INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multiobjective optimization (CMOO). When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the tradeoffs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of nondominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose inverse design methodology for constrained multiobjective optimization (INFORM): a two-step approach for sample-efficient CMOO of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on: 1) a neural network (NN) verifier; 2) NN; and 3) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of nondominated solutions. In the second step, we choose the regions of interest around the nondominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to $29\times $ and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.