Parameter adaptive multimodal optimization and its application in smart lighting

Abstract

In many engineering applications exact models of underlying physical phenomena are not available and design and control strategies are difficult to develop. Uncertain measurements and unpredictable disturbances further complicate the systems design. Often multiple solutions in the design space must be explored and evaluated. In the proposed research, a novel approach to multimodal optimization (Speciated Parameter Adaptive Differential Evolution, or SPADE) is developed and evaluated to address these challenges. Specifically, the SPADE algorithm is applied to a set of systems design problems in the emerging area of smart lighting systems design.

Differential evolution is a class of evolutionary optimization methods that has been successful in a variety of difficult multimodal problem sets. Recently, the JADE algorithm has been developed in our laboratory and provides the capability to adapt algorithm control parameters to a range of different objective function characteristics at different phases of the evolutionary search. JADE has been successful in solving high dimension multimodal optimization problems, and was awarded first place in an international competition. The SPADE algorithm considered in this research is a further refinement of JADE, and introduces the principle of speciation in order to find multiple likely solutions to large multimodal problems. In SPADE, the population evolves into different species corresponding to clusters of candidate solutions. Separate species evolve in parallel and converge to multiple regions of the search space. The speciated populations are guided by the Minimum Description Length (MDL) principle that minimizes the complexity of the data set representation. Adaptive crossover between species further supports flexibility of the search process.

This thesis is focused on the application of the SPADE family of algorithms to the design of "smart" lighting systems that meet objectives for efficiency, productivity, and health. In this approach, the requirements and constraints are expressed in terms of characteristics of the light field. The light field is considered in general terms as a five-dimensional map representing the light irradiance (related to the perceived brightness of the light) and the directional characteristics of the light rays. The five-dimensional light field is reconstructed by means of discrete sensor sampling and estimation. Our approach to light field analysis utilizes the ray tracing simulation program to generate a simulated representation of the high dimensional data. In addition, the program is used to simulate a basic angular light sensor that could be used in experimental studies and control implementations. The estimation is achieved by the Kriging spatial estimation technique. In this research, we utilize the color sensor to carry out experimental studies of five-dimensional light field reconstruction and light source configurations design. The five-dimensional light field is set as the target, and the resulting problem space is high dimensional and multimodal with respect to the configuration and parametric characteristics of light sources. The outcome of this research demonstrates and evaluates the capability of the SPADE algorithm to design a configuration of light sources in the smart space testbed room to meet specified requirements.