Access to other people and to labor are essential factors for economic prosperity in an area. The face-to-face interactions trigger knowledge spillovers which are an important component of economic growth. [1]. Therefore, it is important to provide a sufficient level for so called «social interaction potential».[1] Social interaction potential can be measured as a number of people accessed from a specific zone at a reasonable time range and is suggested to be a tool in shaping urban policy. [2] Nowadays many areas have a spatial shape such that accessing other people for those living outside densely populated centers often requires longer travel distance. This implies higher travel time or else higher travel speed. Speed in its turn is constrained by negative impacts: pollution, noise and accidents. It is demonstrated that there is close linear relationship between CO2 emission and vehicle speed if constant.[3] So the question is, how to reallocate residences in a sustainable way in order to provide the residents with a sufficient social interaction potential, while keeping low density and at a reasonable travel speed.
Thus, here we present a model which optimizes (re)allocation of residences and jobs in order to provide a sufficient social interaction potential, job accessibility and keep speed the lowest possible. This is the dynamic linear model with the minimization objective function, constraints which provide the minimum of social interaction potential, but at the same time low density. There is also a constraint controlling the spatial change, as we want to restrict the number of reallocations to be done. Besides, as it implies long-term strategic decision-making, the model foresees break-down of the decision process into the sequence of decision steps over time.
In this presentation, we will introduce the context and objectives of the study. Next, we explain the problem and present the mathematical formulation of the associated combinatorial optimization problem. Then, we present different numerical results as well as urban configurations corresponding to the diverse objectives.

**Mots clés : ** dynamic optimization, allocation, SIP, urban, speed, sustainable