Subsea field layout optimization (part II)–the location-allocation problem of manifolds

The Design and Synthesis of Batch/Semicontinuous Processes

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

Optimising crop planning in conjunction with intra-seasonal water allocation necessitates the use of daily water budget calculations to determine the timing and amount of irrigation events, which complicates the solution of the problem to global optimality. The main objective of this research was to compare the intra-seasonal water allocation of a mixed integer nonlinear programming (MINLP) model with that of differential evolution (DE), to allocate a limited amount of water while considering irrigable area and the irrigation schedule that will maximise the total gross margin. Results show that both solution procedures adhere to economic theory of water allocation under limited water supply. The conclusion is that the MINLP model most likely achieved very near global optimality as the solutions of the two models were very close to each other. DE holds promise to solve more complex models involving risk and multiple crops.

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

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

Microgrids have become valuable assets because they improve the reliability of consumers while integrating renewables via distributed energy resources (DERs). Thus, making them cost-efficient is essential to secure their proliferation. This paper proposes a new method for the optimal design of microgrids. The proposed two-stage method optimizes the size and the location of the DERs, i.e., the renewable energy sources (RESs), distributed generation (DG) units, and battery energy storage systems (BESSs). Furthermore, the overall operation of the microgrid is optimized using a stochastic scenario-based approach, considering grid-connected and unintentional islanded modes. The proposed method also considers internal network reinforcements. Thus, the first stage is an energy-based approach, formulated as a mixed-integer linear programming (MILP) problem, and it is used to size the DERs, whereas the second stage uses an optimal AC power flow (AC-OPF) to formulate a mixed-integer nonlinear programming (MINLP) model that allocates the DERs and selects the best conductor for each circuit. The multi-objective nature of the problem is addressed via Pareto optimization to analyze the trade-off between operational and capital costs. The MINLP model is linearized through piece-wise approximations and solved using commercial solvers. Furthermore, the impact of battery degradation is analyzed through a simple adaptation of the Stage 1 model. Results were obtained with data from the real university campus microgrid CampusGrid, located at the State University of Campinas (UNICAMP), in São Paulo, Brazil.

Genetic algorithm for non-linear mixed integer programming problems and its applications

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.

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.

New approach for scheduling crude oil operations

Optimisation approaches for the synthesis of water treatment plants

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

Cell formation problem mainly addresses how machines should be grouped and parts be processed in cells. In dynamic environments, product mix and demand are changed in each period of the planning horizon. Incorporating such assumption in the model increases flexibility of the system to meet customers' requirements. In this model, to ensure the reliability of the system in presence of unreliable machines, alternative routing process as well as buffer storage are considered to reduce detrimental effects of machine failure. This problem is presented by a nonlinear mixed integer programming model attempting to minimize the overall cost of the system. To solve the model in large scale for practical purposes, a genetic algorithm approach is adopted as the model belongs to NP-hard class of problems. Sensitivity analysis is used to show the validity of the proposed model. Besides, numerical examples are used both, for small-sized and large- sized instances to show the efficiency of the method in finding near optimal solution.

Disasters pose a serious threat to people’ lives and urban environment, affecting the sustainable development of society. Then it's crucial to quickly develop an efficient rescue plan for the disaster area. However, disaster rescue is rather difficult due to the requirement to develop the optimal rescue plan as quickly as possible according to the information of trapped people and rescue teams, and the amount of information will continue to increase as the rescue proceeds. At present, most of the rescue plans are manually made based on previous rescue experience. But obviously these plans might be the not optimal one. Considering the real-time location data of trapped people, this paper develops a Mixed Integer Non-linear Programming (MINLP) model to find the highest efficient rescue plan To solve the model accurately and efficiently, a bi-level decomposition (BLD) algorithm is presented to iteratively solve a discretized Mixed Integer Linear Programming (MILP) model and its nonconvex Non-linear Programming (NLP) model until a converged solution is obtained. In addition, since more trapped people could be found over time, the built rescue units should also be considered when making a rescue plan for a new stage. To further improve the solving efficiency, an accelerated bi-level decomposition (ABLD) algorithm is also proposed. Finally, a real-world disaster rescue is given to validate the superiority of the proposed ABLD algorithm relative to particle swarm optimization (PSO) algorithm and BLD algorithm.

Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm