High school scheduling optimization as continuous problem -

Abstract

High School Scheduling is a tedious task to do manually. It is considered as NP problem where even computers have difficulties to solve. Here we introduce a new approach to solve High School Scheduling programmatically. We model the problem as an optimization one with multiple types of constraints where variables are continuous and functions are continuous and differentiable. Therefore, powerful tools of optimization for continuous functions would be available. Notice that such continuous optimization methods are much faster than discrete optimization methods where a huge number of iterations are usually executed to reach the solution. A lot of papers have been written about this topic and a lot of software has been designed for this purpose. However, most, if not all, interpreted such topic variables as discrete variables where every variable is considered as binary (either 0 or 1). In fact, variables’ type is binary. However, we turn around this problem by inhibiting variables getting away from 0 or 1 by introducing a penalty sub-function in the continuous optimization function. In addition, a nonlinear equality constraint is also added to make the variables binary. We build the continuous model in all its details based on required discrete input. It consists of function to be optimized (including penalty function), linear equality constraint, linear inequality constraint, and nonlinear equality constraint. Corresponding software has been implemented on Matlab. It was tested on two classes with common teachers whose schedule covers seven sessions per day over five days. Very good results were achieved. Little iteration was enough to solve the problem. Varied inputs have been tested and it took always less than one minute to be solved.