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UEC Int’l Mini-Conference No.54 31

SIMP-Based Density Interpolation for Evolutionary Multi-Objective

Topology Optimization

Fermin DEL VALLE-VEGA ∗1 and Hiroyuki Sato 2

1 UEC Exchange Study Program (JUSST Program)
2 Nature Inspired Computing Lab.
The University of Electro-Communications, Tokyo, Japan

Abstract

This work introduces a comprehensive multi-objective topology optimization framework that com-
bines the SIMP (Solid Isotropic Material with Penalization) interpolation method with a specialized
evolutionary algorithm. The process begins with random density initialization, followed by iterative
finite element evaluations and the application of tailored crossover and mutation operators to explore
the design space. Using a high-resolution tetrahedral mesh, a population of 100 candidates evolves
over 200 generations, balancing mass minimization and stiffness retention. Post-processing employs
connectivity and minimum feature-size filters to ensure compatibility with additive manufacturing.
The results demonstrate up to a 30% reduction in mass with less than 5% loss in stiffness, and reveal
significant improvements in the fundamental natural frequency. Pareto-front analyses and detailed
3D visualizations illustrate the trade-offs between structural lightness and performance. Compared
to conventional single-objective approaches, the proposed integrated strategy reduces computational
cost and yields optimized topologies suitable for industrial applications. This methodology paves the
way for the automated design of lightweight, robust components with enhanced dynamic strength,
supporting the feasibility of additive manufacturing.

Keywords: Topology optimization Multi-objective optimization Evolutionary algorithm Solid
Isotropic Material with Penalization Topology filtering Lightweight structures.
1 Introduction straints were also incorporated to eliminate nu-
merical artifacts and disconnected “islands” [3,
Topology optimization seeks the optimal ma- 4]. These advances enabled clear, binary topolo-
terial distribution within a given domain to gies optimized for mass or stiffness, although
satisfy performance criteria under prescribed they remained inherently single-objective.
loads and boundary conditions. Its origins
trace back to Michell’s seminal work on beam Optimizing solely for mass reduction or static
stiffness optimization [1], but it was not un- stiffness often overlooks critical dynamic be-
haviors. Single-objective SIMP designs may
til 1988 that Bendsœand Kikuchi introduced
exhibit natural frequencies close to operating
a homogenization-based finite element scheme
that made practical implementations possi- loads, leading to resonance risk and potential
ble [2]. Shortly thereafter, the SIMP (Solid failure under variable conditions [13]. Moreover,
Isotropic Material with Penalization) method additive manufacturing imposes strict geomet-
gained popularity by applying a power law to ric requirements—such as the avoidance of over-
each element’s density, thereby severely reduc- hangs and excessively thin ligaments—that tra-
ditional density-based outputs cannot guarantee
ing the effective modulus of intermediate densi-
ties. Density filters and minimum-thickness con- without post-processing [8–10]. Finally, balanc-
ing multiple performance metrics via weighted
∗ The author is supported by JASSO Scholarship. sums is often ad hoc and may fail to capture