We do not have near-term plans to add the advanced search capabilities to the online client conjoint simulator. So, I don't have good news for you on that front. However, as you probably realize, (assuming you have a Lighthouse Studio subscription yourself) it doesn't cost you anything to deliver a Lighthouse Studio client simulator to clients who want the sophistication of optimization searches. They would have to install the Windows-based Choice Simulator software on their machine. You would need to send them a single project file that contains all the utility runs and market simulation scenarios. They open that file with their installed simulator software. There is also quite a bit you can do to screw down the Lighthouse Studio client simulator in terms of its settings.
Yes, the Windows-based Choice Simulator (like Lighthouse Studio offers) is not as simple as the online simulator, but it is a beautiful and powerful piece of software.