Pareto fronts offer insight into the best found solutions of a given problem. Several algorithms have been developed to help maintain a well-distributed Pareto front and therefore offer a wide variety of solutions. However, in real-world problems, the Pareto front isn’t necessarily a continuous surface and may contain holes and/or discontinuous lines. These irregular areas on the Pareto front are considered gaps. These gaps can either be natural or artificial. In their research, Pellicer, Escudero, Alzueta, and Deb suggest a three-step procedure to find, validate, and fill these gaps. First, they developed an algorithm to generate gap points. Second, they developed an equation that checks the validity of the gap points. Lastly, a focused algorithm looks for points around the validated gap points to determine if they are natural or artificial. This procedure was used on several test problems that range from two-to-five objectives, including a five-objective real-world problem in the steel industry.
"Filling Gaps on the Pareto Front in Multi- and Many-Objective Optimization,"
Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal: Vol. 9:
2, Article 5.
Available at: https://digitalcommons.morris.umn.edu/horizons/vol9/iss2/5