As launch and manufacturing costs have become affordable, the industrial and academic interest in Low-Earth Orbit (LEO) satellites has increased in recent years. With this interest, the concept of Low-Earth Orbit-based Positioning, Navigation and Timing (LEO-PNT) has also gained popularity as a complementary and/or standalone system in addition to the already existing Global Navigation Satellite Systems (GNSS). This article examines the LEO constellation optimization from the perspective of a LEO-PNT design, identifies and discusses the state-of-art of the LEO satellite constellation optimization approaches, introduces relevant performance and feasibility related metrics and parameters, and addresses key concepts and underlying trade-offs that must be considered for any LEO-PNT system design. In addition, a case study for a LEO-PNT constellation optimization is presented, where we showcase the discussed trade-offs. We present optimization results obtained with the adaptive weighting algorithm “ADaW” applied to the Pareto-optimization algorithm “NSGA-III”. A detailed performance analysis is done for six relevant scenarios with varying receiver location properties, namely by considering indoor/outdoor, rural/urban and line of sight/non-line of sight cases.