IEEE Computational Intelligence Magazine - August 2023 - 52

Meanwhile, common candidates can be found between
FIGURE 6 Structures of Fried network under different damages
scenarios. The size of nodes is proportional to its degree. Highlighted
links are functional, where those in gray color are removed. Seeds are
marked in red, and plain nodes are in green.
become distribution centers to improve the efficiency of
the whole system. For the CS network, the selected seeds
are influential members in this network, and they may
reach a larger influence range when spreading information
or working as manage staff. Compared with the existing
method for determining seeds as in [21], [24],MFEARIM
give diversified solutions that accommodate different damage
situations (i.e., tasks in the algorithm) in one iteration.
The computational efficiency can be greatly improved
using the multitasking optimization technique.
Complex systems may get destructed in different extents
as indicated in [28], [44], and robust solutions are highly
desirable in real-world applications. In the context of typological
perturbances towards networks, this work presents a
promising approach to tackling the influential member detection
problem. Taking the Fried network as an example, the
distribution of selected seeds in the typology is plotted in
Figure 6, where three cases are considered including T1, T3,
and T5. T1 represents a slight damage scenario, T5 represents
a serious one, and T3 represents a balanced one. As shown in
the figure, links tend to be removed as the damage percentage
increases, which causes congestions in the information
diffusion process. Consequently, the seed determination is
impacted due to the lack of integrity. The difference can be
noticed in the given typology, which reflects the effect of the
changeable parameter Per in (3). A larger Per indicates more
structural failures, and most nodes tend be destructed to different
degrees. Under this context, hubs may not be suited
for being selected as seeds when attacks happen. This conclusion
coincides with that in [21], which verifies the significance
of studying the robust influence maximization
problem. The results also enlighten decision makers that the
determination of seeds is expected to be integrated with the
structural features, and the multitasking optimization
approach may provide useful candidates to tackle multiple
practical scenarios.
52 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2023
seeds for T1, T3, and T5. In this manner, the efficacy of the
designed asynchronous strategy is demonstrated. Considering
that the required computational budget increases as more
links are disconnected, promising candidates can be obtained
in the search towards T1 at a relatively low cost. Employing
the multitasking optimization theory, low-cost tasks are
solved in priority, and propose valuable knowledge and alternatives
for high-cost tasks. The convergence of the algorithm
is thus accelerated. As listed in Table VII, a reduced computational
budget is achieved for MFEARIM. The results are competitive
compared with the state-of-the-art approaches shown
in Tables IV and VIII, and an efficient solver is constructed
for decision makers to solve the diffusion dilemmas.
In addition, the solution of the RIM problem can be
taken as a data mining task from networked systems.
Results in Fig. 6 and Fig. S4 of the supplementary material
also validate that the crux of structural information in the
excavation procedure. As an objective description of complicated
systems, the network structure implies the indepth
information and preferences in the composition process.
For example, the typology in Figure 6 exhibits a
power-law degree distribution [42], and an aggregation
tendency exists between key nodes. Formed by nodes and
links, networks constitute discrete decision variables, preventing
a direct employment of plenty of the existing optimizers.
In this work, elaborated operators are devoted to
exploiting knowledge pertaining to the network, and
exploring the whole solution space to gradually promote
the performance. Diversified information from seeds' micro
scope, the network's macro scope, and stochastic factors
are fully considered, and competitive search ability is
guaranteed. This work may shed some light on further
studies towards solving network-related and discrete optimization
problems. The local search procedure and the
transfer operation are practicable on handling other complex
optimization problems.
VI. Conclusion and Discussions
Based on the existing studies on the influence maximization
problem and the network robustness theory, the
robustness of information diffusion processes on networks
has been introduced in this paper. The influence ability of
seeds in networks suffering from varying structural losses is
comprehensively considered as different tasks. MFEARIM
has been proposed to solve the seed determination problem,
and makes up for the deficiency of existing solutions.
Experimental results validate the effectiveness of the
designed operators, and indicate the significance and effectiveness
of the evolutionary multitasking theory on this
network-based optimization problem. This work also highlights
the remarkable impact caused by structural losses on
the information diffusion process. The obtained seeds have
arobustinfluence ability and can deal with different
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