Discrete Nonlinear Programming for Optimal Design of LED Arrays

1. Discrete Nonlinear Programming for Optimal Design of LED Arrays Andrei Gribok, Vivek Agarwal, D. L. Page, and M. A. Abidi University of Tennessee, Knoxville, Tennessee 37996-2100, Email: agribok@utk.edu Objective To achieve proper traffic lights intensity, chromaticity and longetivity. Schematic Layout Traffic Lights Flood Design Problem Statement The solution requires the search among 260 possible combination of LED’s Constrains Mixing Color and Brightness Cost Function The constrains are in terms of chromaticity coordinates and lumens. For example Green Branch and Bound Method Chromaticity Diagram with boundary conditions for Green The area bounded by the trapezoid is the boundary condition for Green. The solution obtained from branch and bound method should be within this area. Original Problem Problem 1 Problem 2 y Problem 6 Problem 3 Problem 4 Problem 5 x Infeasible Infeasible Infeasible Optimal Solution Results The Branch and Bound (B&B) method relaxes all the integrality conditions and solves the resulting LP problem. From the obtained set of solutions the B&B finds the most optimal solution that satisfy the original integrality condition. Non-Feasible Solution Feasible Solution (0.1106,0.6692) (0.0489,0.6290) y y x x This work is supported by the University Research Program in Robotics under grant submitted by SIEMENS CORPORATION Flood Design and Traffic Lights: Courtesy: SIEMENS CORPORATION