Mixed-integer Nonlinear Programming Techniques Research Articles

Comparing perspective reformulations for piecewise-convex optimization

We aim at generalizing formulations for non-convex piecewise-linear problems to mathematical programs whose non-convexities are only expressed in terms of piecewise-convex univariate functions. This is motivated by solving Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique. We theoretically and computationally compare different formulations, showing that, unlike in the linear case, they are not equivalent when perspective reformulation is applied to strengthen the formulation of each single segment.

Systematic Design of Solvent Recovery Pathways: Integrating Economics and Environmental Metrics

The increasing trend of solvent usage by chemical industries has caused an upsurge in hazardous waste solvents and, consequently, increased their toxicity potential within the environment. The increase in overall carbon and ecological footprints due to conventional waste handling techniques such as incineration and onsite and offsite disposal can hardly be overstated. Even though solvent recovery methods present a better alternative to these techniques, analysis is generally centered on economics. This paper presents a framework that evaluates the economic and sustainability metrics of solvent recovery processes. In the first approach, standalone software (SimaPro) was used to evaluate the impact of the recovery process. The framework was extended by incorporating the economics, Sustainable Process Index (SPI), and Emergy metrics. Thus, solvent recovery challenges have been transformed into a multiobjective optimization problem that is solved through superstructure and mixed-integer nonlinear programming techniques. The applicability of the framework is illustrated by two comprehensive case studies with varying complexities, and the results are compared with conventional methods. The results indicate that about 76–85% of the ecological and energy burden can be prevented if solvent recovery is the preferred option to incineration.

Domain Partition of the Hydro Production Function for Solving Efficiently the Short-Term Generation Scheduling Problem

Short-term generation scheduling (STGS) is a fundamental task in the operational planning analysis of hydroelectric plants. For the multi-unit case, the STGS is represented as a large-scale nonconvex mixed-integer nonlinear optimization model. Then, considering the (usual) short time for providing a solution, it is vital to exploit all the structural properties of the problem at hand. The main issue for exploiting this problem is the hydro production function (HPF), which is a nonlinear nonconvex relationship between power, head, and turbined outflow of a generating unit (GU). Nevertheless, the HPF usually presents operating regions where the function is convex and regions in which it is concave due to physical reasons. Inspired by sequential convex mixed-integer nonlinear programming techniques, this paper proposes partitioning the domain of the HPF in regions in which it is convex and those in which it is concave. The HPF is approximated by a piecewise linear function using the logarithmic aggregation convex combination (LACC) model in convex regions. In turn, in the concave regions, the HPF is replaced by a convex hull approach, which, combined with symmetry strategies, reduces the number of binary variables in the resulting optimization problem. Using several computational instances of a 50-unit hydroelectric plant, we show that the partitioning-based proposed strategy significantly reduces the computational time compared to two other efficient MILP formulations.

Enhanced sourcing strategy for centralized multitier multiple suppliers network with failure risks

PurposeThis paper attempts to address three key objectives. The primary aim is to enhance sourcing strategy for a centralized and coordinated multitier multiple suppliers networks with uncertain demand and supplier failure risks. The second objective is to enumerate all possible practical supplier(s) failure scenarios and quantify expected loss of demand cost. Finally, the work illustrates statistical experimentation to identify “influential” variables that can significantly impact the expected supply network and loss costs.Design/methodology/approachA seven-step solution framework is proposed to derive an optimal sourcing strategy for the specific network configuration with varied supplier failure scenarios. Five distinct models are formulated to address all possible scenarios of supplier failure events. Mixed-integer nonlinear programming technique is used to derive expected supply network cost and loss cost. The solution framework is verified using a real-life case.FindingsA cross-case analysis indicates that an increase in suppliers' failure risk (SFR) probabilities or customer demand rate increases the expected loss of demand costs for a multitier supply network. Besides, an increase in unit component prices increases the expected supply network cost.Research limitations/implicationsA two-tier automotive supply network for a single product is considered for all case studies.Practical implicationsThe enhanced strategy can facilitate practitioners enumerate different supply network failure scenarios and implement the best solution.Originality/valueThere is no evidence of earlier research to derive optimal sourcing strategy for a centralized, coordinated multitier multiple supplier's network, considering demand uncertainties and SFR.

Minotaur: a mixed-integer nonlinear optimization toolkit

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications.

Pband: A General Signal Progression Model With Phase Optimization Along Urban Arterial

Overlapping phase and split phase are two typical phase patterns at signalized intersections in practice. The existing bandwidth-oriented progression control schemes mainly focus on overlapping phase to adopt the various layout of intersections and volumes rather than split phase. To address this issue, a two-way signal progression model, namely Pband, is developed to simultaneously optimize phase pattern choice from overlapping phase or split phase, phase sequence, and offsets. Also, the proposed Pband is formulated with a mixed integer nonlinear programming technique to guarantee an optimal solution. A numerical test based on a field arterial from the county of Jiashan, Jiaxing, China is employed to validate Pband under designed traffic patterns and signal timings. Numerical results have indicated that the Pband can show promise in increasing progression bandwidths and reducing average travel delay and the number of stops via traffic simulation experiments compared with the conventional Multiband model.

Energy Dispatch of Decentralized Hybrid Power System

The continuous geometric growth in energy demand coupled with high operation cost of power systems have made renewable energy sources (RES) more attractive. This paper presents an optimal design and energy management strategy of photovoltaic-diesel-battery (PDB) decentralized hybrid power system (DHPS) that minimizes operating costs and provides reliable power supply. The nonlinear objective cost function is formulated for the economic dispatch problem taking into consideration various operating constraints. The diesel generator (DG) minimum operation efficiency is expanded and solved using Newton-Quasi method. The DG is constrained to operate between the proposed minimum and rated efficiency during its operation in order to achieve desired load factor. Mixed integer nonlinear programming (MINLP) technique is explored to optimize the utilization of RES to reliable supply. A combined dispatch strategy which minimizes daily fuel consumption cost by the maximization of RES using a set of prioritized rules was developed and compared with the MINLP technique. The performance of the proposed combined strategy is validated by simulating the following operating scenarios: single household and community daily load profiles. The results show the effectiveness of the proposed combined dispatch algorithm as it reduces DG fuel consumption cost and improves supply reliability. Consequently, the effectiveness of these strategies encourages the integration of DHPS in remote and isolated communities

A MINLP technique for optimal placement of multiple DG units in distribution systems

Loss reduction is one of the prime objectives for planning of distributed generation (DG). To improve performance of distribution systems, optimal placement of distributed generator is critically important, as DG benefits are site and size specific. Optimal placement of multiple DG units is non-convex and non-linear optimization problem. The methodology proposed in this paper solves Mixed Integer Non-Linear Programming (MINLP) formulation for loss minimization. The proposed methodology simplifies the problem by dividing it in two phases, namely Siting Planning Model (SPM) and Capacity Planning Model (CPM) thereby reducing the search space and computational time. The SPM model selects the candidate buses based on Combined Loss Sensitivity (CLS). In CPM, optimal locations and sizes are obtained by integrating Sequential Quadratic Programming (SQP) and Branch and Bound (BAB) algorithm for MINLP problem. The performance of the proposed method is tested on IEEE 33-bus and IEEE 69-bus distribution system for placement of single and multiple DG units capable of delivering either real or both real and reactive power. The obtained results are then compared with three basic classes of optimization methods, viz., Exhaustive Load Flow (ELF), Improved Analytical (IA) and Particle Swarm Optimization (PSO). The key advantage of the proposed method is that it simultaneously considers placement of multiple DG units giving better optimal solution in reasonably less computational time.

Model-based structural optimization of seawater desalination plants

Membrane-based processes and thermal desalination plants are two alternatives to overcome the problem of fresh water supply by means of seawater desalination. In this work the combination of two types of desalination technologies, a reverse osmosis network (RON) and a forward-feed multi-effect distillation (FF-MED), in a hybrid plant is considered as a structural optimization problem. Deterministic mixed-integer non-linear programming techniques (MINLP) are used to rigorously optimize operational parameters and process structure simultaneously. A generalized superstructure for the hybrid desalination plant is constructed and conceptual design considerations are used to reduce its complexity. A mathematical model for the whole plant and an economical objective function are provided. The resulting model is highly nonlinear and non-convex. A stepwise optimization strategy is proposed, including a specialized initialization scheme to robustly compute good initial solutions with a minimum of user interaction. Results for various specifications illustrate the application of the proposed optimization model. The performance of the suggested method is compared to that obtained with the global solver BARON.

Reactive Power Provision in Electricity Markets Considering Voltage Stability and Transmission Congestion

This article presents a new algorithm for optimal reactive power procurement in pool electricity markets. Due to the significant impact of reactive power flow on the system voltage stability and transmission loss, the objective function of the proposed algorithm is minimization of the market payment for reactive power and system energy loss, simultaneously maximizing voltage stability margin. Moreover, as another object, the algorithm tries to decrease the probability of the transmission congestion during reactive power market clearing. A four-step multi-objective mixed-integer non-linear programming technique that uses the genetic algorithm in combination with a sequential quadratic programming method is implemented in MATLAB (The MathWorks, Natick, Massachusetts, USA) to solve the proposed problem. Numerical studies on the IEEE-RTS test system show the suitability of the proposed method.

Multiobjective Design of Calorific Value Adjustment Process using Process Simulators

In this work, we present a solution procedure for design of a chemical process for effectively adjusting calorific values in an offshore regasification terminal. To tackle the technical and commercial issue in the liquefied natural gas (LNG) industry caused by differences of LNG calorific values between importing countries, many methods and configurations are being studied. This design problem is defined in two parts: a generalized disjunctive programming (GDP) problem with one objective and a multiobjective problem for minimizing the operating costs and the performance of natural gas liquids (NGLs). First, the GDP problem has been mathematically reformulated as a mixed-integer nonlinear programming (MINLP) problems, and the MINLP technique incorporated into the process simulator using its own optimization capabilities has been suggested. For solving the resulting bicriterion problem with the MINLP problem, we have suggested the heuristic procedure that reduces the number of discrete solutions which are n...

Efficient Optimization-Based Design of Distillation Processes for Homogeneous Azeotropic Mixtures

Rigorous optimization is a valuable tool that can support the engineer to tap the full economic potential of a distillation process. Unfortunately, the solution of these large-scale discrete-continuous optimization problems usually suffers from a lack of robustness, long computational times, and a low reliability toward good local optima. In this paper, the rigorous optimization of complex distillation processes for azeotropic multicomponent mixtures is achieved with outstanding robustness, reliability, and efficiency through progress on two levels. First, the integration within a process synthesis framework allows a reduction of the complexity of the optimization superstructure and provides an excellent initialization by shortcut evaluation with the rectification body method. Second, the reformulation as a purely continuous optimization problem enables a solution with reliable and efficient NLP solvers. Moreover, the continuous reformulation considers a particular tight column model formulation such that the introduction of special nonlinear constraints to force integer decisions could be largely avoided. A careful initialization phase and a stepwise solution procedure with gradually tightened bounds facilitate a robust and efficient solution. Different superstructures for the tray optimization of distillation columns are tested. The methods are illustrated by three demanding case studies. The first case study considers the conceptual design as well as the rigorous optimization of a curved boundary process for the complete separation of an azeotropic four-component mixture. The rigorous optimization of a pressure swing process for the separation of a highly nonideal five component mixture is presented in the second case study. Finally, the third case study covers the rigorous optimization of an extractive separation within a complex column system. All case studies could be robustly solved due to the favorable initialization phase. The continuously reformulated problems required significantly less computational time and identified local optima of better quality as compared to the mixed-integer nonlinear programming techniques (MINLP) solution.

Solving a dynamic separation problem using MINLP techniques

In the present paper a dynamic separation problem is modeled and solved using Mixed Integer Nonlinear Programming (MINLP) techniques. The objective is to maximize the profit for continuous cyclic operation, and at the same time, to find the optimal configuration for the separation column system. The dynamics of the chromatographic separation process are modeled as a boundary value problem which is solved, within the optimization, using an iterative finite difference method. The separation of a fructose-glucose mixture is solved using the Extended Cutting Plane (ECP) method. It is shown that the production planning can be done efficiently for different purity requirements, such that all the output of a system can be utilized. Using a process design that is optimized it is thus possible to use existing complex systems, or to design new systems, more efficiently and also to reduce the energy costs or the costs in general. The presented problem is a challenging application involving time-consuming calculations that, though the high capacity of todays computers, underlines the role of robust and fast numerical tools within optimization.

Design of separation process of azeotropic mixtures based on the green chemical principles

This paper presents an integrated methodology for synthesis of separation process of azeotropic mixture based on the green chemical principles, which inherently incorporates environmental factors into the separation process synthesis. Characterization of the environmental impact of a chemical process is carried out on the basis of our established environmental impact database (containing nine indices). The superstructure is optimized more effectively and reliably by integrating the mathematical programming approach using multi-objective mixed integer non-linear programming techniques and heuristic approach. The complexity and size of synthesis search space were greatly reduced by applying the thermodynamic insights into the selection of separation techniques. The proposed methodology was highlighted through two industrial examples, one is the separation of azeotropic mixture of dimethyl carbonate and methanol, the other is the separation of azeotropic mixture of isopropanol and water.

Mixed-integer nonlinear programming techniques for process systems engineering

Mixed-integer nonlinear programming techniques for process systems engineering

Mixed-integer nonlinear programming techniques for process systems engineering

This paper presents an overview of mixed-integer nonlinear programming techniques by first providing a unified treatment of the Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The extension of these methods is also considered for logic based representations. Finally, an overview of the applications in many areas in process engineering is presented.

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.