We have stumbled upon a number of different image optimization plugins, some work well, some are just a free teaser leading you to purchase their fee based version.
Short Pixel does offer a free version that can optimize up to 100 images after you have installed it. Once you have optimized 100 images it offers you different packages for their fee based plugin. We have found Short Pixel to work extremely well. You can run a bulk optimization for pre-existing websites with a library of images that works fairly quickly – it just depends on how many images are in the library. Once the bulk optimization has been run you can keep Short Pixel as an active plugin to optimize any future images you may upload to WordPress.