This work presents a new approach for interval-based uncertainty analysis. The proposed approach integrates a local search strategy as the worst-case-scenario technique of anti-optimization with a constrained multi-objective genetic algorithm. Anti-optimization is a term for an approach to safety factors in engineering structures which is described as pessimistic and searching for least favorable responses, in combination with optimization techniques but in contrast to probabilistic approaches. The algorithm is applied and evaluated to be efficient and effective in producing good results via target matching problems: a simulated topology and shape optimization problem where a 'target' geometry set is predefined as the Pareto optimal solution and a constrained multiobjective optimization problem formulated such that the design solutions will evolve and converge towards the target geometry set.