Explain the optimal pattern in the contracts of public private Participation construction, exploitation and transfer (BOT) Applied to Contracts Theory

In recent decade in developing countries, lack of government budget or lack of access to modern technology, persuade governments to attract private sector participation in the economy. One of the most common methods is Public-Private Partnership agreements. The real implementation of this type of partnership needs to set contracts that satisfies preferences of both parties. This research aims to solve this problem using the solutions available in the Contracts Therory Knowledge. Theoretical modeling with analyzing public-private partnership model, provide an optimal model for BOT contract. We use library method to explain the basic contract and mathematical modeling  by MATLAB software with Particle Swarm Optimization to specify the parameters of utility functions and to provide optimal contract.  The simulation results for an optimal contract were calculated using the supposed parameters (life time, incom, costs, future incoms discount rate, salvage value of project costs) 38 years (project utilization time), 78% (principal participation after transfer time), 45% (principal participation during the operation), 7% (riskes to the principal). The results showed that  these parameters are fully matched with the theoretical properties of the model and the principals utility is maximum beside the agent participation.