Integer Non-linear Programming Optimization Model Research Articles

Simultaneous identification of the number, location and release intensity of groundwater contamination sources based on simulation optimization and ensemble surrogate model

Abstract In most instances, the number, location and release intensity of groundwater contamination sources (GCSs) are all unknown. The 0-1 mixed integer nonlinear programming optimization model (0-1 MINPOM) used previously could only identify the location and release intensity for GCSs. Thus a 0-1 MINPOM was improved and applied to simultaneously identify the number, location and release history of GCSs. In addition, to reduce the time of calling the simulation model for iterative calculation, the deep belief neural network (DBNN), long short-term memory network (LSTM) and Kriging method were applied to establish an ensemble surrogate model of the simulation model to replace the simulation model for iterative calculation. The results show that compared with the three single surrogate models, the ensemble surrogate model has the highest approximation accuracy to the simulation model, and could save 99% of the calculation time when iterative calculation was performed in place of the simulation model. The improved 0-1 MINPOM could identify the number, location, and release history of GCSs simultaneously. The accuracy of identifying the number of GCSs was 100%, and the accuracies of identifying the locations and release history were above 95.12% and 83.51%, respectively.

Onsite generation system sizing for manufacturing plant considering renewable sources towards sustainability

Onsite generation system with renewable sources for manufacturing plant is considered a critical alternative energy source that can improve the sustainability and resilience for manufacturers. The optimal sizing for all the components of the onsite generation system under the variations of the uncertain energy demand from manufacturing plant plays a critical role in achieving a cost-effective operational mode. In this paper, a Mixed Integer Non-Linear Programming optimization model is proposed for sizing the capacity of onsite generation system with renewable sources and battery energy storage system for the manufacturers considering the energy loads from both manufacturing system and HVAC system in a typical manufacturing plant. An integrated simulation model is used to capture the variations of the plant-level electricity demand including both manufacturing and HVAC systems so that it can be used as the input to the proposed optimization model. Both linearization and meta-heuristic solution strategies are discussed and compared when solving the proposed optimization model considering both solution quality and computational time. A case study employing the relevant data of a real auto component manufacturing plant as well as the data of the renewable sources in the Chicago area is implemented to illustrate the effectiveness of the proposed model.

The application of 0–1 mixed integer nonlinear programming optimization model based on a surrogate model to identify the groundwater pollution source

The optimization model is presently used for the identification of pollution sources and it is based on non-linear programming optimization. The decision variables in this model are continuous, resulting in a weak recognition of integer variables including pollution source location. In addition, as the number of pollution sources increase, so the calculated load increases exponentially and accuracy decreases. Compared with previous studies, this study makes a series of improvements by adopting a 0–1 mixed integer nonlinear programming optimization model to enable the simultaneous identification of both location (integer variable) and the release intensity (continuous variable) of the pollution source. One of the constraints in the optimization model is a simulation component which requires thousands of calls during the calculation process and therefore requires considerable computational load. To avoid this problem, the Kriging surrogate model is established in this study to reduce computational load, while at the same time ensuring the accuracy of the simulation results. The identification result is solved using a genetic algorithm (GA) and represents the real location of the pollution source, while release intensities are close to actual ones with small relative errors. The Kriging surrogate model is based on a 0–1 mixed integer nonlinear programming optimization model and can simultaneously identify both the location and the release intensity of the pollution source with a high degree of accuracy and by using short computational times.

Robust investment model for long-range capacity expansion of chemical processing networks under uncertain demand forecast scenarios

The problem of long-range capacity expansion planning for chemical processing networks under uncertain demand forecast scenarios is addressed. This optimization problem involves capacity expansion timing and sizing of each chemical processing unit to maximize the expected net present value while considering the deviation of net present values and the excess capacity over a given time horizon. A multiperiod mixed integer nonlinear programming optimization model that is both solution and model robust for any realization of demand scenarios is developed using the two-stage stochastic programming modeling framework. Two example problems are considered to illustrate the effectiveness of the model. Especially, the use of the model is illustrated on a real problem arising from investment planning in Korean petrochemical industry.