considered to be dominated by another plan in the generation if:

NumHuj ⫺ NumHui PCGSj ⫺ PCGSi , , range1 range2

p PCPSj ⫺ PCPSi CmpADj ⫺ CmpADi , bbb . range3 range4

Based on the fitness formula described above, the Paretooptimal plans were selected from a generation based on the fitness values obtained. While dominated plans had a fitness value between 0 and 1, Pareto-optimal plans had fitness values greater than 1. Besides, in this study, a p value of 15 was employed. This value was chosen to pursue Paretooptimality more vigorously. This way, the fitness of those plans with fi more than 1 gets further higher, and the fitness of those plans with fi values less than 1 gets further lower (Balling et al., 2004).

Generating Land-use Plans

The central region of the City of Calgary was chosen as the study city (Plate 1), because the City of Calgary in the province of Alberta represented a rapidly growing city.

Plate 1 Study Area - Central Calgary Region.

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The population of the City of Calgary as on April 2006 was 991,759, which has now exceeded one million. The study area was selected after due consideration of the following facts: • The study area had a decent mix of all common land-use zones such as commercial, industrial, residential, etc. • Within residential category, the study area consisted good proportions of low density, medium density, and high density residential zones • The study area still had considerable room for modifications and if necessary, expansion.

The entire study region was made up of 135 zones. The land-use maps (Plate 1) were obtained from MADGIC, a geospatial data repository in the library of the University of Calgary and from the City of Calgary website. Data were basically in the form of ArcGIS® shapefiles and ERDAS Imagine® files. In order to obtain solutions in a reasonable time while still generating a set of land-use plans diverse enough, the population of the initial generation was chosen as 100 in this study. These plans in the starting generation were generated by a random process wherein integer values were assigned to each of the 100 chromosomes containing 135 genes, corresponding to the 135 zones in the study area. In other words, 100 ⫻ 135 integer values within the range of 0 to 9 were generated at random and assigned to the chromosomes. It should be recalled that among the set of constraints there are constraints that require the values of some land-use zones to remain constant. For instance, Urban Reserve and Direct Control in the original land-use zone always remained the same throughout the genetic algorithm process. Besides, there were other constraints that required the per capita green space and per capita public service space to be above a minimum threshold. During the starting random generation stage, the plans that did not satisfy these constraints were discarded. From this starting generation, the whole GA process involves 100 iterations at the end of which, a generation with 100 final, feasible plans results. In this study, the mutation probability was chosen as 0.05. On the whole, the average time consumed for the experiments that were performed on a 3.2 GHZ Pentium-IV computers with 512 MB RAM was 3,800 seconds for one execution of 100 generations. While the fitness of the initial generation was 1.70, the fitness of the final generation had improved to 168.1, which was about 100 times the overall fitness of the initial generation. This implies that the final plans, while satisfying the constraints, have maximized the per capita green space, per capita space for public service, the housing capacity and the balance of adjacent land uses. From the following table (Table 1) that provides the generational minimum and average values for the four objectives the performance of the GA is obvious. Also, another important point to be noted is that the Pareto set for the starting generation included a mere 10 of the 100 feasible plans, whereas the Pareto set for the final T ABLE 1.

Parameter Average- Initial Gen. Minimum-Initial Gen. Average- Final Gen. Minimum-Final Gen.


T HE I NCREASE

IN

generation included 40 of the 100 feasible plans. This was determined after an average run of at least 10 times of the 100 generations. A maximum of 66 was achieved, i.e., 66 Pareto-optimal sets were obtained in one generation. Let us take an in-depth look at the Pareto-optimality criteria and investigate how the process of multi-objective optimization improved the Pareto-optimality on a generation-by-generation basis. As the GA fitness function compares the fitness values of the plans within one generation, and it is not possible to compare fitness values between plans in different generations. The “global fitness” for each of the 10,000 plans in the global generation is according to the fitness equations described earlier in the Methodology Section. As it follows from the previous discussion, the global generation also must have a “global Pareto set.” From the total 10,000 plans in the global generation, there were 483 distinctive plans in the global Pareto set. The average value of the global fitness over the 100 plans in each generation is plotted and shown earlier and the following figure (Figure 1) shows their distribution, which clearly shows that the Pareto-optimality has been improving continuously after a particular generation number has been reached and after that particular number, the improvement has been continual as well as consistent.

VR-based V isualization of Par eto Optimal Land-use Plans

Many GAs generate optimal solutions using iterative optimization procedures. However, the work stops there, and then subjective measures are employed to select one plan for implementation. Therefore, there is an increasing need for tools or indicators that can efficiently depict land-use scenes as one comprehensive screenshot rather than a series of noncoherent data layers. Virtual reality visualization can meet such need by facilitating not only presented information, but also enabling seeing and understanding hidden information among datasets. This hidden information includes spatial distribution patterns of land-uses as well as urban design. By using 3D visual scene renderings, planners who are experts in the fields of land-use planning can find out desirable or undesirable patterns. For example, the per capita green space per population might be more than the required value; however, the distribution of the green spaces within the study area is an important factor. A resident might be in a condition to travel several kilometers to access a green space. In order to ensure that the purpose of green spaces is satisfied, they must not be in the required quantity, but must also be well distributed. Another element the land-use plan visualization always overlooked is the aesthetic side of the city. This aesthetic view quality is of significant importance in urban design in these days. For instance, an office building blocking the view of a monumental structure of some other feature of prominence is undesirable, and hence such a land-use cannot be allocated for high-density residential or high-rise buildings, etc. Three-dimensional visualization can greatly facilitate the study of the aesthetic quality of a plan. Furthermore, such

OBJECTIVE V ALUES

PCGS (Sq.mi./ Resident)

PCPS (Sq.mi./ Resident)

376.56 375.2 405.2 405.2

115.59 105.36 175.36 169.36

AFTER

GA I

TERATIONS

Housing Capacity (Number of Housing Units) 2.569 1.536 5.412 2.356

* * * *

107 106 108 107

Neighborhood Compatibility 575.18 505.4 587.37 535

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Figure 1. Distribution of Global Pareto Plans.

visualization tool can be also integrated into public participation systems and aid non-planning experts to get more involved in the planning process. With these advantages of virtual reality visualization in mind, in this study, two Pareto-plans with the highest fitness values were selected and visualization plans generated for these. In order to visualize land-uses, different kinds of information must exist and must be processed: Terrain data (e.g., digital elevation models) or land-use data (e.g., GIS data of the vegetation), or data about existing or planned changes in land use (e.g., CAD construction data, buildings, streets, bridges). Using texture mapping, surface attributes of threedimensional objects, such as color and transparency, can be customized through the projection of images onto these objects. A very simple and recurrently used way of land-use visualization is the draping of air photos or high-resolution satellite images over DTMs. These days, this is possible within a wide range of GIS applications. As the object’s geometry is not changed, this method is only suited for visualizations

from large viewing distances. In this case the missing heights of the plants do not matter (Steuer et al., 1986). Overall, the visualization procedure can be divided into three fundamental steps. In the first step, the 3D digital data of the terrain were obtained from the shape file from the ArcGIS®. In the second step, a conversion program was used to convert the data on the terrain and vegetation in the forest land-use into virtual reality modeling language (LRML) format. In the final step, modifications to alignments and other changes including transformation and orientation, if necessary, were made the 3D image of the land-use is generated on the computer. Particular software belonging to the ArcGIS® family of software, ArcScene was used to perform this conversion. The appropriate land-use shapefile (.shp) was imported within the ArcScene environment, and it was exported using the “Export” functionality into 3D (.wrl format). This could be then used in the virtual reality worlds along with the buildings and other infrastructure components to generate the 3D land use scenario. Shown below (Figures 2 and 3) are the visualizations of two Pareto-optimal plans selected for visualization. From the figures shown here, the two plans can be compared in a very systematic manner. Evaluating them the point of view of the objectives considered in this study, in plan No.1 (Figure 2), it can be seen that the green spaces are properly distributed around the housing areas. The green spaces are evenly distributed so that the residents from the high-density residential area can access the green space without much commuting. On the other hand, in the second plan (Figure 3), it can be seen that there are three residential regions (two high-density and one low-density) competing for meager green space which is also not evenly distributed. It should be noted that both these are Paretooptimal plans with very high fitness values. They satisfy the constraints that the green spaces must be more than the threshold values. However, it is not necessary, that the green spaces must be distributed evenly all over the region. Hence, we can see that there are a lot of practical constraints, all of which may not be included in the GA, but can be observed using visualization plans. Consequently, plan No.1 can be selected for implementation. Thus, the usefulness of visualization in evaluating CPOPs (Competing Pareto-optimal plans) is evident. Moreover, using various LODs and studying the same scene from multiple view-

Figure 2. Pareto-optimal plan No.1

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Figure 3. Pareto-optimal plan No.2

points, numerous aspects that might not otherwise be obvious can be found. Subjective features such as scene quality can be studied in a more reliable manner. The same scene can be viewed with varying levels of detail.

For instance, when viewing from a distance, the finer details are not obvious. This notion can be used to efficiently model the scene. Based on the viewer’s position in a scene, the objects can be rendered accordingly (Figure 4).

Figure 4. Using 3D Visualization to study the same scene from varying


LOD .

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Conclusions

Urban planning problems are mutually inter-related and trying to solve them in isolation will never lead to a permanent or long-lasting solution. One of the foremost steps in solving these problems is to get a bird’s eye view of the problem scenario as a whole, while simultaneously concentrating on the minutiae of the constituent elements. This is a mammoth task, considering the innumerable components and factors that constitute each one of the aforementioned problems. In this study, land-use planning is formulated as a multi-objective optimization problem, which is solved using genetic algorithms. The results, instead of being merely being presented as a Pareto set with a pool of candidate solutions, are evaluated using a visualization tool. This helps in the process of informed decision-making, thereby facilitating the selection of the optimum plan by planners, decision-makers, and administrators. Also, with PPGIS (Public Participation GIS) becoming the norm of the day, such visualizations can be hosted online and the feedback of the general public, who are the ultimate consumers, can be obtained. Such visual representations are excellent tools to overcome the barriers of scale and those imposed by viewpoints. In other words, the same scene can be studied at various viewpoints which may not be accessible from the real-world. Future studies can focus on the aspects of visualization such as real-time scene rendering for large scale visualizations and automatic scene generation from Pareto plans.

Acknowledgments

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) under discovery Grant No. 312166-05, the Hong Kong Research Grants Council (RGC) under Grant No. CUHK 444107, and the Direct Grant of the Chinese University of Hong Kong are gratefully acknowledged.

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