GPUs are a key enabler of the revolution in machine learning and high performance computing, functioning as de facto co-processors to accelerate large-scale computation. As the programming stack and tool support have matured, GPUs have also become accessible to programmers, who may lack detailed knowledge of the underlying architecture and fail to fully leverage the GPU's computation power. GEVO (Gpu optimization using EVOlutionary computation) is a tool for automatically discovering optimization opportunities and tuning the performance of GPU kernels in the LLVM representation. GEVO uses population-based search to find edits to GPU code compiled to LLVM-IR and improves performance on desired criteria while retaining required functionality. We demonstrate that GEVO improves the execution time of the GPU programs in the Rodinia benchmark suite and the machine learning models, SVM and ResNet18, on NVIDIA Tesla P100. For the Rodinia benchmarks, GEVO improves GPU kernel runtime performance by an average of 49.48% and by as much as 412% over the fully compiler-optimized baseline. If kernel output accuracy is relaxed to tolerate up to 1% error, GEVO can find kernel variants that outperform the baseline version by an average of 51.08%. For the machine learning workloads, GEVO achieves kernel performance improvement for SVM on the MNIST handwriting recognition (3.24X) and the a9a income prediction (2.93X) datasets with no loss of model accuracy. GEVO achieves 1.79X kernel performance improvement on image classification using ResNet18/CIFAR-10, with less than 1% model accuracy reduction.