A novel differential evolution mapping technique for generic combinatorial optimization problems

Differential evolution is primarily designed and used to solve continuous optimization problems. Therefore, it has not been widely considered as applicable for real-world problems that are characterized by permutation-based combinatorial domains. Many algorithms for solving discrete problems using differential evolution have been proposed, some of which have achieved promising results. However, to enhance their performance, they require improvements in many aspects, such as their convergence speeds, computational times and capabilities to solve large discrete problems. In this paper, we present a new mapping method that may be used with differential evolution to solve combinatorial optimization problems. This paper focuses specifically on the mapping component and its effect on the performance of differential evolution. Our method maps continuous variables to discrete ones, while at the same time, it directs the discrete solutions produced towards optimality, by using the best solution in each generation as a guide. To judge its performance, its solutions for instances of well-known discrete problems, namely: 0/1 knapsack, traveling salesman and traveling thief problems, are compared with those obtained by 8 other state-of-the-art mapping techniques. To do this, all mapping techniques are used with the same differential evolution settings. The results demonstrated that our technique significantly outperforms the other mapping methods in terms of the average error from the best-known solution for the traveling salesman problems, and achieves promising results for both the 0/1 knapsack and the traveling thief problems.     

New approach to identify the initial condition in degenerate hyperbolic equation

This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.     

Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

A constrained portfolio selection model at considering risk-adjusted measure by using hybrid meta-heuristic algorithms

Portfolio selection is a key issue in the business world and financial fields. This article presents a new decision making method of portfolio optimization (PO) issues in different risk measures by using new evolutionary computing method and cardinality constrains which is mentioned as hybrid meta-heuristic algorithms. Based on mean–variance (MV) Method by Markowitz we collected three risk levels; mean absolute deviation (MAD), semi variance (SV) and variance with skewness (VWS). The developed algorithms are Electromagnetism-like algorithm (EM), particle swarm optimization (PSO), genetic algorithm (GA), genetic network programming (GNP) and simulated annealing (SA). Also a diversification mechanism strategy is implemented and hybridized with the developed algorithms to increase the diversity and overcome local optimality. The sustainability of this proposed model is verified by 50 factories on the Iranian stock exchange. Finally, experimental results of proposed algorithms with cardinality constraint are compared with each other by four effective metrics in which the algorithms performance for achieving the optimal solution discussed. In addition, we have done the analysis of variance technique to confirm the validity and accurately analyze of the results which the success of this method was proved.     

Maximization of quadruple phase boundary for alkaline membrane fuel cell using non-stoichiometric α-MnO2 as cathode catalyst

Oxygen can only be reduced at the quadruple phase boundary (catalyst, carbon support, ionomer and oxygen) of the cathode catalyst layer with non-conducting electrocatalyst. To maximize the quadruple phase boundary sites is crucial to increase the peak power density of each membrane electrode assembly. The quadruple phase boundary is depending on the ratio of catalyst, carbon support and ionomer. The loading of catalyst layer is also crucial to the fuel cell performance. In this study, non-stoichiometric α-MnO₂ manganese dioxide nanorod material has been synthesized and the ratios of carbon, ionomer and catalyst loadings were optimized in alkaline membrane fuel cell. In total, ten membrane electrode assemblies have been manufactured and tested. Taguchi design method has been applied in order to understand the effect of each parameter. The conclusion finds out the ionomer has more influence on the alkaline membrane fuel cell peak power performance than carbon and loading.     

基于时间延迟的多类型维修与经济生产批量联合优化研究

针对目前未能较好的综合考虑多维修类型与经济生产批量联合优化的问题，首先考虑多类型维修关系，基于时间延迟理论求出故障和缺陷次数的表达式；其次，在此基础上，综合考虑生产费用和维修费用的基础上，构建了多类型维修和经济生产批量联合优化模型，以单位时间内总费用最小为优化目标，获得最优检查间隔期和经济生产批量；最后，通过算例分析验证了模型的有效性，说明了第一类缺陷检查次数的多少对费用和经济生产批量影响不大。     

Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges

Although topology optimization is established for linear static problems, more effort is required for solving nonlinear plastic problems. A new topology optimization approach with equivalent static loads (ESLs) is suggested to find the optimum topologies and locations of plastic hinges of thin-walled crash boxes by considering crash-induced deformation, the main crash energy-absorbing mechanism. Together with finite element method crashworthiness analyses, considering all nonlinearities with rate-dependent plasticity, the method was developed using an appropriate time-incremental scheme of ESLs without removing any high values of loads. Analyses show that the crash boxes with optimum topologies have energy-absorbing capabilities equivalent to the original structure. The proposed method is evaluated for two crashes: a crash box at low speed and a double cell subjected to high-speed collision. The results indicate that this method captures nonlinear crushing behaviours and accurate locations of plastic hinges where, if proper reinforcements are made, energy absorption can be enhanced.     

Hierarchical sampling optimization of particle filter for global robot localization in pervasive network environment

This paper presents a hierarchical framework for managing the sampling distribution of a particle filter (PF) that estimates the global positions of mobile robots in a large‐scale area. The key concept is to gradually improve the accuracy of the global localization by fusing sensor information with different characteristics. The sensor observations are the received signal strength indications (RSSIs) of Wi‐Fi devices as network facilities and the range of a laser scanner. First, the RSSI data used for determining certain global areas within which the robot is located are represented as RSSI bins. In addition, the results of the RSSI bins contain the uncertainty of localization, which is utilized for calculating the optimal sampling size of the PF to cover the regions of the RSSI bins. The range data are then used to estimate the precise position of the robot in the regions of the RSSI bins using the core process of the PF. The experimental results demonstrate superior performance compared with other approaches in terms of the success rate of the global localization and the amount of computation for managing the optimal sampling size.     

POD-assisted strategies for structural topology optimization

We propose a new numerical tool for structural optimization design. To cut down the computational burden typical of the Solid Isotropic Material with Penalization (SIMP) method, we apply Proper Orthogonal Decomposition on SIMP snapshots computed on a fixed grid to construct a rough structure (predictor) which becomes the input of a SIMP procedure performed on an anisotropic adapted mesh (corrector). The benefit of the proposed design tool is to deliver smooth and sharp layouts which require a contained computational effort before moving to the 3D printing production phase.     

Multiphase topology optimization with a single variable using the phase-field design method

In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction-diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time.