Search API - Search widget with Facet OR Exposed filters clean url
This module should help you getting rid of ugly URLs when using exposed filters:
https://www.drupal.org/project/query_parameters_to_url


  ...
  
  An example of a dirty URL like that could be:
  example.com/events?field_category_id[0]=100&amp;field_category_id1=101&amp;field_author_name[0]=John
  
  Using this module you can transform the URL into:
  example.com/events/p/field_category_id/0__100--1__101/field_author_name/John
  
  Or an even shorter URL if you use the provided alter hooks:
  example.com/events/p/cat_id/0__100--1__101/name/John
  
  Isn't that a joy to look at?
  
  ...


Please refer also to this question to achieve the same thing writing your own module.