A grammar-based optimization approach for walkable urban fabrics considering pedestrian accessibility and infrastructure cost

Research framework

The overall research framework combines shape grammars and multi-objective optimization in a generative environment for urban fabrics addressing selected trade-offs. We hypothesize that this approach can provide more dynamic and efficient solution-finding and decision-making toward climate-resilient cities than conventional methods. While a multi-objective process does not necessarily find a definitive solution that must be directly implemented, as urban design involves many different factors, a computational process driven by several key design goals can stimulate a greater understanding of the design problem, thus supporting deisgners.

Shape grammars—Chicago Urban Grammar

Shape grammars rely on implementing transformation rules that apply recursively to an initial shape to generate a set of designs (design language). According to Stiny (1980), shape grammars consists of applying simple visual rules to transform one shape into another, requiring an initial state, a set of instructions, and a termination condition. Shape grammars allow one to either describe or generate designs in the same language, providing the means to elaborate complex designs or create new design languages. We test the conjecture that using shape grammars in an optimization framework improves the solution-finding process by filtering the design space of topological variations toward meaningful solutions that belong to existing design languages.

The application of shape grammars in urban design is still limited compared to architecture, although a body of related literature exists. Teeling (1996) presented the first urban grammar for describing a neighborhood in Friedrichshafen, a German city, while Mayall and Hall (2005) proposed a grammar to define landscape object types. Duarte et al. (2007) developed an urban grammar for the ancient fabric of the complex urban form of the Marrakesh medina, and Duarte and Beirão (2011) explored shape grammars to support flexible urban planning. Despite previous applications of shape grammars in urban design, our work is, to the best of our knowledge, among the first to combine the synthetic capability of shape grammars with multi-criteria optimization to find solutions with improved urban performance.

To test this framework, Chicago’s urban fabric was encoded into a shape grammar (Figure 1), which was then connected to a multi-objective optimization algorithm to push generations of urban fabrics toward optimal performance within the language defined by the grammar. In brief, the first set of rules (Rules 1 to 8) place two main perpendicular axes (av = main vertical axis, ah = main horizontal axis) and create a square grid of half-mile (approximately 800 m). These axes correspond to the city’s major roads and determine admissible subdivision operations, resulting in typical blocks with 330 by 660 feet (100 m × 200 m). The grammar can generate urban arrangements that vary from eight east-west blocks by four north-south blocks to four east-west blocks by eight north-south blocks, and the possible combinations therein. The second set of rules (Rules 10–17) are applied to the typical blocks, altering the positioning of alleys. These rules define different parcels, which, can in turn be divided into plots. Different applications of these rules generate a wide variety of urban fabrics within the Chicago language, each with different distances between destinations in the grid, as depicted in Figure 1. The generated fabrics can then be assessed using the quantitative urban metrics described in the next section.OPEN IN VIEWER

Fitness functions for fabric design: Physical Proximity Index and estimated infrastructure cost

The framework proposed here uses two criteria to drive optimization: walkability and infrastructure cost. The concept of walkability is challenging to define or operationalize, and it depends on many factors that have been widely discussed (Dovey and Pafka, 2020; Ewing and Cervero, 2010; Forsyth et al., 2008; Gehl, 2010; Pushkarev and Zupan, 1976). Nevertheless, it is broadly accepted that pedestrian accessibility, understood here as proximity to amenities, has substantial implications for the walkability of an urban area. Thus, although it is not the only metric for measuring walkability, pedestrian accessibility is one of its most addressed urban features since the likelihood of walking trips decreases with greater distances (Sevtsuk et al., 2016).

Accordingly, a considerable body of research has estimated walkability by measuring distances to amenities, focusing on grid design and amenities positioning. Brewster et al. (2009) assessed walkability in urban developments using Walkscore (Walkscore, 2020), a distance-based indicator. Carr et al., (2011) validated WalkScore for estimating access to walkable amenities, while Nourian et al. (2015) proposed accessibility measures based on an “Easiest Path” algorithm, developing a toolkit that provides actual temporal distances between locations. Lima et al., (2016) explored algorithmic systems for generating and evaluating urban morphologies, setting the distance to amenities as a criterion. In a similar context, Dogan et al. (2020) presented a computational design toolkit to model active transportation and evaluate pedestrian accessibility to amenities and public transport, while Sevtsuk et al. (2016) assessed the pedestrian accessibility of different grid layouts. Most recently, Koohsari et al. (2021) concluded that WalkScore was positively correlated with several perceived walkable environmental attributes, and there was a medium correlation between WalkScore and overall perceived walkability.

In addition, several authors address walkability assessment through a broader perspective, taking other features into consideration. For instance, Cervero and Kockelman (1997) address density, diversity, and design and Dovey and Pafka (2020) advocate that density, mix, and pedestrian access are key factors for understanding and measuring walkability. More recently, Otsuka et al. (2021) developed an adapted version of WalkScore, including traffic noise, pedestrian casualties, road speed limits, and air quality as metrics. However, considering this preliminary study’s focus on observing the usefulness of a grammar-based approach for managing trade-offs at an urban scale, adopting a single metric (pedestrian accessibility) to estimate walkability allowed us to explore a bidimensional trade-off, providing simplicity and accuracy to our analyses. It is understood that in many design contexts, an automated multi-objective approach for several prioritized objectives would provide only a starting point for synthesizing all competing concerns.

As it relates to sustainability, adopting low carbon transportation modes such as walking and cycling is recognized as crucial in carbon demand reduction strategies (Maibach et al. 2009; Nazelle et al., 2010; Lovelace et al., 2011; Rabl and Audrey de Nazelle, 2012). In this regard, Yamagata et al. (2019) state that walkability is a key performance indicator for achieving low carbon cities, as it reduces the number of cars without losing convenience and comfort. Nevertheless, efforts toward more connected cities have often relied on allowing people to move faster (using motorized transportation) around ever-expanding urban fabrics, rather than bringing urban services closer.

This paper builds on this research thread by using the Physical Proximity Calculator, a CityMetrics tool (Lima, 2017), to assess and optimize urban fabrics walkability through pedestrian accessibility. The Physical Proximity Calculator (PPC) computes the Physical Proximity Index (PPI) on scale of 0–1 by calculating the smallest distance between two or more points of interest, considering the street network and relationship between distance and likelihood of walking instead of using other transportation. For instance, a 400 m (5 min walk) or less distance between two locations corresponds to a Physical Proximity Index (PPI) of 1. The index decreases as the distance approaches 1600 m (20 min walk) and is 0 when the distance becomes greater than 1600 m. In our experiments, which aim to estimate the pedestrian accessibility of a given fabric, we set the PPC to calculate the PPIs between each parcel’s corner to the boundary corners of the neighborhood.

In an orthogonal grid system like Chicago, the average distance between all parcels corners and the grid corners is always the same, no matter the size of the urban blocks. However, since PPI does not use distances on a linear scale above and below the stated thresholds, the average distance to the corners and the average PPI of the entire neighborhood are slightly different. Maximizing the PPI of a neighborhood means looking for arrangements that avoid distances larger than 1600 m (PPI = 0) while not further prioritizing distances smaller than 400 m (PPI = 1). Therefore, maximizing PPI as a fitness function means obtaining more homogeneous proximity values, in this case, distances to the grid’s corners within a neighborhood and providing more balanced proximity values to more blocks and people. Figure 2 illustrates the differences between each of these quantities. For instance, fabric 1 and fabric 5 show opposite PPI and standard deviation distances, meaning that the former is less balanced (less homogeneous distances to the boundary) than the latter. Thus, the main question regarding walkability in this study is where should certain rules be applied to promote more proximity-balanced fabrics?OPEN IN VIEWER

Moreover, for Chicago, the boundary corners serve as mass transit stops for buses, which tend to run along the main N-S and E-W streets, as well as elevated or subway trains in specific neighborhoods. Thus, the algorithm expresses the pedestrian accessibility of a given parcel by calculating the average physical proximity indexes of its corners. When considered an entire district, these calculations provide information about the whole urban fabric.

In theory, pedestrian accessibility to destinations should increase as street networks get denser, and the possibility of connecting basic urban needs through shorter paths improves. In this regard, Zhao et al. (2019) concluded that urban areas with orthogonal street grids and high street density have good accessibility. However, as estimated by street length, infrastructure cost proportionally increases with the density of street networks, outlining a trade-off to be addressed toward less CO₂ emitting and more climate-resilient cities.

Multi-objective optimization: managing pedestrian accessibility and infrastructure cost trade-off

Multi-objective optimization (MOO) is a computational methodology that supports decision-making in the presence of trade-offs between two or more conflicting objectives. It enables the exploration of complex search spaces while managing and prioritizing multiple objectives (Brown, 2016). While it has been used extensively in aerospace engineering, mechanical engineering, and economics for decades, forms of multi-objective optimization have recently become more common in architecture and related design fields (Brown, 2019; Cichocka et al., 2017; Coello and Romero, 2003; Evins et al., 2012; Marler and Arora, 2004).

For a meaningful multi-objective optimization problem, there is no single solution that simultaneously optimizes all objective functions. In this context, optimal solutions occur when none of the objective functions can be enriched without worsening others. This kind of solution is called Pareto optimal or non-dominated, and without additional preference information or post-Pareto analysis, all Pareto optimal solutions in an optimization problem are considered to be equally viable. The set of all Pareto solutions (often presented graphically) is called the Pareto frontier, also known as the Pareto front or Pareto set. While a theoretical Pareto front exists for a design problem, optimization algorithms attempt to “find” the front through increasingly accurate approximations.

At an urban design level, Navarro-Mateu et al. (2018) and Makki et al. (2019) are among the firsts to implement MOO in the generation of urban fabrics, shedding some light on addressing conflicting objectives at this scale. However, neither work considers a grammar-based approach or walkability criteria. Lima et al. (2021) have also addressed the use of MOO for walkable urban fabrics generation, although without employing a grammar-based framework, and Feng and Peponis (2021) analyze urban grids from a cost perspective, using syntactic measures.

Although pedestrian accessibility and street lengths are not always in rivalry, Sevtsuk et al. (2016) conclude that when various dimensions for plot frontage and depth, block length, and street width are combined, smaller blocks (denser street networks) tend to generate higher pedestrian accessibility than larger blocks. Thus, we address the pedestrian accessibility versus infrastructure cost trade-off as a case study to verify the utility of a grammar-based multi-objective optimization approach. The goal is to better understand this issue and evaluate more efficient solution-finding strategies. Optimization is thus explored here as a tool for discovering potentially improved designs or even directions for further modification, rather than a deterministic approach for selecting a single, perfect solution.

Methodology

We implemented two case studies to explore our approach and generate optimal alternative fabrics for the Chicago area using a Rhinoceros/Grasshopper software environment. The aim was to find solutions that maximized the Physical Proximity Index while minimizing the street network length, using the proposed Chicago grammar.

The next step was to translate the grammar into a parametric design environment. Granadeiro et al. (2013b) note several strategies for “genetification” of shape grammars into parametric systems for optimization while still encoding all possible solutions and allowing crossover and mutation to operate (Geyer, 2008; Granadeiro et al., 2013a; Mckay and Pennington, 2006; Schnier and Gero, 1998). In this research, we created input variables based on different ID numbers, each corresponding to a Chicago rule. Additional input values were set to apply the rules with different rotations. To establish a meaningful variable structure for the optimization algorithm, we have sorted the ID numbers in ascending order according to the total street length provided by a rule. For instance, Rule 16 was assigned the highest ID, while Rule 12 was assigned the lowest. Thus, inputting higher numbers means increasing the street network density and the infrastructure cost, while inputting lower numbers means the opposite.

Considering the current availability of multi-objective optimization (MOO) tools in Grasshopper, four state-of-the-art MOO add-ons were evaluated for this research: Octopus, a tool that employs Strength Pareto Evolutionary Algorithm 2 (SPEA-2) and fast hypervolume-based many-objective optimization algorithm (HypE); Opossum, that uses Non-Dominated Sorting Genetic Algorithm II (NSGA-II) (Deb et al., 2000) and Particle Swarm algorithms; Design Space Exploration (Brown et al., 2020), which uses NSGA-II; and Wallacei X (Makki et al., 2020) that also employs NSGA-II.

Among these possibilities, we opted for NSGA-II because it prioritizes the diversity of solutions by using a crowding distance mechanism, emphasizing non-dominated solutions; requires lower computational costs; and can find a much better spread of solutions and better convergence near the Pareto front compared to SPEA (Deb et al., 2000). Although the NSGA-II algorithm is commonly used with continuous input variables, its performance has also been tested with discrete variables (Anagnostopoulos and Mamanis, 2010; Wu et al., 2017). For instance, NSGA-II has been used on problems with discrete variables to optimize power converters (Visairo et al., 2012), mechatronic systems (El-Kribi et al., 2013), and in a typical building optimization problem, improving solution quality and convergence speed (Brownlee and Wright, 2015).

Following these examples, our choice for NSGA-II relies on four primary aspects: avoiding dependence on the initial solution to convergence toward optimal solutions, decreasing the time required to run the algorithm, avoiding being stuck with suboptimal solutions, and the existence of a Rhinoceros/Grasshopper tool to implement optimization procedures. Thus, Wallacei X was the chosen tool because it uses NSGA-II in a way that was compatible with our implementation of the shape grammars in Grasshopper, which relies on the gene pool component, and its data visualization interface also provided more freedom of analysis.

Study area

McKinley Park, a southwest community of Chicago, was the neighborhood selected as study area. It is a dense suburban zone with 14,484 residents, good walkability, and good land-use diversity (Niche, 2021). Our study area consisted of an 800 × 800 m grid portion with almost all blocks aligned north-south and the following features: 7400 m of alleys, an average Physical Proximity Index of 0.645, a total of 453 street intersections, and an average parcel area of 7619 m² (Figure 3, above).OPEN IN VIEWER

Case study 1

The first case study applied Chicago’s urban rules in a restricted manner, with rules applied to create combinations of either east-west or north-south rows of typical blocks (100 m × 200 m). This repetition of block type emulates a situation that often occurs in the city (Figure 3, bottom-left). This case study comprised modeling stages 1–3 and encompassed a total of eight genes and 48 values, resulting in a design space of 1e6 solutions.

Case study 2

The second case study applied Chicago’s urban rules flexibly, meaning that each block could have different alley layouts, thereby expanding block arrangements configurations (Figure 3, bottom-right). This case study also comprised stages 1–3 and addressed 64 genes and 352 values, resulting in a design space of 2.2e43 solutions. While this can lead to considerable irregularity, it can generate significantly more diverse designs, potentially increasing the likelihood of obtaining designs with better performance.