This paper explores the challenges that multi-objective genetic algorithms (MOGAs) face in converging to the true Pareto-optimal front. It identifies problem features that can cause convergence difficulties and proposes methods to construct test problems with controlled difficulty levels. The study draws on single-objective optimization problems to transfer known difficult features (such as multimodality or deception) to multi-objective problems. Additionally, it introduces specific multi-objective optimization features to create more complex test problems. The construction methodology allows for the incorporation of various aspects of single-objective test functions, making it easier to develop test problems with similar difficulties for multi-objective optimization. The paper also discusses the importance of maintaining diversity in the Pareto-optimal solutions and the challenges posed by constraints. Finally, it presents a generic two-objective optimization problem with controlled convexity, non-convexity, and discreteness in the Pareto-optimal front, demonstrating how these features can be introduced through appropriate functions.This paper explores the challenges that multi-objective genetic algorithms (MOGAs) face in converging to the true Pareto-optimal front. It identifies problem features that can cause convergence difficulties and proposes methods to construct test problems with controlled difficulty levels. The study draws on single-objective optimization problems to transfer known difficult features (such as multimodality or deception) to multi-objective problems. Additionally, it introduces specific multi-objective optimization features to create more complex test problems. The construction methodology allows for the incorporation of various aspects of single-objective test functions, making it easier to develop test problems with similar difficulties for multi-objective optimization. The paper also discusses the importance of maintaining diversity in the Pareto-optimal solutions and the challenges posed by constraints. Finally, it presents a generic two-objective optimization problem with controlled convexity, non-convexity, and discreteness in the Pareto-optimal front, demonstrating how these features can be introduced through appropriate functions.