Differential Evolution Algorithms For Resource Investment Problems

It is necessary to forecast the feasibility of the project. The project scheduling problem is to estimate the scheme in the prediction state. The project scheduling problem belongs to complex optimization problems. It has two main problems which are the resource constrained project scheduling problems and resource investment project scheduling problems. The resource constrained project scheduling problems aim to minimize the makespan subject to a constant resource availability; the resource investment project scheduling problems aim to minimize the project cost without exceeding the deadline.My research focused on the resource investment project scheduling problems. The cost of the project is caused by the usage of resource, such as manpower and material. In order to make the model of the problem closer to the practical problem that need to continually complicate the model of the problem. The research is to deepen a single objective problem to a multi-objective problem.The problem model of the first work is the resource investment project scheduling problem with tardiness, which is a single objective problem to minimize the project cost when the project completes with delay. The final result is a scheme which has suitable makespan and less project cost by introducing the delay penalty. The original model is improved by not completely limited the fnish time of the project. We use the differential evolution algorithm to solve this problem and apply the local search operation to the better solutions of each generation for much more better solutions. Tested by experimental cases and by the comparison with genetic algorithm, we can see that this algorithm is very effective to solve this problem. But it is still a single objective problem.For large project, especially the project of long cycle time, it needs to consider the influence of the time value of money to the project cost as well as the capital foreign which is not mentioned by original problem. In the meanwhile, resource is availale in the interval of the providing and expulsion time. Based on these factors, the objective function of the second work is to maximize the net present value of the project cash flows. The net present value is equal to the sum of the cash of each time in the process of the project discounted to the start time. The larger the numerical value of the project is, the better the investment benefit of the project obtains. We adopt the framework of the differential evolution combined with two local search operations to enhance the search ability. By comparison with genetic algorithm, the advantage of the differential evolution algorihtm to deal with this problem is obvious. But it is still a single objective problem.In real life, a variety of uncertainties, which lead to delay the construction of project or make the shortage of resource and even collapse, appear during the cycle of a large project. It is necessary to evaluate the ability of the scheduling scheme to settle the uncertainties, which is the robustness of the scheduling scheme. The stronger the robustness is, the stronger the ability of a project to cope with perturbation as well as the higher the credibility is. The third work considers a scheme which has not only the shorter makespan and less cost, but also the higher robustness. The problem model is the stochastic resource investment project scheduling problem, which is a multi-objective problem. We use the multi-objective differential evolution algorithm and three stages in mutation strategy as well as the crowding entropy to select the non-dominated solutions. This algorithm has significant advantages to deal with this problem by comparison with other algorithms.The differential evolution algorithm is a simple yet fast heuristic optimization method. This is the reason that we adopt the framework of the differential evolution algorithm to design the algorithm. The operators have mutation, crossover, selection and the local search. The mutation is to generate the mutant individual by make the targeted individual plus the difference of the other two individuals. The crossover is to obtain the trail individual by dealing with the mutant individual and the targeted individual. The individual with higher fitness value goes to the next generation under the comparision of fiteness value between the trail individual and the targeted individual. Then continually iterated until the problem converges. The local search operator is introduced to prevent the premature local convergence of the problem. It has been proved that this algorithm can effectively solve the complicated optimization problems.