case, proposing a bi-objective optimization heuristic of functional configuration based on the relevant objective functions from the validation study. We end with a discussion and conclusion in Sections \[sec\_discussion\] and \[sec\_conclusion\].

Model description {#sec_model}
=================

Agents and rules
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The world is represented by a square lattice $(L_{i,j})_{1\leq i,j\leq N}$ composed of cells that are empty or occupied (Fig. \[fig\_lattice\]). This is denoted by a function $\delta(i,j,t)\in\{0,1\}$, where time $t$ follows an iterative sequence $t\in\mathbb{T} = \tau\mathbb{N} = \{0, \tau, 2\tau, ...\}$ [@golden2012modeling] with a regular time step $\tau$. Another evolving structure is laid out on top of the lattice: a Euclidean network $G(t)=(V(t),E(t))$ whose vertices $V$ are a finite subset of the world and edges $E$ (its agents) represent *roads*. In the beginning, the lattice is empty: $\delta(i,j,0)=0$, and the network is either initialized randomly (e.g. uniformly) or set to a user-specified configuration $G(0)=(V_0,E_0)$. In order to translate functional mechanisms into the growth of a city, we assume that the initial vertices include a subset formed by *city centers*, $C_0\subset V_0$, which have integer *activities*, denoted by $a:C_0\rightarrow\{1,\ldots,a_{\max}\}$.

To characterize the urban structures emerging in this world, we define in general a set of $k$ functions of the lattice, 