Developing more energy-efficient and environmentally friendly transportation technologies, that can enable to use significantly less petroleum and to reduce regulated emissions while meeting or exceeding drivers' performance expectations, has always been one of the main challenges in automotive technology. Therefore, based on an experimental dataset, metamodels were generated using design of computer experiments and central composite design technique in order to accurately predict carbon monoxide (CO), oxides of nitrogen (NO x ), hydrocarbon (HC) and carbon dioxide (CO 2 ) emissions, mean effective pressure and exergy destruction due to heat transfer and combustion process. Combustion metamodels was evaluated varying air-fuel ratio, ignition timing [( • CAD) Crank Angle Degrees], compression ratio, and combustion duration ( • ) on the performance of a Spark Ignition (SI) engine at constant speed of 750 rpm. Because SI gasoline engines always encounter the decreased thermal efficiency and increased toxic emissions at idle (Jurgen in Automotive electronics handbook, McGraw-Hill, New York, 1995). The Akaike information criterion was applied to automatically select the best metamodel for each case.

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This work develops a systematic methodology able to identify the desired work points, the metamodels were evaluated varying air-fuel ratio, ignition timing, compression ratio, and combustion duration using design of computer experiments and RSM. It provide the possibility to determine optimal control parameters, according to selected objectives and operating constraints. This methodology is able to automatically identify the optimal engine calibration with less computational effort. Only in this way, the reliability of an integrated metamodel/optimizer approach can be included in a general-purpose that is to identify the engine calibration that minimizes motor vehicle emissions according to European emission standards (European Union in Off J Eur Union 50, 2007). As long as it improves mean effective pressure and reduces exergy destruction due to heat transfer and combustion process. Since, in internal combustion engines, more than 30-40 % of fuel energy wastes through the exhaust and just 12-25 % of the fuel energy converts to useful work. So, researchers are motivated to recover the heat from the waste sources in engines using the ways which not only reduce the demand of fossil fuels, but also reduce the harmful greenhouse gases and help to energy saving (Hatami et al. in Neural Comput Appl 25(7-8):2079-2090. The advantages of this contribution include the ability to study a wide range of parametric space and to independently evaluate physical and chemical processes, and detailed in-cylinder information, which is normally not available or is inaccessible in experiments. The uncertainty of the information in this unexplored design region can be quantified. Finally, the problem of optimizing involves three optimization fronts, energetic, economic and ecological (Chica and Torres in Int J Interact Des Manuf 12(1): 2018).