Optimal Sizing and Allocation of Distributed Energy Resources in Microgrids Considering Internal Network Reinforcements

Reformulation, linearization, and a hybrid iterated local search algorithm for economic lot-sizing and sequencing in hybrid flow shop problems

A new, R-graph based, superstructure and corresponding MINLP model for designing conventional distillation columns are presented. A GDP representation (GR) of the superstructure is first constructed, then it is transformed to MINLP representation to which, in turn, additional trivial improvements are added. The new model has been tested on binary mixture examples, and the obtained results are compared to the results of an MINLP model which developed according to the GDP model of Yeomans and Grossmann. 9 The new model yields shorter computation time and provides better local optima. Additionally, the new model has been used for optimizing a complex multicomponent separation system consisting of several distillation columns. In order to handle such a complex system with a huge number of nonlinear equations, the outer approximation algorithm is modified to provide good initial values for the NLP subproblems. Distillation is one of the most widespread processes applied for separating multicomponent liquid mixtures. It is used for working up large volume or stream, and it requires high investment and operation outlays. The significance of the design of economically optimal distillation processes is of no question. Enormous interest has also been addressed to the area of designing optimal heat integrated distillation columns and distillation sequences. Minimizing the cost of a distillation process implies finding the optimal configuration of each individual column, as well. In the present article we consider staged column models only. The number of stages, and the stage numbers of the feed and side-stream points, are discrete decision variables. The total cost of a column may be modeled as the sum of the fix (capital) cost, depending on the number of stages and on the column diameter, and the variable (operation) cost related to the utility consumption. The objective of the design procedure is to find the optimal configuration of the column, which has the minimum total (annualized) cost. In order to model these processes, discrete decisions are required for calculating the number of stages. Optimizing single columns is a well-known procedure; all the basic textbooks outline how to do it in an easy manner. 1 After approximately determining the minimum and the estimated optimal number of theoretical stages, optimizing over the continuous variables is performed at varied values of the discrete variables. This is a 2-dimension discrete array of continuous optimization tasks in the case of a single-feed, two-product column, because there are merely two column sections in this case. This task becomes much more difficult if several feeds and side-products are to be taken into account. The real problem, however, is synthesizing a distillation sequence, or a system of advanced distillation columns, or a complex flowsheet containing distillation units when the number of distillation columns and their connections are not known in advance. In order to solve the complex synthesis problem outlined above, a proper superstructure for a single column, together with a proper generalized disjunctive programming (GDP) model or a proper mixed-integer nonlinear programming (MINLP) model, is a minimum requirement. Once such a model works well for a single column, the problem of more complex flowsheets may also be addressed. Mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) are the two exact methodologies commonly applied for solving process engineering problems with discrete decisions. The former includes algebraic equations describing the process, and binary variables related to discrete decisions. The latter method uses logic variables and expressions to represent the problem. 2 Both formulations have been successfully applied to rigorous models of distillation columns. Both methods apply a fixed maximum number of stages, and the actually used stages are selected from this set. Mathematical formulations that represent rigorous models of distillation column configurations fall into two categories: (i) one task-one equipment (OTOE) representations and (ii) variable task-equipment (VTE) representations. 3

This paper presents a new mixed-integer nonlinear programming (MINLP) model for the optimal operation of unbalanced three-phase droop-based microgrids. The proposed MINLP model can be seen as an extension of an optimal power flow for microgrids operating in islanded mode, that aims to minimize the total amount of unsupplied demand and the total distributed generator (DG) generation cost. Since the slack bus concept is not longer valid, the proposed model considers the frequency and voltage magnitude reference as variables. In this case, DGs units operate with droop control to balance the system and provide a frequency and voltage magnitude reference. Additionally, a set of efficient linearizations are introduced in order to approximate the original MINLP problem into a mixed-integer linear programming (MILP) model that can be solved using commercial solvers. The proposed model has been tested in a 25-bus unbalanced three-phase microgrid and a large 124-node grid, considering different operational and time-coupling constraints for the DGs and the battery systems (BSs). Load curtailment and different modes of operation for the wind turbines have also been tested. Finally, an error assessment between the original MINLP and the approximated MILP model has been conducted.

Optimal Antibody Purification Strategies Using Data-Driven Models

An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach

Optimal location, selection, and operation of battery energy storage systems and renewable distributed generation in medium–low voltage distribution networks

The location-allocation problem of manifolds, which is a part of subsea field layout optimization, directly affects the flowline cost. This problem has always been studied as a mixed-integer nonlinear programming (MINLP) problem, or an integer linear programming (ILP) problem when there are location options for the facilities. Making a MINLP model is surely convenient to interpret the optimization problem. However, finding the global optimum of the MINLP model is very hard. Hence, practically, engineers use approximation algorithms to search a good local optimum or give several good location options based on their experience and knowledge to reduce the MINLP model into an ILP model. Nevertheless, the global optimum of the original MINLP model is no longer guaranteed. In this study, enlightened by the graphic theories, we propose a new method in which we reduce the MINLP model into an ILP model---more precisely, a binary linear programming (BLP) model---without compromise of achieving global optimum, but also with extremely high efficiency. The breakthrough in both efficiency and accuracy of our method for the location-allocation problem of manifolds and wellheads is well demonstrated in various cases with comparison to the published methods and the commercial MINLP solver from LINDO. Besides, we also provide our results for larger-scale problems which were considered infeasible for the commercial MINLP solver. More generally, our method can be regarded as a specific MINLP/NIP (nonlinear integer programming) solver which can be used for many other applications. This work is the second of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.

The Design and Synthesis of Batch/Semicontinuous Processes

A master–slave solving method with adaptive model reformulation technique for water network synthesis using MINLP

A behavior-centered framework for real-time control and load-shedding using aggregated residential energy resources in distribution microgrids

In this paper, we develop a mathematical model of a technician routeing and scheduling problem with time windows (TRSPTW) and overnight shifts, which we title the ‘overnight TRSPTW’. This problem is motivated by a real application in the telecommunications industry in Saskatchewan, Canada. A mixed-integer nonlinear programming (MINLP) model is employed to achieve two key objectives: (1) minimising the total costs associated with technicians and subcontractors, including travel costs, accommodation costs and penalty costs caused by late starts and (2) minimising imbalanced workloads. Furthermore, the present work aims to determine the daily assignment of technicians to communities, depots and routes; find a high-quality schedule for technicians’ start times in communities and lunch breaks and determine the daily assignment of tasks to the subcontractor. The bi-objective MINLP model used to solve the overnight TRSPTW is a typical NP-hard problem in combinatorial optimisation. As such, we introduce a new hybrid category of TRSPTW that combines centroid-based clustering, which is an unsupervised machine learning (ML) approach, with a bi-objective zebra optimisation algorithm (BOZOA). The resultant algorithm blends the advantages of the ZOA and ML to strike a balance between the exploration and exploitation of the solution region. Finally, we compare our results with those obtained using an exact solver for small-, medium-, and large-sized instances. The performance evaluation and validation results revealed that the proposed ML-based BOZOA provides very good performance in solving TRSPTWs at a variety of scales with respect to the optimality criteria, including, number of taken iterations, infeasibility, optimality error and complementarity compared with both an exact solver and two inspired algorithms from ZOA. Highlights An ML-based bi-objective zebra optimisation algorithm to treat large-scale TRSPs Centroid-based clustering on the population of zebras to avoid bias towards a specific search space Making a trade-off between exploration and exploitation of the feasible region in the developed algorithm A new MINLP model of a weighted bi-objective TRSP with limited capacity depots Workload function, penalty function for lateness, subcontracts, time windows for tasks and breaks Experiments using real data to show the performance of the model and solution method

This research studies the cellular manufacturing system (CMS) controlled by kanban mechanism which defective items are produced in any production run of each product and rework is carried out to transform them into serviceable items. We consider and compare two different policies for rework where in the first policy rework is completed within the same production cycle and in the second policy rework done after N production cycles. Recently Aghajani et al. (2012) explain policy 2 and proposed a mixed-integer nonlinear programming (MINLP) model for this policy. In order to minimize total cost, MINLP model was developed for policy 1 to find simultaneously the optimal number of kanban, batch size, and number of batches. The cost function includes the cost of setup, holding, and transportation. Due to the high combinatorial structure of the problem, particle swarm optimization (PSO), and simulated annealing (SA) algorithms as meta-heuristic methods are proposed to solve the problem and numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms. It is shown that both PSO and SA result are in a near optimal solution but the PSO algorithm gives a better performance than the SA method. Also, sensitivity analysis is carried out to study the effect of defective rate, holding cost, and setup cost variations on the total system cost is discussed the performance of these policies in different conditions.

A bi-level optimization model is proposed for locating billboards on road network links in cities. Since billboard locations are largely driven by the flow on the underlying network, factors that impact traffic considerations of users are accounted for, including link congestion and road link pricing. Safety aspects associated with billboard distraction to users of the network are also incorporated within the proposed Mixed Integer Non-Linear Programming (MINLP) model. The model is multi-objective in nature, and it is solved through adopting the augmented ε -constraint method to obtain a sample of non-dominated points on the Pareto front. Due to the non-convexity induced by the bi-level structure of the model, a model reformulation scheme based on the use of equilibrium conditions is presented. A linearization scheme is also adopted that involves the introduction of mixed integer variables.

Global optimization of multiscenario mixed integer nonlinear programming models arising in the synthesis of integrated water networks under uncertainty

To solve the problem of long logistics delivery time in supply chain, a Mixed Integer Non-linear Program (MINLP) model is built by using Mixed Integer nonlinear programming theory. Firstly, the General algebraic modeling system (GAMS) is used to build the model to fully integrate each parameter of logistics transportation, the total distribution time of the supply chain network, the coverage radius of the logistics base, the number of users, the total capacity of the logistics base, the mode of railway and road transportation, the nonlinear programming model is built and solved by DICOPT solver in GAMS. The cost of logistics can be decreased, transportation time can be reduced, and the logistics system's operating efficiency can be increased in the long term with the help of this algorithm. The proper operation of the logistics system is critical in encouraging the supply chain circulation of various industries and has a direct impact on the society's economic development. The optimal logistics distribution plan with 5 logistics bases covered users of 18 and railway capacity of 2. With the same railway capacity and the same total budget, the larger the number of covered users, the greater the total distribution time increases, but the larger the total budget, the growth of the total distribution time slows down significantly. Experiments show that MINLP model can solve the problem of logistics-based layout optimization in nonlinear logistics management.