Mixed-integer Nonlinear Programming Optimization Model Research Articles

Exploring optimal pathways of the high-CO2 content natural gas source to chemicals and fuels using superstructure multi-objective optimization

This study aims to develop a mathematical formulation of superstructure multi-objective optimization to find optimal pathways of high-CO2 natural gas and PV-hydrogen to chemicals and fuels integrated with CO2 sequestration. A mixed-integer nonlinear programming optimization model is used to compete along 56 pathways in the superstructure optimization network. The model was developed with the general algebraic modeling system and computed with the standard branch and bound (SBB) solver to maximize annual net profit and minimize annual net CO2 emissions. The result shows the selected products in 2020 are liquefied natural gas, methanol, dimethyl ether, formic acid, and acetic acid, with annual net profits and net CO2 emissions of 38.17 million $/year and −8.47 million tons of CO2/year, respectively. In the projection analysis, the annual net profit growth results at a compounding annual growth rate of 7.85% per year between 2020 and 2060, while annual net CO2 emissions decrease until −16.37 million tons of CO2/year in 2060. In 2030, blue acetic acid will be selected via all separation processes. For 2050, the synfuel via partial membrane separation is selected. The other products, formic acid, methanol, and acetic acid via membrane separation (full and partial), will always be selected between 2020 and 2060. Therefore, this could be a future strategy for monetizing high–CO2–content natural gas sources with low-carbon process development.

Cost-based site and capacity optimization of multi-energy storage system in the regional integrated energy networks

The unbalance between the renewable energy sources and user loads reduces the performance improvement of regional integrated energy systems (RIES), in which the multi-energy storage system with battery and heat tank is necessarily integrated. This paper aims to optimize the sites and capacities of multi-energy storage systems in the RIES. A RIES model including renewable wind power, power distribution network, district heating network, multi-energy storage system, and heat pump to convert electricity to heat is constructed. An optimization method combining a mixed-integer nonlinear programming optimization model is proposed to minimize the comprehensive cost of RIES. The second-order cone relaxation method performs convex relaxation of the power flow constraints, and the district heat network is operated under a constant-flow-variable-temperature strategy. The original optimization model is transformed into a mixed-integer second-order cone programming problem to solve. Three solution methods, including enumeration method, improved enumeration method and genetic algorithm, are employed to determine the optimum installation locations, and they are compared in computation time and efficiency. The results demonstrate that the distributed hybrid integration of electricity and thermal energy storages improves the RIES economy by collaborating the power and heat balances and reducing the purchased electricity from the grid. By integrating the hybrid storage system, the curtailed wind is reduced by 53.9%, and the economy is improved by 13.4%.

Cost Optimization of Reinforced Concrete Section According to Flexural Cracking

A series of distributed flexural cracks develop in reinforced concrete flexural elements under the working load. The control of cracking in reinforced concrete is an important issue that must be considered in the design of reinforced concrete structures. Crack width and spacing are influenced by several factors, including the steel percentage, its distribution in the concrete cross-section, the concrete cover, and the concrete properties. In practice, however, a compromise must be made between cracking, durability, and ease of construction and cost. This study presents the optimal design of a reinforced concrete cross-section, using the optimization method of mixed-integer nonlinear programming (MINLP) and the Eurocode standard. The MINLP optimization model OPTCON was developed for this purpose. The model contains the objective function of the material cost considering the crack width requirements. The crack width requirements can be satisfied by direct calculation or by limiting the bar spacing. Due to the different crack width requirements, two different economic designs of reinforced concrete sections were proposed. The case study presented in this study demonstrates the value of the presented optimization approach. A direct comparison between different methods for modelling cracking in reinforced concrete cross-sections, which has not been done before, is also presented.

Economic viability and optimization of solar microgrids with hybrid storage in a non-interconnected zone in Colombia

A developing country that does not have adequate energy solutions in non-interconnected zones (ZNIs) undoubtedly experiences adverse effects in terms of its competitiveness, as well as economic and social development. The primary sources of electrical energy in these communities are diesel generators, which are expensive and not environment-friendly. This paper seeks to describe how to reduce the consumption of this fossil fuel in ZNIs. The technical and economical implementation of a small-scale photovoltaic system with and without a hybrid energy storage system connected to the grid is studied, based on the incentive policy of the Colombian regulation. A mixed-integer nonlinear programming optimization model was developed, which includes the storage costs of a lead-acid battery and supercapacitor, to analyze the benefits of the electricity tariff and to maximize the revenues of the photovoltaic generation system. The conclusions of this study offer policy suggestions and economic incentives to enhance the use of renewable energy sources in the ZNIs of Colombia.

Groundwater contamination sources identification based on kernel extreme learning machine and its effect due to wavelet denoising technique.

Measurements of contaminant concentrations inevitably contain noise because of accidental and systematic errors. However, groundwater contamination sources identification (GCSI) is highly dependent on the data measurements, which directly affect the accuracy of the identification results. Thus, in the present study, the wavelet hierarchical threshold denoising method was employed to denoise concentration measurements and the denoised measurements were then used for GCSI. A 0-1 mixed-integer nonlinear programming optimization model (0-1 MINLP) based on a kernel extreme learning machine (KELM) was applied to identify the location and release history of a contamination source. The results showed the following. (1) The wavelet hierarchical threshold denoising method was not very effective when applied to concentration measurements observed every 2months (the number of measurements is small and relatively discrete) compared with those obtained every 2days (the number of measurements is large and relatively continuous). (2) When the concentration measurements containing noise were employed for GCSI, the identifications results were further from the true values when the measurements contained more noise. The approximation of the identification results to the true values improved when the denoised concentration measurements were employed for GCSI. (3) The 0-1 MINLP based on the surrogate KELM model could simultaneously identify the location and release history of contamination sources, as well reducing the computational load and decreasing the calculation time by 96.5% when solving the 0-1 MINLP.

Identification of groundwater contamination sources using a statistical algorithm based on an improved Kalman filter and simulation optimization

Identification of groundwater contamination sources, as a solution to an inverse problem, is mainly based on simulation optimization methods. However, the establishment and solution of an optimization model are extremely complicated for the inverse problem, where many decision variables need to be identified. Combining simulation optimization methods with other mathematical methods can effectively avoid this shortcoming. In order to identify features of contamination sources, the Kalman filter is combined with a mixed-integer nonlinear programming optimization model (MINLP). Firstly, the Kalman filter is improved by U-D decomposition (a matrix decomposition method) to identify the number and approximate locations of real contamination sources among potential contamination sources. A 0–1MINLP solution is then employed to identify the accurate location and release history of the contamination source. Kriging is used to produce a surrogate model for the numerical simulation model. The surrogate model approximates the numerical simulation model, which can be embedded in the 0–1MINLP instead of the numerical simulation model and it can be called directly during the iteration of the optimization model, thereby avoiding manually coupling the numerical simulation model with the optimization model during the solution process. Results demonstrate that the improved Kalman filter exhibits better numerical stability, where it can effectively avoid the filter divergence problem as well as solve the number and approximate locations of contamination sources in the inverse identification problem. The accurate location and release history of the contamination source can be effectively identified by using the 0–1MINLP.

Application of Mixed-Integer Nonlinear Optimization Programming Based on Ensemble Surrogate Model for Dense Nonaqueous Phase Liquid Source Identification in Groundwater

Groundwater contamination source identification (GCSI) is critical for taking effective measures to protect groundwater resources, assess risks, mitigate disasters, and design remediation strategies. Simulation–optimization techniques have been effective tools for GCSI. However, previous studies have applied individual surrogate models when replacing simulation models, rather than making efforts to combine various methods to improve the approximation accuracy of the surrogate model over the simulation model. In this study, the kernel extreme learning machine (KELM) model was proposed to enhance the surrogate model, and to approach GCSI problems, especially those of dense nonaqueous phase liquid-contaminated aquifers, more effectively. In addition, a kriging model and a support vector regression (SVR) model were built and compared with the KELM model, and various ensemble surrogate (ES) modeling techniques were applied to establish four ES models. Results showed that the KELM model was more accurate than the kriging and SVR models; however, the ES models performed much better than the three individual surrogate models. The most precise ES model increased the certainty coefficient (R2) to 0.9837, whereas limiting the maximum relative error to 13.14%. Finally, a mixed-integer nonlinear programming optimization model was established to identify the groundwater contamination source in terms of location and release history, and simultaneously assess aquifer parameters. The ES model developed in this article could reasonably predict the system response under given operation conditions. Replacement of the simulation model by the ES model considerably reduced the computation burden of the simulation–optimization process and simultaneously achieved high computation accuracy.

Optimal design of single-story steel building structures based on parametric MINLP optimization

The paper presents an optimal design of single-story industrial steel building structures based on the parametric mixed-integer non-linear programming (MINLP) optimization approach and Eurocode specifications. The optimal design of the structures was investigated for factors which have significant influence on the structure mass: vertical variable load on the structure, horizontal variable load, structure span, structure height, type of standard cross-sections and strength of structural steel.For this purpose, parametric MINLP optimization was performed for a number of combinations between different parameters, i.e. different values of the mentioned influence factors. The single-story steel building superstructure was generated and the MINLP optimization model developed. The objective function of the structure's mass was defined. The modified outer-approximation/equality-relaxation (OA/ER) algorithm and the three-phase MINLP strategy were used to perform the optimization. The minimal possible structure mass, the optimal topology and the optimal standard cross-sections were obtained through each individual MINLP optimization. Based on the obtained optimal results, the recommended optimal design for single-story/single-bay structures and the comparative mass diagrams were developed.

MINLP optimization model for the nonlinear discrete time–cost trade-off problem

This paper presents the mixed-integer nonlinear programming (MINLP) optimization model for the nonlinear discrete time-cost trade-off problem (NDTCTP). The nonlinear total project cost objective function of the proposed MINLP optimization model is subjected to a rigorous system of generalized precedence relationship constraints between project activities, project duration constraints, logical constraints, and a budget constraint. By means of the proposed MINLP optimization model, one can obtain the minimum total project cost, the project schedule with the optimal discrete start times and the optimal discrete durations of the activities, as well as the optimal time-cost curves of the project. The proposed model yields the exact optimum solution of the NDTCTP. Solving the NDTCTP, using the proposed MINLP model, avoids the need for (piece-wise) linear approximation of the nonlinear expressions. The MINLP model handles the discrete variables explicitly and requires no rounding of the continuous solution into an integer solution. The applicability of the proposed optimization model is not limited to weakly NDTCTPs. A numerical example from the literature and an example of the project time-cost trade-off analysis are presented at the end of the paper in order to show the advantages of the proposed model.