Nonlinear Programming Approach Research Articles

Performance Optimization of a Spark Ignition Engine Fueled with Gasoline-Bioethanol (E85) Using RSM and Non-Linear Programming Approach

The aims of this work are to obtain the characteristics and the performance optimization of the spark-ignition engine and single-cylinder by using the gasoline-bioethanol fuel blend in composition 15%-85% (E85). The Response Surface Methodology (RSM) and the Non-Linear Programming are applied in this work in order to find the area and the optimization point of the engine performances. The engine operates on different engine speeds in the range 2000–8000 RPM (increment 1000 RPM), ignition timing in interval 12–28 BTDC (increment 4 BTDC) and compression ratio in range 12–13 (increment 0.5). All the performance engine parameters of E85 fuel are better than gasoline engine performance except for specific fuel consumption and thermal efficiency that is worse than E0. Those results will be obtained when the engine parameters work on the compression ratio, 16-20 BTDC (before top dead center) of ignition timing, and higher than 4000 RPM (revolution per minute). Meanwhile, the optimization of the engine performances has been done by using Box Behnken design of response surface methodology. The methodology shows that the optimal values of the engine performance are obtained for 13:1 of compression ratio (CR), 24 BTDC of Ignition Timing (IT) and 7240 RPM of engine speed. The result of this study has revealed that at optimal parameters the values of the brake power, brake torque, thermal efficiency, mean effective pressure, specific fuel consumption, CO and HC emissions have been 12.68 HP, 12.90 Nm, 32.4%, 1083.8 kPa, 0.004224 kg/hp h, 2.6% and 89.9 ppm respectively.

A Nonlinear Goal Programming Approach with a Modified Search Algorithm to Achieve Student Outcomes in College Education

A Nonlinear Goal Programming Approach with a Modified Search Algorithm to Achieve Student Outcomes in College Education

Optimized packing unequal spheres into a multiconnected domain: mixed-integer non-linear programming approach

The problem of packing unequal spheres into a multiconnected domain (container) is considered. Given a set of spheres, the objective is to maximize the packing factor. The problem is considered as a knapsack problem and modelled as a mixed-integer non-linear programming. Characteristics of the model are indicated. We propose a new solution method based on a combination of a branch-and-bound approach and the known local optimization method. The search procedure is represented by a tree which allows handling all possible subsets of spheres. We develop a set of truncation rules to reduce the number of variants under test. The local optimization algorithm proceeds from the assumption of spheres radii being variable. A number of numerical examples are given.

Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach

An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.

One-step optimization strategy in the simulated moving bed process with asynchronous movement of ports: A VariCol case study

The VariCol process is a variant of the conventional simulated moving bed (SMB) process, distinguished by the asynchronous shifting of the inlet and outlet ports of the chromatographic column train. This feature allows for a more flexible operation in column utilization and can also achieve higher separation performances. However, to take full benefit out of it, the operating parameters, such as the strategy for port switching, must be optimal. in this paper, a novel methodology for optimizing those parameters, based on a single NLP (non-linear programming), is proposed. The main advantage of this approach is that it significantly reduces the complexity of the original MINLP (mixed-integer non-linear programming) formulation currently discussed in the literature. The proposed optimization problem is built, considering that the average column configuration of three zones provides the necessary and sufficient information to describe the VariCol process. Several optimization scenarios for the enantioseparation of 1,1´-bi-2-naphthol and aminoglutethimide were considered to evaluate the proposed methodology and to compare the performance of VariCol and SMB processes. The results have shown that with the single NLP approach, it is possible to explore the optimal solution in all the VariCol process domains with less computational effort than other optimization strategies reported in the literature. That is a great advantage, especially in the context of real-time applications.

Quantifying and managing the water-energy-food nexus in dry regions food insecurity: New methods and evidence

Ensuring water, energy, and food security with minimum damage to groundwater resources is a key challenge to achieve sustainable development in arid areas. To address this scientific and policy challenge, a Multi-Criteria Decision-Making (MCDM)-nonlinear programming approach is developed for informing debates over improved management of the groundwater, energy, and food nexus that optimally allocates resources to food production to improve economic benefit and control groundwater depletion. Furthermore, this approach is capable of evaluating management policies affecting resource planning at a regional level. The approach is applied to the Neishaboor basin in northeast Iran. The main results are: (i) economic profit and food production depend on groundwater availability and energy use, which raise environmental protection challenges; (ii) the solutions could be used to define optimal policy strategies for sustainable management of groundwater, energy, food, and simultaneously achieve economic and environmental goals; (iii) improved irrigation efficiency would be considered as an efficient strategy under conditions of growing water scarcity. The results of this research can inform policy makers on effective strategies for integrated groundwater, energy, and food planning.

Optimization of Sampling for Monitoring Chemicals in the Food Supply Chain Using a Risk-Based Approach: The Case of Aflatoxins and Dioxins in the Dutch Dairy Chain.

Food safety monitoring faces the challenge of tackling multiple chemicals along the various stages of the food supply chain. Our study developed a methodology for optimizing sampling for monitoring multiple chemicals along the dairy supply chain. We used a mixed integer nonlinear programming approach to maximize the performance of the sampling in terms of reducing the risk of the potential disability adjusted life years (DALYs) in the population. Decision variables are the number of samples collected and analyzed at each stage of the food chain (feed mills, dairy farms, milk trucks, and dairy processing plants) for each chemical, given a predefined budget. The model was applied to the case of monitoring for aflatoxin B1/M1(AFB1/M1) and dioxins in a hypothetical Dutch dairy supply chain, and results were calculated for various contamination scenarios defined in terms of contamination fraction and concentrations. Considering various monitoring budgets for both chemicals, monitoring for AFB1/M1 showed to be more effective than for dioxins in most of the considered scenarios, because AFB1/M1 could result into more DALYs than dioxins when both chemicals are in same contamination fraction, and costs for analyzing one AFB1/M1 sample are lower than for one dioxins sample. The results suggest that relatively more resources be spent on monitoring AFB1/M1 when both chemicals’ contamination fractions are low; when both contamination fractions are higher, relatively more budget should be addressed to monitoring dioxins.

Innovative numerical form-finding of tensegrity structures

An innovative numerical platform for the form-finding of tensegrity structures is proposed. A particular objective function is introduced based on LU-decomposition of the force density matrix. The required rank deficiency of the force density matrix, which is a crucial quantity in the form-finding process, is then pursued by minimisation of the mentioned objective function. The gradient and hessian of the objective function are also derived explicitly. This critical feature enables us to efficiently employ powerful nonlinear programming approaches in the form-finding problems. Four numerical examples are provided to validate the feasibility and effectiveness of the method proposed. The results compared and contrasted from different aspects with existing analytical and some well-known numerical solutions. The comparisons verify that the method proposed is highly accurate and fast; therefore, it can be used as a compelling alternative to the available numerical form-finding methods.

Using the hierarchical Kriging model to optimize the structural dynamics of rocket engines

Traditional fine models are often inefficient in optimizing the dynamics of complex structural systems such as large liquid rocket engines. To enhance the design efficiency, this paper proposes a fast optimization method based on finite element modeling, central Latin hypercube experimental design with minimax criteria, hierarchical Kriging surrogate model, and combined multi-island genetic algorithm + nonlinear sequential quadratic programming approach. First, a low-frequency dynamic fine finite element model of the entire engine structure was established, and the sampling points were obtained by considering the experimental design and a hierarchical Kriging model that describes the relationship between the design variables of the engine structure parameters and the modal frequency characteristics. Next, the height of the frame, size of the gimbal mount, and stiffness and installation angle of the servo mechanism were considered as design variables. To satisfy the design requirements in terms of the first modal frequency of the engine structure and realize the optimal design of the modal characteristics, the global optimization of the high-precision Kriging model was performed in the design space by using the hybrid optimization algorithm. Finally, the optimization results were substituted into the finite element model to perform the modal analysis, and modal tests were conducted to verify the effectiveness of the optimization method in realizing large-scale structural system optimization. The results indicated that the first modal frequency of the engine structure was increased from 7.53 Hz to 11.50 Hz and the optimization results could satisfy the requirements for the dynamics design. The proposed optimization design method can considerably improve the optimization efficiency by ensuring high accuracy of the results. The presented modeling strategies and optimization concepts can be applied to several engineering applications and provide novel solutions for the dynamic optimization problems of large and complex structures.

Two penalized mixed–integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models

<p style='text-indent:20px;'>In classical regression analysis, the ordinary least–squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least–squares regression. In this situation, robust estimators are widely used because of their lack of sensitivity to outlying data points. Multicollinearity is another common problem in multiple regression models with inappropriate effects on the least–squares estimators. So, it is of great importance to use the estimation methods provided to tackle the mentioned problems. As known, robust regressions are among the popular methods for analyzing the data that are contaminated with outliers. In this guideline, here we suggest two mixed–integer nonlinear optimization models which their solutions can be considered as appropriate estimators when the outliers and multicollinearity simultaneously appear in the data set. Capable to be effectively solved by metaheuristic algorithms, the models are designed based on penalization schemes with the ability of down–weighting or ignoring unusual data and multicollinearity effects. We establish that our models are computationally advantageous in the perspective of the flop count. We also deal with a robust ridge methodology. Finally, three real data sets are analyzed to examine performance of the proposed methods.</p>

A mixed integer nonlinear programming approach for integrated bio-refinery and petroleum refinery topology optimization

Abstract The conversion of biomass into gasoline and diesel in bio-refinery process is an attractive process given its carbon neutral and sustainable nature. The economics of bio-refinery can be improved via integration with petroleum refinery, whereby bio-refinery intermediates can be processed into gasoline and diesel in the well-established petroleum refinery processing units, i. e., hydrocracking (HC) and fluidized catalytic cracking (FCC) units. However, the integration of the new bio-refinery into the existing petroleum refinery may not give the optimum solution given the capacities constraints of the existing petroleum refinery upgrading units such as FCC and HC units. Thus, this work proposed a superstructure comprising new bio-refinery and new petroleum refinery block diagrams. The superstructure was formulated into mixed integer nonlinear programming (MINLP) model. The model was coded into general algebraic modeling system (GAMS) platform and solved using global optimum solver, LINDOGLOBAL. The model application was demonstrated using representative case study. The model results showed that the optimum integrated bio-refinery and petroleum refinery topology favors the upgrading of bio-refinery intermediates using petroleum refinery HC unit under one-through operation mode with a marginal increase in the profit of about 0.39% compared to the second optimum case of upgrading bio-refinery intermediate using petroleum refinery FCC unit under gasoline operation mode. Thus, the decision in selecting the most suitable topology can be made based on the market demand for gasoline and diesel as the topology that uses FCC maximizes gasoline production and the topology that uses HC maximizes diesel production.

High-Fidelity Harmonic Generation in Optical Micro-Resonators Using BFGS Algorithm.

Harmonic generation is an attractive research field that finds a variety of application areas. However, harmonic generation within a medium of micron-scale interaction length limits the magnitude of nonlinear coupling and leads to poor harmonic generation efficiency. In this study, we present a constrained non-linear programming approach based on the Quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to obtain high-fidelity harmonic generation in optical micro-resonators. Using this approach, one can achieve high-intensity harmonic generation in a simple Fabry–Perot type optical micro-resonator. The generation of super-intense harmonics at a typical ultraviolet (UV)-ablation frequency of 820 THz and at pure yellow-light (515 THz) is investigated in particular. Moreover, we achieved more than 98% accuracy compared to well-known theoretical results. Our approach enables the design of highly efficient microscale harmonic generators to be used in integrated photonic devices.

Analysis of biomass polygeneration integrated energy system based on a mixed-integer nonlinear programming optimization method

The increase of climate disasters and air pollution has caused an urgent need for the clean and low carbon energy transition. In this background, polygeneration represents an innovative and promising concept. The purpose of this study is to provide a generic modelling and optimization strategy to evaluate the polygeneration systems in urban areas. A biomass polygeneration integrated energy system, providing electricity, heating and cooling as well as chemical product, is proposed and evaluated in this work. The feasibility of biomass polygeneration integrated energy system in different regions is also investigated by case study. A mixed-integer nonlinear programming approach has been formulated in General Algebraic Modeling System to address the following issues: a) selection of technologies, types and numbers of equipment to match the energy demand of end users; b) strategic planning and process designing from both economic and environmental perspectives; c) representation of the relationships and trade-offs between the trigeneration and chemical conversion steps; d) operation strategies for biomass polygeneration integrated energy system with time dependent process and boundary conditions. Moreover, the proposed biomass polygeneration integrated energy system is compared to the conventional natural gas-based combined cooling heating and power system as the reference.

A fuzzy nonlinear programming approach for planning energy-efficient wafer fabrication factories

Wafer fabrication is an energy-consuming process. Achieving energy efficiency is, therefore, crucial for wafer fabrication factories (wafer fabs). However, limited studies have focused on resolving product quality problems for improving energy efficiency. This study proposed a novel fuzzy nonlinear programming (FNLP) approach for minimizing energy wastage caused by product quality problems. In the proposed methodology, first, the process of resolving the quality problems of a product is modeled as a fuzzy yield learning process. Then, the energy saved by the yield learning process is quantified. The total power consumption is obtained by summing the power consumptions of all the products in a wafer fab. Subsequently, an FNLP model is formulated and optimized to minimize the total energy consumption in the wafer fab by optimizing the product mix. The data from a wafer fab is used to demonstrate the applicability of the proposed FNLP approach. According to the experimental results, the total power consumption at a future period can be reduced by 17.2% by optimizing the product mix.

A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

Optimization for multi-objective sum of linear and linear fractional programming problem: fuzzy nonlinear programming approach

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

Optimal offshore wind farms connection considering the wind capacity maximisation – a Benders decomposition approach

This study presents a new methodology to determine the optimal Offshore Wind Farms connection point in a power system, with the purpose of maximising the wind power penetration, considering a Benders decomposition approach to represent the security constraints related to the ‘’ contingency criterion. The proposed algorithm uses a mixed-integer non-linear programming approach associated with a non-linear programming, and it is evaluated in a tutorial system (IEEE 14-Bus) and two networks from the literature: a small case (IEEE RTS-79), and a medium and real case (Brazilian Birds System). In each case, three points geographically close to each other are selected as candidates in the onshore grid for the wind power injection. The experiments conducted clearly show that the connection decision from the proposed approach led to the maximum safe wind power penetration among the candidate options, which proves its applicability and effectiveness, even for more complex networks, and considering all single transmission line contingencies for safe operation.

Optimization of real-world outdoor campaign allocations

In this paper, we investigate the outdoor campaign allocation problem OCAP , which asks for the distribution of campaign items to billboards considering a number of constraints. In particular, for a metropolitan city with a large number of billboards, the problem becomes challenging. We propose a genetic algorithm-based method to allocate campaign items effectively, and we compare our results with those of nonlinear integer programming and greedy approaches. Real-world data sets are collected with the given constraints of the price class ratios of billboards located in Istanbul and the budgets of the given campaigns. The methods are evaluated in terms of the efficiency of the constructed plans and the construction time of the planning. The results reveal that the genetic algorithm-based approach gives close to optimal results in the shortest scheduling time for the OCAP, and it scales linearly with the increasing data sizes.

Fuzzy metrics and cost optimization of a fault-tolerant system with vacationing and unreliable server

A finite population fuzzy model for the fault-tolerant system (FTS) is studied by considering the general distributed repair time, server vacation, and server breakdown. The concept of imperfect recovery, along with reboot process, is considered for the evaluation of fuzzy performance indices of an FTS supported by warm standbys. If the faults in the system are not detected successfully, then FTS reconfigures itself automatically by rebooting. When the system becomes free from the assigned repair jobs, the idle server can take a vacation and returns from the vacation in case a machine fails and requires repair. The single failure-prone server can provide the repair of failed machines with a slower rate in the breakdown state also. The parametric non-linear programming approach is implemented for the evaluation of performance metrics in a fuzzified environment using system parameters as a trapezoidal fuzzy number. The supplementary variable and recursive approaches are employed to obtain the system size distribution of the M/G/1 model by taking remaining repair time as a supplementary variable. The cost analysis is performed in order to determine the suitable control parameters using harmony search approach. The impacts of the sensitive system parameters on the performance of FTS are explored by evaluating numerical results for specific distributions of repair time.

Optimum location of outrigger in tall buildings using finite element analysis and gradient-based optimization method

In this study, the optimum locations of outriggers minimizing the top drift of tall buildings are identified using a gradient-based nonlinear programming approach. Since the proposed optimization method uses finite element analysis to evaluate the objective function for arbitrarily configured buildings, the discontinuity due to design variables (such as outrigger locations) is overcome by piecewise linear and quadratic interpolation functions. A series of optimum designs for three analysis models with different vertical profiles were performed to investigate the relation between outrigger stiffness and optimum location by changing the cross-sectional area of outriggers. As outrigger cross-sectional area increases, the optimum outrigger location moves down in the structure. The design result demonstrates that correlation between outrigger stiffness in a practical range and its optimum location is negligible; thus, for design purposes, variables related to outrigger optimum location and its stiffness can be dealt with separately.