Alex Marquardt discusses improving search relevance in Elasticsearch by combining stemmers and multi-word synonyms. The approach involves using stemmers to reduce synonym lists by extracting word stems before applying synonyms, thus simplifying the process of handling different word forms. The article provides a detailed explanation of implementing custom analyzers and mappings in Elasticsearch, showcasing how to define index-time and search-time analyzers with a synonym graph token filter. By applying this setup to a test index, the blog demonstrates enhanced search results, where synonymous and stemmed terms are effectively matched, improving the accuracy and relevance of search queries. Additionally, Marquardt mentions Elastic Cloud and Elastic App Search as tools for users seeking a simplified, out-of-the-box search experience.