If you're talking about Linq, then I guess you're using Merchello.Context.Service.ProductService to do the search, which do query on DB, thus being slow. Consider doing the search on Examine Indexer (treat it as local cache) instead.

Step 1: Add your own key to Merchello's Product Examine index

        #region Customizing Examine Indexer
        // Basing on https://our.umbraco.com/packages/collaboration/merchello/merchello/61912-Searching-for-products-by-partial-sku-and-getting-IPublishedContent-back#comment-210571
        //Add event to allow searching by site section
        ProductIndexer.GatheringNodeData += ProductIndexerSite_GatheringNodeData;

Step 2: Then you can do the search on the Index

var searcher = Examine.ExamineManager.Instance.SearchProviderCollection["MerchelloProductSearcher"];
// Search Style 2: Showing a "AND" case for each category, combining with "OR" case inside keyword
// Basing on And vs Or at the 1st filtering. See https://our.umbraco.com/documentation/reference/searching/examine/overview-explanation#fluent-api
var searchCriteria = searcher.CreateSearchCriteria(BooleanOperation.And);
// Here, add your own Lucene filters
var productVariantResults = searcher.Search(searchCriteria).OrderByDescending(x => x.Score).ToList();

In my case, I added all collectionKeys into Product Indexer field "staticCollectionKeys", so my Examine/Lucene query looks like this:

                    foreach (string normalField in normalFields)
                    {
                        builder.Append($"staticCollectionKeys: (+{normalField.Replace(" ", " +")}) ");
                    }

Study on Examine Indexer & Lucene Query, which will help you to boost the performance.

Or you can also look into Andrew Wilson's solution, which is much cleaner and easier if it's good enough for your requirement. https://our.umbraco.com/packages/collaboration/merchello/merchello/94099-filters#comment-297596

My requirement on search is too complicated, search-by-collection is just one of the requirements, so I need to use Lucene query and adding custom Examine index field.

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