PHP7 - optimize images ( Compress without losing quality )

I have a problem with my project. I want to optimize images on it. I tried to convert images to .webp, but I found that it not supported by browsers.

When I test my website on PageSpeedInsight of Google, it's given me warning about messages and I need to compress them. and at the same time, he gives me the new compress picture, perfectly and with small size.

But I try to do that with PHP, but I can't get the same result of google page Insight.

Message from pageSpeedInsight:

Image formats like JPEG 2000, JPEG XR, and WebP often provide better compression than PNG or JPEG, which means faster downloads and less data consumption

Is there any best solution to optimize images? I use a native PHP framework (MVC).