Finding near-optimum and diverse solutions for a large-scale engineering design problem

Optimization problems in real-world usually involve a large number of variables and constraints. Moreover, practitioners also need to find a reasonable solution quickly, despite the fact that solution evaluation can be expensive. In addressing such optimization tasks, practitioners often have a completely different set of objectives than the usual trend of finding a single and accurate optimal solution. First, with the limited computational time availability and large dimension, it is not accepted (and in most occasions, not possible) to find the exact optimum solution of the problem, rather the focus must be spent to identify a near-optimal solution in a quick computational time. Second, instead of concentrating on a single solution, practitioners are often interested in evaluating a diverse set of solutions from the search space having similar objective values. Third, when a solution is finally chosen, practitioners are interested in exploring its vicinity to understand the trade-off between objective value and constraint violation, so that a more informed description of the problem can be ascertained. We highlight all these practicalities through a large-scale engineering design problem and present a suitable evolutionary-cum-classical, single-cum-multi-objective optimization method. The methods are generic and can be applied to other complex optimization tasks.