On the detection of nearly optimal solutions in the context of single-objective space mission design problems

Abstract

When making decisions, having multiple options available for a possible realization of the same project can be advantageous. One way to increase the number of interesting choices is to consider, in addition to the optimal solution x*, also nearly optimal or approximate solutions; these alternative solutions differ from x* and can be in different regions -in the design space -but fulfil certain proximity to its function value f(x*). The scope of this article is the efficient computation and discretization of the set E of e-approximate solutions for scalar optimization problems. To accomplish this task, two strategies to archive and update the data of the search procedure will be suggested and investigated. To make emphasis on data storage efficiency, a way to manage significant and insignificant parameters is also presented. Further on, differential evolution will be used together with the new archivers for the computation of E. Finally, the behaviour of the archiver, as well as the efficiency of the resulting search procedure, will be demonstrated on some academic functions as well as on three models related to space mission design.

Seeking Multiple Solutions: An Updated Survey on Niching Methods and Their Applications

“…Other examples include a niching method used to detect multiple nearly optimal solutions for space mission design problems [171], and a niching PSO method was developed for identification of static equilibria via potential energy optimization [172]. Though many more examples can be found in literature, we hope the above list suffices to demonstrate a common pattern, i.e., the importance and usefulness of niching methods going beyond the boundaries of many application areas.…”