*6.1. Scenario 1*

The first step of the framework involves partitioning the region into a number of zonal clusters. The k-means clustering algorithm of Figure 3 is utilised; the resulting zonal cluster is displayed in Figure 6A. A total of eight zonal clusters within the region have been identified. The next step involves assigning a land use to each zonal cluster. This enables the allocation of zones for positioning different building types in. This is achieved via the assignment model represented by Equations (3)–(5). It is desired to place four land-use zone types, namely three residential zones, two mixed-use zones, two commercial zones and one industrial zone. The resulting zones assigned are displayed in Figure 7B and Table 1. The building types desired to be placed, along with the associated maximum noise generated and noise sensitivity thresholds for each building, are displayed in Table 2.

**Figure 7.** (**A**) Resulting zonal cluster where location nodes (in yellow) are grouped to the zone clusters (square); (**B**) Pattern matching between zones and allocated locations.


**Table 1.** Land-use distribution.

**Table 2.** Building type and associated noise characteristics.


The construction cost associated with each node is as follows: for nodes 1, 5, 7, 10, 17 and 18, construction cost is given as \$503,124; for nodes 2, 3, 6, 13, 14, 15 and 19, construction cost is \$209,353; and for nodes 4, 8, 9, 11, 12 and 16, the construction cost is given as \$100,111.

The third stage involves an implementation of the strategic decision-support model for allocating buildings and determining the traffic assignment and any investments required in the connecting infrastructure of the region. Since the region is new, no existing network is present. A sample network shape utilised to outline the expected linking structure between the eight zones identified is depicted in Figure 8.

**Figure 8.** Transportation network of case example, where the numbered squares are the zones, and the arrows indicated the travel networks between the zones.

Lexicographic Optimisation Results

Let:

$$B\_1 = \min\_z \sum\_{t \in T} \sum\_{f \in F\_l} \sum\_{s \in P\_l} z\_{fs} \overline{C\_s} \tag{45}$$

$$B\_2 = \min\_z \sum\_{t \in T} \sum\_{f \in F\_l} \sum\_{s \in P\_l} \sum\_{r \in P} z\_{fs} M\_{rs} \tag{46}$$

$$B\_3 = \min\_{\mathbf{x}} \sum\_{(i,j)\in L^R} \sum\_{m\in \Gamma} \varepsilon\_m d\_{ij} \mathbf{x}\_{ij} t\_{ij} \left(\mathbf{x}\_{ij}\right) \tag{47}$$

The preference assumed over the objective functions is given as follows: *B*<sup>3</sup> *B*<sup>2</sup> *B*1, where the relationship *a b* highlights the preferential ranking of *a* in comparison to *b*. In the first stage, the carbon emissions on the transport network, *B*3, are minimised (via minimising the total system travel time of the network). The emission factors associated with each transportation mode analysed in the smart city are given in Table 3, as obtained from [53]. Preference in the second stage is given to minimising the total sum of noise pollution within the region: *B*2. In the final stage of the lexicographic approach, the construction cost involved with constructing buildings at each location is minimised. Through applications of the lexicographic algorithm, the lexicographic Pareto optimal solutions obtained are displayed in Table 4. As is displayed, in the initial run, carbon emissions are minimised, while the rest of the objectives are evaluated (without being optimised yet). In the second lexicographic run, the carbon emissions remain at their minimum level, while noise pollution decreases by 45% and construction costs increase by 21%, in comparison to the first stage of the lexicographic run. In the third lexicographic run, both carbon emissions and noise pollution stay at their minimum levels (due to the constrained optimisation), while construction cost cannot be minimised further without violating the constraints placed on the carbon emissions and noise pollution functions.


**Table 3.** Emission factors for each transportation mode analysed.


**Table 4.** Lexicographic optimisation with the order *B*<sup>3</sup> *B*<sup>2</sup> *B*<sup>1</sup> .

#### *6.2. Scenario 2*

In the second set of experiments, the case example of Figure 5 is slightly modified to allow for an extensive computational analysis of the model developed. A total of 350 random instances are generated for examining the behaviour of the bilevel model. The size of the networks considered starts at 10 nodes and is incremented by 5 nodes until 40 nodes are reached. Travel distances are assumed to be proportional to the Euclidian distance between the zones, while buildings to be placed are assumed to be 40–90% of the number of nodes considered in the instance generated, in order to generate an encompassing set of scenarios. Figure 9 displays the average computational time required to yield an optimum solution, along with the percentage of instances solved to optimality within a 1000 s time limit. As can be seen, beyond 20 nodes, as the instance size increases, the average computation time increases and the percentage of instances solved to optimality decreases.

#### *6.3. Comparison with Other Metaheuristics*

In this section, common optimisation algorithm approaches adopted in the literature, including genetic algorithms (GA) [54] and particle swarm optimisation (PSO) [55], are contrasted with the proposed exact approach. Based on rigorous tests, the population size, mutation rate and crossover rate of 250, 0.05 and 0.7, respectively, were adopted in the GA, whereas for PSO, population size was set as 250, while acceleration constant and weight parameters were set as 3 and 0.4, respectively. As can be seen from Figure 10A, the solving time of the GA is better than both PSO and the proposed exact approach, though solution accuracy is better in the proposed exact approach. The results of Figure 10B highlight that even though the metaheuristic approaches can be faster in producing a

solution, the solution quality of the exact approach will always be better. In addition, for the case considered herein, the fastest approach to generate a solution is obtained using a GA, though PSO can be slightly more accurate in terms of solution quality in contrast to the GA.

**Figure 9.** Box plot highlighting performance of the model proposed as instance size increases.

**Figure 10.** (**A**) Solving time and (**B**) percentage (%) optimality of solution quality comparison between the genetic algorithm (GA), particle swarm optimisation (PSO) and the exact approach.

#### *6.4. Multi-objective Variant*

A pure Pareto-based formulation is applied, which relies on optimising all the objective functions simultaneously. The solution strategy adopted herein is referred to as the -constraint method, which relies on optimising a single objective function while accounting for the remaining objectives using constraints. A parametric variation of the right-hand side (RHS) of the constrained functions then ensues to generate the efficient Pareto points on the frontier. The reader is referred to [56] for additional information on the implementation of the -constraint method adopted.

The results obtained on application of the -constraint method to the case study presented above are displayed in Figure 11A–C. In addition, Table 5 presents the optimised values of extreme points used to plot the tradeoff curve. In Figure 11A, a clear tradeoff exists between minimising noise and minimising carbon-equivalent emissions. In Figure 11B, a tradeoff is shown between minimising layout cost and minimising noise, while Figure 11C displays the tradeoff between minimising layout cost and minimising carbon-equivalent emissions.

**Figure 11.** (**A**) Pareto curve highlighting the trade-off between noise minimisation and carbon-equivalent emission minimisation; (**B**) Pareto curve highlighting the trade-off between noise minimisation and layout cost minimisation; (**C**) Pareto curve highlighting the trade-off between layout cost minimisation and carbon-equivalent emission minimisation.

**Table 5.** Payoff table between all objective functions considered.


The importance of the Pareto curves produced lies in the fact that the decision-maker is now able to visualise the magnitude of the impact associated with each efficient solution produced.

#### *6.5. Discussion and Insight*

In comparison to some of the approaches in the literature, the proposed framework targets key strategic operational research problems that are encountered in the urban design of smart cities. For instance, in [57], the authors consider using integer optimisation to maximise floor area while accounting for sunlight in urban design. A mixed integer program was developed in [58] for designing building interiors. Integer programming was utilised in [59] for urban street network design. As can be noticed, there is a lack of focus on optimisation problems encountered in the strategic design of

urban areas, where traffic and building layout are both integrated. The proposed approach in this article tackles this gap by proposing a mathematical optimisation model which integrates the latter. In addition, multiple objectives are rarely adopted in urban design optimisation [12]. As a result, through the proposed framework herein using multi-objective optimisation, the decision-maker can visualise the different tradeoffs that result when incorporating all objective functions considered.

#### **7. Conclusions**

Globally, we have witnessed a shift towards developing smart cities to deal with the challenges of rising population and urbanisation rates, along with the necessity of ensuring sustainable development. It seems therefore necessary to incorporate intelligent and robust urban planning frameworks that can simultaneously target transport and land-use considerations in smart cities.

In this paper, a framework, based on mathematical optimisation for the strategic planning of zoning, facility location and transport network design in smart cities was proposed. The framework combines some strategic operational research problems, including the clustering problem, the assignment problem, the facility location problem and the network design problem, in a systematic fashion. An algorithm based on k-means clustering is applied to divide a given region into zones, and an assignment problem is then solved to determine the land-use types within the region. The final stage of the framework involves solving a bilevel model that accounts for the hierarchical decision making of urban planners and travel network users. The proposed bilevel model considers the location decisions of buildings within a smart city setting, along with the investment decisions related to expansion of the underling transportation network. Multiple objective functions were formulated to target the triple bottom-line of sustainability in order to ensure a sustainable urban layout of the smart city. In particular, as a social factor, noise pollution in the region was minimised; as an environmental factor, carbon-equivalent emissions on the transportation network were minimised; and as an economic factor, the construction cost of buildings was minimised. A solution approach based on converting the bilevel model into a single-level model was outlined, along with a linearization procedure. A lexicographic optimisation approach was utilised to handle the multi-objective nature of the developed model. In addition, the -constraint method, which generates the Pareto front when considering all objective functions involved, was also adopted.

The proposed model was applied on a realistic case example for the design of the urban structure of a smart city. A lexicographic approach highlighted variations in cost of up to 52% when carbon emissions are given first preference by decision-makers. The -constraint method highlighted that a trade-off cost of up to 471% can result when simultaneously optimising the objective functions involved. In order to examine the computational performance of the proposed approach, a total of 350 instances were solved. Results demonstrate that solving time increased rapidly once the transportation network size of the instance generated exceeded 30 nodes. On average, the proposed model was able to solve 72% of the proposed instances within the imposed 1000 s time limit.

A comparison was also conducted between the proposed exact approach and metaheuristic solving algorithms including a GA and PSO. Results indicated that the GA was the fastest in terms of solution time, although solution accuracy was on average reduced by 68% compared to the results obtained when utilising the exact approach.

The proposed framework integrates several key operational research problems that are representative of certain aspects of the urban design problem involved in smart cities. However, several limitations are associated with the proposed approach. First, a deeper investigation into all facets of urban design that are associated with smart cities is lacking, since only several operational research problems are tackled in the framework developed. Second, the incorporation of tactic decision-making problems, such as vehicle routing, was missing from the proposed framework. Future works will thus look at these two areas.

**Author Contributions:** Conceptualization, A.WA.H. and E.G.V.; Data curation, A.WA.H.; Formal analysis, A.WA.H; Funding acquisition, E.G.V. and A.H.; Investigation, A.WA.H.; Methodology, A.WA.H, A.A., and A.H.; Supervision, E.G.V. and A.H.; Validation, A.H.; Writing—original draft, A.WA.H and A.A.

**Funding:** Authors would like to acknowledge the Brazilian Government for their support by the CNPq (National Council for Scientific and Technological Development)

**Conflicts of Interest:** The authors declare no conflict of interest.
