A Hybrid Method for Constrained Optimization of the Spatial Arrangement of Urban Land Uses to Reduce the Inconsistency

Considering to the compatibility of the urban land uses is one of the important issues in optimization of their spatial arrangement. The most common way of mitigating the negative effects of conflicting land uses on each other is to maintain a certain distance between them. Due to the need to investigate a high amount of information for optimization of the different land uses arrangement and limitations of the precise methods, researchers have focused on the meta-heuristic methods (e.g. genetic algorithm) to solve such problems. Furthermore, because of the need to notice multiple objectives and criteria, multi-objective optimization methods have been considered. To ensure adequate separation distances between incompatible land uses, they can be entered as constraints to these types of optimization methods.
In this research, a hybrid method is proposed to meet distance constraints in an optimization problem for locating multiple land uses. For this purpose, a multi-objective genetic algorithm was used to maximize the location suitability and compatibility of the land uses. Simulated Annealing (SA) method was applied to repair infeasible individuals and meet distance constraints in related solutions. SA is a probabilistic technique for approximating the global optimum of a given function. Simulated annealing starts with an initial solution. A neighboring solution is then selected. If the neighbor solution is better than the current solution, is considered as the current solution. Otherwise, the candidate solution, is accepted as the current solution based on the acceptance probability to escape local optima.
In this study, the solutions are generated by the genetic algorithm. Each gene of the chromosome represents the location of a candidate site. After generating the population, the distance constraints are checked and infeasible solutions are determined. A solution to which all the distance constraints are met is the feasible solution, otherwise the solution is infeasible. Repairing the infeasible chromosomes were done as follows:• Identify the gene (s) which makes the chromosome infeasible
• Identify the neighbors of that gene (s) according to the distances between genes
• Create new solutions using neighbors
• Calculate the rate violations of new solution
• If all new solutions are infeasible, the solution will be replaced by the solution by minimum violation.
• If only one feasible solution is generated, the initial solution will be replaced by it.
• If more than one feasible solutions are generated, the values of the objective functions are
calculated for feasible solutions. Non-dominated solutions are identified. Among them, the solution which has lesser difference with the initial solution, is selected.
The results of the research show that the proposed method can be effective in repairing infeasible individuals and converting them to feasible ones, with regard to distance constraints. In this method, for each infeasible individual, several alternatives are generated, from which the closest feasible solution to the original solution, with the better objective function values, can be selected.
Increasing the number of neighbors for each site in SA will make it easier to get feasible solutions.
By the way, by entering the farther neighbors, there may be more distance between the initial solution and the new solution that replaces it.