Solving Expensive Multimodal Optimization Problem by a Decomposition Differential Evolution Algorithm.

An expensive multimodal optimization problem (EMMOP) is that the computation of the objective function is time consuming and it has multiple global optima. This article proposes a decomposition differential evolution (DE) based on the radial basis function (RBF) for EMMOPs, called D/REM. It mainly consists of two phases: the promising subregions detection (PSD) and the local search phase (LSP). In PSD, a population update strategy is designed and the mean-shift clustering is employed to predict the promising subregions of EMMOP. In LSP, a local RBF surrogate model is constructed for each promising subregion and each local RBF surrogate model tracks a global optimum of EMMOP. In this way, an EMMOP is decomposed into many expensive global optimization subproblems. To handle these subproblems, a popular DE variant, JADE, acts as the search engine to deal with these subproblems. A large number of numerical experiments unambiguously validate that D/REM can solve EMMOPs effectively and efficiently.

A viscoelastic-viscoplastic constitutive model for polymer bonded explosives under low impact loading.

Viscoplastic work is very important to explosive ignition under impact loading. At present, a large number of constitutive models only consider the viscoelastic and damage behavior of explosives, ignoring the plastic effect under low impact loading. A new viscoelastic-viscoplastic (VE-VP) model was developed and studied to describe the dynamic mechanical behaviors of polymer-bonded explosives (PBXs). The total strain was assumed to be the sum of the viscoelastic (VE) and viscoplastic (VP) components. A generalized Maxwell model was used to determine the VE responses. A VP model was developed by using the classical J2 rate-dependent model with isotropic hardening. Viscoplastic flow was considered in hyperbolic sinusoidal form. The explicit algorithms of VE model were proposed and assessed by using two different integration methods. The accuracy and efficiency of these two methods are similar at high strain rates. The coupled algorithms of VE-VP model were developed by referring to the classical elasto-viscoplasticity (EVP) provided and using the expression of incremental relaxation modulus. The proposed model was implemented in the ABAQUS using a user-subroutine (VUMAT) to predict the response behaviors of PBX 9501 under low impact loading. Several numerical simulations illustrated the computational efficiency and the accuracy of the proposed methods. The model predictions were compared with experimental data, and reasonable agreement was obtained.

A Penalty-Based Differential Evolution for Multimodal Optimization.

It is very difficult to locate multiple global optimal solutions (GOSs) of multimodal optimization problems (MMOPs). To deal with this issue, a penalty-based multimodal optimization differential evolution (DE), called PMODE, is developed in this article. In PMODE, a penalty strategy with a dynamic penalty radius is constructed to solve MMOPs. An elite selection mechanism is designed to identify and select elite solutions. The neighboring areas of these elite solutions are penalized. PMODE uses a popular DE variant-JADE as its search engine. The proposed PMODE is compared with several other state-of-the-art multimodal optimization algorithms on 20 MMOPs used in the IEEE CEC2013 special session. The experimental results show that PMODE performs better than other state-of-the-art methods.