Hisanori Nonaka

Zero-one quadratic programming algorithm for resource leveling of manufacturing process schedules

In industrial plant construction scheduling, it is necessary to minimize the fluctuation or the maximum peak of the fluctuation or the maximum peak value of the daily resources amount, which is calculated as the sum of daily resources for each process. Minimization of the fluctuation or the maximum peak value corresponds to leveling the pile of resources. To perform this resource leveling, we need to decide on an objective function which is a monotone function that simply increases with the degree of resources leveling and then solve the optimization problem by fixing the process start dates while minimizing the objective function. Industrial plant construction is, however, in many cases a large-scale scheduling with an entire period of more than 1000 days and more than 100 processes, so it is very difficult to obtain a global optimization solution. In this study, we have developed an algorithm which solves a large-scale optimization problem to level necessary resources. This algorithm can quickly search for a good suboptimal solution close to the global optimal solution of a 0-1 quadratic programming problem. The algorithm searches by repeating a pivot operation using variable selection rules for resources leveling. We applied this algorithm to large-scale scheduling for an actual plant construction schedule, and successfully obtained a practical suboptimal solution within a few minutes (CPU power: 28MIPS). The results suggest that the algorithm is practical for resources leveling of large-scale construction scheduling.

Sub-optimal solution screening in optimization by neural networks

The authors discuss a convergence condition of the Hopfield neural network to get the optimal or sub-optimal solutions of combinatorial optimization problems. For the TSP (traveling salesman problem), the condition to get its feasible solutions to coincide with the minimum points of the Hopfield neural network requires that the penalty parameter, which is the weight of a constraint function, must be greater than the distance between three consecutive cities in the solutions. It is proposed that by utilizing this condition, it would be possible to control the quality of solutions. The result was applied to TSPs with 4 and 16 cities, and confirmed that all the sub-optimal solutions could be eliminated. The optimal solution was obtained efficiently.<<ETX>>

New Approaches to Large-Scale Scheduling Problems: Constraint Directed Programming and Neural Networks

Industrial plant construction involves a large number of component installation tasks, such as setting up pumps, pipes, and other mechanical and electrical devices. During the construction, mutually related tasks make up a scheduling unit known as an activity, or a task. Computer aided methods have been employed to scheduling of activities, to improve construction efficiency and reliability.