4.3 Results Using Hybrid Algorithms
Figures 4 and 5 present results obtained with two hybrid algorithms: a sequential
two step algorithm (Fig. 4) and an integrated algorithm (Fig. 5).
Figure 4 shows that, although the local search is launched (starting from best
solutions provided by the global search algorithm SPEA2 after 120 evaluations)
relatively far from the Pareto front, despite the limited budget, it behaves well (i.e. a
few solutions converge already on the front and their spread is good) [10].
Figure 5 shows the results obtained with an integrated hybrid algorithm called
Archive-based Multi-Objective Evolutionary Algorithm with Memory-based
Adaptive Partitioning of search space (AMOEA-MAP) [7]. Despite the limited
computational budget allowed (200 evaluations) this algorithm exhibits excellent
performances compared to NSGA-II. It also outperforms the sequential algorithm.
Fig. 4 Solution path of the
local search method applied
after 120 evaluations of global
search algorithm SPEA2 [8]
0.043
0.045
0.047
0.049
0.051
0.053
0.055
0.07
0.12
0.17
0.22
0.27
0.32
operational costs (monetary units)
climate change GWP100 (kg. CO2 - Eq)
AMOEA-MAP (200)
NSGAII (200)
NSGAII (1000)
Fig. 5 Approximation of the
Pareto front as a function of
the number of simulator
evaluations: hybrid algorithm
(AMOEA-MAP) versus
NSGAII optimizer [7]
A Synthesis of Optimization Approaches …
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