Comparing multi-objective non-evolutionary NLPQL and evolutionary genetic algorithm optimization of a DI diesel engine: DoE estimation and creating surrogate model Ali Navid, Shahram Khalilarya, Hadi Taghavifar ⇑ Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran article info Article history: Received 2 May 2016 Received in revised form 9 August 2016 Accepted 10 August 2016 Keywords: Design of experiment Diesel engine Epsilon-SVR MOGA NLPQL abstract This study is concerned with the application of two major kinds of optimization algorithms on the base- line diesel engine in the class of evolutionary and non-evolutionary algorithms. The multi-objective genetic algorithm and non-linear programming by quadratic Lagrangian (NLPQL) method have com- pletely different functions in optimizing and finding the global optimal design. The design variables are injection angle, half spray cone angle, inner distance of the bowl wall, and the bowl radius, while the objectives include NOx emission, spray droplet diameter, indicated mean effective pressure (IMEP), and indicated specific fuel consumption (ISFC). The restrictions were set on the objectives to distinguish between feasible designs and infeasible designs to sort those cases that cannot fulfill the demands of die- sel engine designers and emission control measures. It is found that a design with deeper bowl and more encircled shape (higher swirl motion) is more suitable for NO x emission control, whereas designs with a bigger bowl radius, and closer inner wall distance of the bowl (Di) may lead to higher engine efficiency indices. Moreover, it was revealed that the NLPQL could rapidly search for the best design at Run ID 41 compared to genetic algorithm, which is able to find the global optima at last runs (ID 84). Both techniques introduce almost the same geometrical shape of the combustion chamber with a negligible contrast in the injection system. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Internal combustion engines (ICE) are the primary power pro- duction unit in the vehicles that has experienced a continuous change in structure and operational conditions in order to achieve higher power rate and lower engine out emissions. Meantime, the advent of computers and application of its processing in the com- putation of governing equations in discretized form marked a new era in ICEs optimization and rapid development. The computer modeling in the computational fluid dynamics (CFD) format had a drastic role in the fast progress of the engine simulation. Along the evolution of computer programming to elevate the engine per- formance, the engine optimization methods have been created. The ultimate goal of the engine optimization includes identification of a set of design variables giving the minimum/maximum amount of the objective function of interest. Following, there are three main- stream approaches in optimization. The first category is the engine optimization with parametric study, where several parameters of the engine were evaluated to find the best combination of param- eters that yield the best engine performance/emissions [1–3]. The second class of engine optimization involves the engine optimiza- tion with non-evolutionary algorithms that is more efficient when a large number of design variables are available [4–7]. The perfor- mance of the non-evolutionary method depends on the gradient of spatial data. Finally, the last method is through evolutionary framework, which has gained more popularity in engine http://dx.doi.org/10.1016/j.enconman.2016.08.014 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved. Abbreviations: CFD, computational fluid dynamics; DDM, discrete droplet model; DI, direct injection; Di, bowl middle diameter; DoE, design of experiment; GA, genetic algorithm; GDI, gasoline direct injection; HPCR, high pressure common rail; HRR, heat release rate; ICE, internal combustion engine; IMEP, indicated mean effective pressure; ISFC, indicated specific fuel consumption; MOGA, multi- objective genetic algorithm; NLPQL, nonlinear programming by quadratic lagran- gian; PDF, probability density function; PSO, particle swarm optimization; R4, bowl radius; SQP, sequential quadratic programming; SIMPLE, semi-implicit method for pressure-linked equation; SMD, spray mean diameter; SVM, support vector machine; SVR, support vector regression; TDC, top dead center; VGT, variable geometry turbocharging. ⇑ Corresponding author at: Mechanical Engineering Department, Technical Education Faculty, Urmia University, Urmia, West Azerbaijan 57561-15311, Iran. E-mail addresses: h.taghavifar@urmia.ac.ir, haditaghavifar@yahoo.com (H. Taghavifar). Energy Conversion and Management 126 (2016) 385–399 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman