Modifying microbial cells to overproduce bioproducts of interest is a challenging design task, requiring in-depth knowledge of cell physiology and rational inference of design strategies that could improve production while maintaining cellular homeostasis. This work investigates the design of growth-coupled cell strains that could couple production with growth, a widely used approach for strain design. We first propose this type of design as a multi-objective optimisation problem through mathematical modelling. Then, we introduce an improved nondominated sorting genetic algorithm to tackle optimisation challenges inherent in such a design task and identify high-quality design strategies. Our case studies demonstrate the promise of the proposed approach in designing high-production strains in the field of biomanufacturing.