2D Bin Packing Algorithm

I have spent some time researching 2d bin packing algorithm. I have no extensive experience in algorithm especially in advanced math but I can code :)

The perfect example of what I need to achieve is demonstrated here http://www.cutlistoptimizer.com. It works, but I can't figure out what algorithm it uses.

I have tried many approaches some of them are very simple like https://codeincomplete.com/posts/bin-packing/ DEMO here, but it doesn't support rotation which is essential.

Most promising for me was https://ssbothwell.github.io/greedypacker-react/ Not sure am I doing something wrong but it doesn't calculate best fit for me. I have tried different combinations with different algorithms.

DEMO DATA: Sheet size: w:2655, h: 2100

{ w: 900, h: 320 },
 { w: 320, h: 900 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 900, h: 320 },
 { w: 386, h: 310},
 { w: 386, h: 310},
 { w: 386, h: 310},
 { w: 386, h: 310},
 { w: 386, h: 310},
 { w: 860,  h: 320},
 { w: 860,  h: 320},
 { w: 564,  h: 310 },
 { w: 452,  h: 293},
 { w: 720,  h: 530},
 { w: 720,  h: 530},
 { w: 696,  h: 530},
 { w: 696,  h: 100 }

These parts should fit within one sheet.

Reference image

After some time of researching, I have figure out that probably I should use a genetic algorithm in order to evolve these heuristic approaches. Does this make any sense?