A rigorous, mixed-integer, nonlineal programming model (MINLP) for synthesis and optimal operation of cogeneration seawater desalination plants

Mixed Integer Nonlinear Programming model for the optimal design of fired heaters

The size of heat transfer enhancement equipment has an important effect on the efficiency of heat exchangers and Heat exchanger network (HEN) structure. A novel mixed integer nonlinear programming (MINLP) model of HEN synthesis considering the types and size of enhancement equipment is proposed, solved by hybrid genetic algorithm/simulated annealing algorithm (GA/SA). In this model, the type and size of the enhancement equipment are set as the integers and continuous variables, respectively, and the enhanced equipment costs and operating costs associated with pressure drop are added in the total annual cost (TAC). The MINLP mathematical model of simultaneous synthesis is established by the combining of heat transfer coefficient and pressure drop models of heat exchangers for enhancement equipment and the HEN synthesis model based on the stage-wise superstructure. The new method has distinctive advantages over existing design methods, as the new MINLP model can effectively achieve simultaneous optimization of the types and size of enhancement equipment and HEN. Finally, the feasibility and effectiveness of the proposed model are proved through concrete case analysis.

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.

Optimization of alternative structures of integrated power and desalination plants

Optimal synthesis and design of Heat Recovery Steam Generation (HRSG) via mathematical programming

THE DESIGN AND SYNTHESIS OF BATCH/SEMICONTINUOUS PROCESSES

A multiperiod minlp model for improving the flexibility of heat exchanger networks

Simultaneous optimisation and heat integration of evaporation systems including mechanical vapour recompression and background process

This paper deals with the problem regarding the optimal placement and sizing of distribution static compensators (D-STATCOMs) in radial and meshed distribution networks. These grids consider industrial, residential, and commercial loads within a daily operation scenario. The optimal reactive power flow compensation problem is formulated through a mixed-integer nonlinear programming (MINLP) model. The objective function is associated with the minimization of the expected energy losses costs for a year of operation by considering the investment costs of D-STATCOMs. To solve the MINLP model, the application of a master–slave optimization approach is proposed, which combines the salp swarm algorithm (SSA) in the master stage and the matricial backward/forward power flow method in the slave stage. The master stage is entrusted with defining the optimal nodal location and sizes of the D-STATCOMs, while the slave stage deals with the power flow solution to determine the expected annual energy losses costs for each combination of nodes and sizes for the D-STATCOMs as provided by the SSA. To validate the effectiveness of the proposed master–slave optimizer, the IEEE 33-bus grid was selected as a test feeder. Numerical comparisons were made against the exact solution of the MINLP model with different solvers in the general algebraic modeling system (GAMS) software. All the simulations of the master–slave approach were implemented in the MATLAB programming environment (version 2021b). Numerical results showed that the SSA can provide multiple possible solutions for the studied problem, with small variations in the final objective function, which makes the proposed approach an efficient tool for decision-making in distribution companies.

Trajectory planning for autonomous underwater vehicles in the presence of obstacles and a nonlinear flow field using mixed integer nonlinear programming

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

This paper deals with the problem of the optimal reconfiguration of medium voltage distribution networks by proposing a mixed-integer nonlinear programming (MINLP) model. This optimization model has as objective function the minimization of the total power losses in all the branches of the network constrained by active and reactive power balance equations, voltage regulation bounds and device capabilities, among others. The proposed MINLP formulation works with branch-to-node incidence that allows representing the active and reactive power flow in branches as a function of the real and imaginary parts of the voltages and currents. The solution of the MINLP model is reached through the general algebraic modeling system widely know as GAMS package by presenting it in a tutorial form. This software allows implementing in compact form the proposed model and solve it via branch and bound methods. Two test feeders composed by 5 and 14 nodes permits demonstrating the fidelity of the proposed MINLP model regarding power losses minimization when compared with literature reports.

A Rigorous MINLP Model for the Optimal Synthesis and Operation of Utility Plants

Water condensate collection system by using MINLP model

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