Towards a new Praxis in optinformatics targeting knowledge re-use in evolutionary computation: simultaneous problem learning and optimization

Abstract

As the field of evolutionary optimization continues to expand, it is becoming increasingly common to incorporate various machine learning approaches, such as clustering, classification, and regression models, to improve algorithmic efficiency. However, we note that although problem learning is popularly used in improving the ongoing optimization process, little effort is ever made in extracting re-usable domain knowledge. In other words, the acquired knowledge is seldom transferred and exploited for future design exercises. Focusing on evolutionary optimization, in this paper we investigate the concept of simultaneous problem learning and optimization inspired by the following notions: (1) that prior/dynamically acquired knowledge can enhance the effectiveness of evolutionary search, and (2) that evolution can be geared towards gathering crucial knowledge about the underlying problem. Taking benchmark functions as well as an engineering (process) design problem into consideration, we demonstrate the efficacy of a novel classifier-assisted constrained EA towards simultaneous evolutionary search and problem learning.

Appendix

The filling phase of a generic composites manufacturing process is governed by the following PDEs [13]:

$$\nabla \cdot \left( {h \frac{\varvec{K}}{\mu } \nabla p} \right) = \frac{\partial h}{\partial t},$$

(6)

$$\rho C_{p} \frac{\partial T}{\partial t} + \rho_{r} C_{pr} \left( {\varvec{u} \cdot \nabla T} \right) = \nabla \cdot \left( {k \nabla T} \right) + \left( {1 - V_{f} } \right) \cdot \dot{H},$$

(7)

$$\varphi \frac{\partial \alpha }{\partial t} + \varvec{u} \cdot \nabla \alpha = \left( {1 - V_{f} } \right) \cdot R_{\alpha } .$$

(8)

Equation 6 governs the fluid flow in porous media. Here, h is the thickness of the mould cavity, p is the local resin pressure, K is the reinforcement permeability, t is the time, and ∂h/∂t represents the speed of mould closure. Note that ∂h/∂t is zero throughout the RTM cycle, but is zero or strictly negative for the I/C-LCM cycle (due to decreasing cavity thickness during the in situ mould compression phase). The viscosity μ of the resin is a function of the local temperature T and the degree of resin conversion α. The relation may be captured by the following widely used rheological model,

$$\mu = A_{\mu } e^{{E_{\mu } /R T}} \left( {\frac{{\alpha_{g} }}{{\alpha_{g} - \alpha }}} \right)^{a + b\alpha } ,$$

(9)

where α _g is the degree of cure at which resin gel conversion occurs, R is the universal gas constant, E _µ is the activation energy, and A _µ , a and b are other experimentally determined constants.

Equation 7 is a lumped energy equation which governs the temperature distribution within the mould. The material properties ρ, C _p , and k represent the average density, specific heat capacity, and thermal conductivity of the resin-fibre system, respectively. Further, u is the volume averaged resin flow velocity, V _f is the fibre volume fraction, and $\dot{H}$ is a source term representing the thermal energy generated by the resin during its exothermic polymerization reaction.

Finally, Eq. 8 models how the degree of resin conversion varies in the part during filling. Therein, R _α represents the rate of resin polymerization. Kamal and Sourour [30] proposed the following general model which is widely used to describe the polymerization reaction,

$$R_{\alpha } = \left( {A_{1} \cdot e^{{\left( { - E_{1} /R T} \right)}} + A_{2} \cdot e^{{\left( { - E_{2} /R T} \right)}} \cdot \alpha^{{m_{1} }} } \right) \cdot \left( {1 - \alpha } \right)^{{m_{2} }} ,$$

(10)

where A ₁, A ₂, E ₁, E ₂, m ₁, and m ₂ are experimentally determined constants.

For complete details on the material properties and empirical constants used in the composites manufacturing case study, the reader is referred to [13].