Integrated framework of system dynamics and meta-heuristic for multi-objective land use planning problem

Abstract

Land use optimization as a resource allocation problem can be defined as the process of assigning different land uses to a region. Sustainable development also involves the exploitation of environmental resources, investment orientation, technology development, and industrial changes in a coordinated form. This paper studies the multi-objective sustainable land use planning problem and proposes an integrated framework, including simulation, forecasting, and optimization approaches for this problem. Land use optimization, a multifaceted process, requires complex decisions, including selection of land uses, forecasting land use allocation percentage, and assigning locations to land uses. The land use allocation percentage in the selected horizons is simulated and predicted by designing a System Dynamics (SD) model based on socio-economic variables. Furthermore, land use assignment is accomplished with a multi-objective integer programming model that is solved using augmented ε-constraint and non-dominated sorting genetic algorithm II (NSGA-II) methods. According to the results of the SD model, land use changes depend on population growth rate and labor productivity variables. Among the possible scenarios, a scenario focusing more on sustainable planning is chosen and the forecasting results of this scenario are used for optimal land use allocation. The computational results show that the augmented ε-constraint method cannot solve this problem even for medium sizes. The NSGA-II method not only solves the problem at large sizes over a reasonable time, but also generates good-quality solutions. NSGA-II showed better performance in metrics, including number of non-dominated Pareto solutions (NNPS), mean ideal distance (MID), and dispersion metric (DM). Integrated framework is implemented to allocate four types of land uses consisting of residential, commercial, industrial, and agricultural to a given region with 900 cells.

Appendix 1: Equations in SD

Other equations are used in the proposed system dynamics are as follows:

$$ {\text{PO}} = {\text{POP}} \times {\text{POR}} $$

(24)

$$ {\text{AP}} = {\text{EAR}} \times {\text{PO}} $$

(25)

$$ {\text{EP}} = {\text{EPR}} \times {\text{AP}} $$

(26)

$$ J = {\text{EP}} = {\text{WF}} $$

(27)

$$ {\text{NP}} = {\text{NPC}} \times {\text{GDP}} $$

(28)

$$ {\text{JC}} = {\text{NP}} + {\text{WF}} $$

(29)

$$ {\text{PG}} = ({\text{PGR}} + {\text{PC}}) \times {\text{POP}} $$

(30)

$$ {\text{IL}} = {\text{RLU}} + {\text{ILU}} + {\text{CLU}} + {\text{FLU}} $$

(31)

$$ {\text{LC}} = {\text{IL/DLpP}} $$

(32)

$$ {\text{NF}} = L{\text{/IL}} $$

(33)

$$ {\text{LU}} = {\text{NF}} \times L $$

(34)

$$ {\text{IMG}} = {\text{Max}}\left( {{\text{JC}},\,{\text{LC}}} \right) - {\text{POP}} $$

(35)

Equation (35) is used to formulate the phenomenon of migration. This equation is based on the assumption that immigrating to city occurs when there is one of two conditions: (1) there is a vacancy for population and (2) there is vacancy for employment. On this basis, if the maximum available capacity for population and employment is greater than the current population, immigration to the city will occur. The negative value of the PC parameter means that (1) the city does not have the capacity of the current population; and (2) the city does not have the capacity of employment for the current population. Accordingly, a number of people are migrating from the city.