A fast hypervolume driven selection mechanism for many-objective optimisation problems

Solutions to real-world problems often require the simultaneous optimisation of multiple conflicting objectives. In the presence of four or more objectives, the problem is referred to as a "many-objective optimisation problem". A problem of this category introduces many challenges, one of which is the effective and efficient selection of optimal solutions. The hypervolume indicator (or s-metric), i.e. the size of dominated objective space, is an effective selection criterion for many-objective optimisation. The indicator is used to measure the quality of a non-dominated set, and can be used to sort solutions for selection as part of the contributing hypervolume indicator. However, hypervolume based selection methods can have a very high, if not infeasible, computational cost. The present study proposes a novel hypervolume driven selection mechanism for many-objective problems, whilst maintaining a feasible computational cost. This approach, named the Hypervolume Adaptive Grid Algorithm (HAGA), uses two-phases (narrow and broad) to prevent population-wide calculation of the contributing hypervolume indicator. Instead, HAGA only calculates the contributing hypervolume indicator for grid populations, i.e. for a few solutions, which are close in proximity (in the objective space) to a candidate solution when in competition for survival. The result is a trade-off between complete accuracy in selecting the fittest individuals in regards to hypervolume quality, and a feasible computational time in many-objective space. The real-world efficiency of the proposed selection mechanism is demonstrated within the optimisation of a classifier for concealed weapon detection.