Mixed Integer Nonlinear Programming Algorithm Research Articles

The Research of Microgrid Optimized Dispatching Method Based on MEA

Integration of large scale renewable energy sources and electric cars into power grid will bring new opportunities and challenges to the operation, control of the power grid and the power market .The microgrid , which integration the distributed generation systems, energy storage element and loads ,has been seen as one effective way to solve the problems. This paper proposed a MEA-based scheduling algorithm, and studied a microgrid that contains 32 nodes and 50 electric cars. Both the MEA algorithm and mixed integer nonlinear programming algorithm (MINLP) can solve the energy resource scheduling problem,but the results of our simulation shows that the total cost of MEA is higher than that of the MINLP,but there is a significant improvement in the efficiency of execution.The results shows that we can use MEA to achieve optimal scheduling,it also verify the effectiveness of the algorithm.

Design of Sustainable Product Systems and Supply Chains with Life Cycle Optimization Based on Functional Unit: General Modeling Framework, Mixed-Integer Nonlinear Programming Algorithms and Case Study on Hydrocarbon Biofuels

We propose a life cycle optimization framework for the design of sustainable product systems and supply chains considering the concept of “functional unit” under economic and environmental criteria. This general modeling framework integrates the life cycle analysis methodology with multiobjective optimization and measures both the economic and environmental performances based on a standard quantity of functional unit associated with final products. The Pareto-optimal frontier returned by the multiobjective optimization problem reveals the trade-off between the economic and environmental objectives. We also present tailored optimization algorithms for efficiently solving the mixed-integer linear fractional programming problems, which result from the life cycle optimization framework. We apply the proposed life cycle optimization framework to a case study on the hydrocarbon biofuels through a spatially explicit model for the county-level supply chain in Illinois. The Pareto-optimal results show that the env...

Planning and scheduling of flexible process networks under uncertainty with stochastic inventory: MINLP models and algorithm

The tactical planning and scheduling of chemical process networks consisting of both dedicated and flexible processes under demand and supply uncertainty is addressed. To integrate the stochastic inventory control decisions with the production planning and scheduling, a mixed‐integer nonlinear programming (MINLP) model is proposed that captures the stochastic nature of the demand variations and supply delays using the guaranteed‐service approach. The model takes into account multiple tradeoffs and simultaneously determines the optimal selection of production schemes, purchase amounts of raw materials, sales of final products, production levels of processes, detailed cyclic production schedules for flexible processes, and working inventory and safety stock levels of all chemicals involved in the process network. To globally optimize the resulting nonconvex MINLP problems with modest computational times, the model properties are exploited and a tailored branch‐and‐refine algorithm based on the successive piecewise linear approximation is proposed. To handle the degeneracy of alternative optima in assignment configurations of production scheduling, three symmetry breaking cuts are further developed to accelerate the solution process. The application of the model and the performance of the proposed algorithm are illustrated through three examples with up to 25 chemicals and 16 processes including at most 8 production schemes for each flexible process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1511–1532, 2013

On the generalization of ECP and OA methods to nonsmooth convex MINLP problems

In this article, generalization of some mixed-integer nonlinear programming algorithms to cover convex nonsmooth problems is studied. In the extended cutting plane method, gradients are replaced by the subgradients of the convex function and the resulting algorithm shall be proved to converge to a global optimum. It is shown through a counterexample that this type of generalization is insufficient with certain versions of the outer approximation algorithm. However, with some modifications to the outer approximation method a special type of nonsmooth functions for which the subdifferential at any point is a convex combination of a finite number of subgradients at the point can be considered. Numerical results with extended cutting plane method are also reported.

Towards globally optimal operation of water supply networks

This paper is concerned with optimal operation of pressurized water supply networks at a fixed point in time. We use a mixed-integer nonlinear programming (MINLP) model incorporating both the nonlinear physical laws and the discrete decisions such as switching pumps on and off. We demonstrate that for instances from our industry partner, these stationary models can be solved to $\epsilon$-global optimality within small running times using problem-specific presolving and state-of-the-art MINLP algorithms. <br> In our modeling, we emphasize the importance of distinguishing between what we call real and imaginary flow, i.e., taking into account that the law of Darcy-Weisbach correlates pressure difference and flow along a pipe if and only if water is available at the high pressure end of a pipe. Our modeling solution extends to the dynamic operative planning problem.

Rigorous-simulation pinch-technology refined approach for process synthesis of the water–gas shift reaction system in an IGCC process with carbon capture

Integrated gasification combined cycle (IGCC) technology is becoming increasingly more competitive among advanced power generation systems suitable for carbon capture. As an emerging technology, many different IGCC process configurations have been heuristically proposed to meet even more aggressive economic and environmental goals. One attractive design combines gasification with a water–gas shift (WGS) reaction system, pressure swing adsorption, and chemical-looping combustion (CLC) for CO 2 removal prior to feeding the fuel gas to the combined cycle for power production. The WGS reaction step is required to convert CO to CO 2 and the extent of conversion is determined by the degree of carbon capture required in the CLC step. As a first towards optimizing the overall energy efficiency of this IGCC process, we apply heat exchanger network synthesis (HENS) to the WGS reaction system. This particular part of the process was chosen because of its evident integration potential (steam required for the WGS reactions can be generated by recovering energy released by the same reactions) and the influence of some of the gasifier parameters (temperature and pressure) on its performance and on all the subsequent parts of the process. After generating alternative designs using Aspen Energy Analyzer (AEA), the HENS problem was formulated in the sequential-modular Aspen Plus simulator using a process superstructure approach and solved by mixed integer nonlinear programming (MINLP) algorithms. The HENS capability is implemented as CAPE-OPEN (CO) compliant unit operation and makes use of MINLP algorithms, namely Generalized Bender's Decomposition (GBD), Outer Approximation (OA), Equality Relaxation (ER), Augmented Penalty (AP), and Simulated Annealing (SA). This MINLP-based HENS was used in the CO-compliant Aspen Plus simulator to obtain a design for the WGS reaction system that provided a cost of energy for the IGCC system with CO 2 capture that was 28% lower than the base case.

Optimal Distribution-Inventory Planning of Industrial Gases. II. MINLP Models and Algorithms for Stochastic Cases

In this article, we consider inventory-distribution planning under uncertainty for industrial gas supply chains by extending the continuous approximation solution strategy proposed in part I of this work. A stochastic inventory approach is proposed and incorporated into a multiperiod two-stage stochastic mixed-integer nonlinear programming (MINLP) model to handle uncertainty in demand and loss or addition of customers. This nonconvex MINLP formulation takes into account customer synergies and simultaneously predicts the optimal sizes of customers’ storage tanks, the safety stock levels, and the estimated delivery cost for replenishments. To globally optimize this stochastic MINLP problem with modest computational time, we develop a tailored branch-and-refine algorithm based on successive piecewise-linear approximation. The solution from the stochastic MINLP is fed into a detailed routing model with a shorter planning horizon to determine the optimal deliveries, replenishments, and inventories. A clustering-based heuristic is proposed for solving the routing model with reasonable computational effort. Three case studies including instances with up to 200 customers are presented to demonstrate the effectiveness of the proposed stochastic models and solution algorithms.

A linear programming-based optimization algorithm for solving nonlinear programming problems

Abstract In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.

Yield optimization of regulated metabolic systems using deterministic branch‐and‐reduce methods

This paper addresses product yield optimization in microorganisms grown in continuous culture. Traditional optimization strategies of random mutagenesis and selection will eventually have limited efficacy, thus requiring more focused strategies. The best candidates for such strategies appear to be mathematical models that capture the essence of metabolic systems and permit optimization with computational methods. In the past, models used for this purpose have been stoichiometric, kinetic in the form of S-systems, or ad hoc. This work presents a deterministic approach based on generalized mass action (GMA) systems. These systems are interesting in that they allow direct merging of stoichiometric and S-system models. Two illustrations are considered. In the first case, the fermentation pathway in Saccharomyces cerevisiae is optimized for ethanol production under steady-state conditions. The model of this pathway is relatively small, with five states and eight rate constants. The second example addresses the maximization of citric acid in the mold Aspergillus niger. For the optimization of this larger pathway system with 30 states and 60 reactions, a Mixed Integer Nonlinear Programming (MINLP) is proposed. It is shown that efficient MINLP algorithms, based on convexification, branch-and-reduce methods, and binary variable selection, are essential for solving these difficult optimization problems.

A trust region SQP algorithm for mixed-integer nonlinear programming

We propose a modified sequential quadratic programming method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when in- or decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a trust region method with Yuan’s second order corrections. It is not assumed that the mixed-integer program is relaxable or, in other words, function values are evaluated only at integer points. The Hessian of the Lagrangian function is approximated by a quasi-Newton update formula subject to the continuous and integer variables. Numerical results are presented for a set of 80 mixed-integer test problems taken from the literature. The surprising result is that the number of function evaluations, the most important performance criterion in practice, is less than the number of function calls needed for solving the corresponding relaxed problem without integer variables.

Modeling optimal dietary pigmentation strategies in farmed Atlantic salmon: Application of mixed-integer non-linear mathematical programming techniques

The most important visual quality characteristic of Atlantic salmon is the red/pink flesh color. The primary source of this coloration in salmon is caused by deposition of relatively large amounts of pigments, such as astaxanthin, obtained from their diet. Astaxanthin is expensive, and in commercial farming practice, dietary color pigments comprises about 15–20% of the total feed cost. One important operational process in commercial fish farms is therefore to minimize pigment costs. Based on recent models on the effects of dietary pigment concentration and fish size on visual color perception of Atlantic salmon, this study has built a mathematical programming model designed to optimize dietary astaxanthin concentrations throughout the grow-out period that results in well-pigmented fish at minimum cost. We have applied a mixed-integer non-linear programming algorithm to solve this problem. Various managerial implications of applying optimization models in product quality management of farmed salmon are discussed.

Applying Optimization Technology in Reservoir Management

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose:to inform the general readership of recent advances in various areas of petroleum engineering. Abstract This paper presents the application of optimization techniques in reservoir management to determine the best development plan that maximizes the economic performance of an asset. A distinguishing characteristic of this approach is that it can evaluate all feasible scenarios for a specific financial objective within a set of well-defined constraints. The output of this integrated workflow is a complete set of decisions that drive capital investment, development scheduling, production, hydrocarbon recovery, and, ultimately, economic performance of the asset. The conventional approach to reservoir management often considers a limited number of development options because of the complexity of the events within an investment plan and the time required for the evaluation. Input into the decision-making process traditionally comes in the form of sensitivity analyses from reservoir simulation, cost engineering, wellbore planning, pipeline networking, and project economic-analysis tools. These technologies are used to simulate performance by examining a specific development scenario, calculating future production, and performing a discounted cash-flow analysis to assess the return on the required investment. The exact scheduling of new infrastructure and production facilities as well as the drilling and stimulation of additional wells is critical to maximizing economic performance, especially if remaining reserves are material in size. These discrete events sometimes receive little attention. While the industry's ability to predict asset performance and assimilate several diverse perspectives together has significantly advanced, many reservoir-management decisions still are based on heuristics, rules of thumb, analogs to other assets, and ease of execution. Use of optimization techniques is not new in the energy business. However, in reservoir management, the technology must cope with more nonlinear phenomena within the physical system, complex and realistic objective functions and constraints, and discrete decisions that occur at distinct points over the asset life. The use of mixed-integer nonlinear programming algorithms can be useful in these situations. These algorithms implicitly construct a tree of all possible development plans and then efficiently prune the branches to eliminate candidates that can be shown to be nonoptimal. The effectiveness of optimization technology is illustrated by applying it to the ongoing expansion of a regional complex of gas reservoirs. The approach is used to determine the development schedule of the different reservoirs and the timing of their wells, the timing and staging of compression, and the development of satellites to meet a contract specification.

Heat integration between processes: Integrated structure and MINLP model

The previous method of integration [Kovač Kralj, A., Glavič, P., & Krajnc, M. (2002). Waste heat integration between processes. Applied Thermal Engineering, 22, 1259–1269] was extended to heat integration between processes using three possible steps: 1. internal integration of individual processes; 2. analysis of possible heat transfer between internally nonintegrated and integrated processes; 3. simultaneous external heat integration between the internally nonintegrated and the best internally integrated processes using the mixed integer nonlinear programming (MINLP). The method is based on energy saving. Simultaneous integration between processes can be performed using MINLP algorithm (step 3), in which alternatives suggested by pinch analysis of the heat transfer between several internally nonintegrated and integrated processes can be included (step 2). The fraction of the maximum integration between processes can be calculated. The integration between the processes can be carried out using all the three steps, or by the first and the third step or by the last step only, depending on the complexity of the problems. The method is very general, it can be used in new designs and in existing processes integration. The approach has been illustrated by integrating four existing complex processes using pinch analysis and MINLP. The objective was to maximize the annual profit of integration between processes and retrofits. The simultaneous MINLP integration of the four processes has selected only two retrofitted ones yielding total additional profit of 1.94 MUSD/a.

A Modular Mixed‐Integer Non‐Linear Programming Algorithm for Synthesis of Chemical Processes

AbstractA modular approach to the formulation and a solution of mixed‐integer non‐linear programming (MINLP) problems are presented, which reduce the size of MINLP and the computational expenses effectively. The method decomposes the synthesis task into three hierarchical levels—the superstructure, the structure, and the modules, with the layer of modules being the most critical to the problem solution. The strategy has been implemented in a simulation environment in which the variables of interest are defined as implicit functions of the optimization variables. The implicit relationships are handled using a data‐oriented process simulation technique (DOPS) that significantly simplify the simulation. The method has been effectively applied to two case studies, one from literature for the synthesis of hydrodesalkylation, and another from industrial process manufacturing methylene diphenylene diisocyanates.

Waste heat integration between processes

Energy integration between several processes has been applied giving more economical and profitable operation. The method for waste heat integration of several processes was analysed to reduce energy usage in three possible steps: 1. retrofit of the individual processes, 2. analysis of efficient transfer of waste heat between: ◦ existing non-retrofitted processes ◦ existing non-retrofitted and efficiently retrofitted processes ◦ efficient retrofits and 3. simultaneous integration between some non-retrofitted and some retrofitted existing processes using mixed integer non-linear programming (MINLP). The integration between the processes can be carried out by all the steps, or by the first and the third steps or only by the last step depending on the complexity of the problems. All the steps can be carried out simultaneously and the MINLP algorithm applied with or without the first and the second step. The approach has been illustrated by four complex processes using pinch analysis and MINLP. The optimal solution of pinch analysis and MINLP yields the same additional savings of 526 000 USD/a and selects the same structure and parameters as the MINLP one.

Comparison of certain MINLP algorithms when applied to a model structure determination and parameter estimation problem

The maximum likelihood method is frequently used in parameter estimation. If the structure of the model is unknown, the maximization of the likelihood function can be replaced by minimizing an information criterion. One criterion that allows this to be done is Akaike’s information criterion (AIC). Minimizing the AIC is a mixed integer non-linear programming (MINLP) problem. In this paper, three different MINLP algorithms are compared in the solution of a simultaneous model structure determination and parameter estimation problem by minimizing the AIC criterion. The problem considered appears in quantitative Fourier transformed infra red (FTIR) spectroscopy where concentration estimates of certain gas components are to be obtained from measured absorbances at different wave numbers. The resulting problem is a large MINLP problem containing several hundreds, or even thousands, of variables including a huge number of possible model structures. It is, however, found that the studied algorithms solve the considered problem in quite a small number of iterations and a reasonable CPU-time.

Retrofit of complex and energy intensive processes

Sequential structural and parameter optimization of retrofitted complex and energy intensive continuous processes has been studied. A method for sequential optimization of retrofits, combined sequential approach has been developed using pinch analysis, an improved optimization procedure and mixed integer nonlinear programming (MINLP) or nonlinear programming (NLP) algorithms. Pinch analysis gives many alternative retrofit designs for postulating a superstructure. The superstructure, material and energy flow rates have been optimized sequentially by a direct search method using ASPEN PLUS simulator with energy and material bounds. The heat exchanger network of the superstructure obtained, flashes and compressor were optimized simultaneously with the MINLP or NLP algorithms. We have realized an additional profit of 2,803 MUSD/yr with the combined sequential approach in a case study of an existing methanol plant.

Exergy as an objective function to MINLP problems in process synthesis

AbstractThe optimal layout of a chemical plant is determined by both economic and environmental aspects. The mathematical approach to this problem is given by representing the process through a superstructure, including any foreseeable process topology. It is described by integer variables, whereas real variables arise from the unit models and the thermodynamic calculations. By including process constraints and an objective function, a Mixed Integer Nonlinear Programming (MINLP) optimization problem is postulated. In this paper MINLP algorithms are combined with a technique for the exergy analysis of chemical processes for the preliminary screening of process alternatives. The exergy analysis as a screening technique is advantageous due to a significantly smaller amount of required data and computing time, compared with true optimization, including cost estimation at an earlier stage of process synthesis and analysis. Thus, a broader solution space can be examined. The subsequent cost analysis has then only to be focused on a reduced set of parameters.

Mixed-integer nonlinear programming techniques for the synthesis of engineering systems

The development of new mixed-integer nonlinear programming (MINLP) algorithms, coupled with advances in computers and software, is opening promising possibilities to rigorously model, optimize, and automate the synthesis of engineering systems. A general overview of the MINLP approach and algorithms will be presented in this paper with the aim of gaining a basic understanding of these techniques. Strengths and weaknesses will be discussed, as well as difficulties and challenges which still need to be overcome. In particular, it will be shown how proper problem representations, effective modeling schemes, and solution strategies can play a crucial role in the successful application of these techniques. The application of MINLP algorithms in synthesis will be illustrated with several examples.