Optimal Inverse Functions Created via Population-Based Optimization

Abstract

Finding optimal inputs for a multiple-input, single-output system is taxing for a system operator. Population-based optimization is used to create sets of functions that produce a locally optimal input based on a desired output. An operator or higher level planner could use one of the functions in real time. For the optimization, each agent in the population uses the cost and output gradients to take steps lowering the cost while maintaining their current output. When an agent reaches an optimal input for its current output, additional agents are generated in the output gradient directions. The new agents then settle to the local optima for the new output values. The set of associated optimal points forms an inverse function, via spline interpolation, from a desired output to an optimal input. In this manner, multiple locally optimal functions can be created. These functions are naturally clustered in input and output spaces allowing for a continuous inverse function. The operator selects the best cluster over the anticipated range of desired outputs and adjusts the set point (desired output) while maintaining optimality. This reduces the demand from controlling multiple inputs, to controlling a single set point with no loss in performance. Results are demonstrated on a sample set of functions and on a robot control problem.

Improved gene expression programming to solve the inverse problem for ordinary differential equations

“…The problem of converting observed data of a physical system into a mathematical model in terms of differential equations is known as the inverse problem [1,2] of differential equations [3,4,5,6]. For instance, if we have previous data of a stock market, we may create an ODEs model for the stock market using previous data and then predict the development trend of the stock market.…”