  This paper introduces a high-performance hybrid algorithm, called Hybrid
Hypervolume Maximization Algorithm (H2MA), for multi-objective optimization
that alternates between exploring the decision space and exploiting the already
obtained non-dominated solutions. The proposal is centered on maximizing the
hypervolume indicator, thus converting the multi-objective problem into a
single-objective one. The exploitation employs gradient-based methods, but
considering a single candidate efficient solution at a time, to overcome
limitations associated with population-based approaches and also to allow an
easy control of the number of solutions provided. There is an interchange
between two steps. The first step is a deterministic local exploration, endowed
with an automatic procedure to detect stagnation. When stagnation is detected,
the search is switched to a second step characterized by a stochastic global
exploration using an evolutionary algorithm. Using five ZDT benchmarks with 30
variables, the performance of the new algorithm is compared to state-of-the-art
algorithms for multi-objective optimization, more specifically NSGA-II, SPEA2,
and SMS-EMOA. The solutions found by the H2MA guide to higher hypervolume and
smaller distance to the true Pareto frontier with significantly less function
evaluations, even when the gradient is estimated numerically. Furthermore,
although only continuous decision spaces have been considered here, discrete
decision spaces could also have been treated, replacing gradient-based search
by hill-climbing. Finally, a thorough explanation is provided to support the
expressive gain in performance that was achieved.
