Symmetry breaking in MILP formulations for Unit Commitment problems

This paper addresses the study of symmetry in Unit Commitment (UC) problems solved by Mixed Integer Linear Programming (MILP) formulations, and using Linear Programming based Branch & Bound MILP solvers. We propose three sets of symmetry breaking constraints for UC MILP formulations exhibiting symmetry, and its impact on three UC MILP models are studied. The case studies involve the solution of 24 instances by three widely used models in the literature, with and without symmetry breaking constraints. The results show that problems that could not be solved to optimality within hours can be solved with a relatively small computational burden if the symmetry breaking constraints are assumed. The proposed symmetry breaking constraints are also compared with the symmetry breaking methods included in two MILP solvers, and the symmetry breaking constraints derived in this work have a distinct advantage over the methods in the MILP solvers.     

A MILP model for N-dimensional allocation

This paper presents a Mixed Integer Linear Programming (MILP) model for the solution of N-dimensional allocation problems. The applicability of the model is presented and demonstrated through some illustrative examples with different numbers of dimensions. Several problems, previously presented in the literature, are solved using the proposed model, such as, one-dimensional scheduling problems, two-dimensional cutting problems, as well as plant layout problems and three-dimensional packing problems. Additionally, some problems in four dimensions are presented and solved using the considered model. The presented model is applicable to a wide variety of allocation problems as it offers a general framework for modelling allocation problems with any given number of continuous or discrete dimensions. The presented problems are formulated as MILP problems where the first four dimensions usually are continuous spatial and time dimensions. Additional dimensions are often of a discrete nature.     

An efficient method for optimal design of large-scale integrated chemical production sites with endogenous uncertainty

Integrated sites are tightly interconnected networks of large-scale chemical processes. Given the large-scale network structure of these sites, disruptions in any of its nodes, or individual chemical processes, can propagate and disrupt the operation of the whole network. Random process failures that reduce or shut down production capacity are among the most common disruptions. The impact of such disruptive events can be mitigated by adding parallel units and/or intermediate storage. In this paper, we address the design of large-scale, integrated sites considering random process failures. In a previous work (Terrazas-Moreno et al., 2010), we proposed a novel mixed-integer linear programming (MILP) model to maximize the average production capacity of an integrated site while minimizing the required capital investment. The present work deals with the solution of large-scale problem instances for which a strategy is proposed that consists of two elements. On one hand, we use Benders decomposition to overcome the combinatorial complexity of the MILP model. On the other hand, we exploit discrete-rate simulation tools to obtain a relevant reduced sample of failure scenarios or states. We first illustrate this strategy in a small example. Next, we address an industrial case study where we use a detailed simulation model to assess the quality of the design obtained from the MILP model.     

Optimal management of logistic activities in multi-site environments

The new emerging area of Enterprise Wide Optimization (EWO) has focused the attention in effectively solving the combined production/distribution scheduling problem. The importance of logistic activities performed in multi-site environments comes from the relative magnitude of the associated transportation costs and the good chance of getting large savings on such expenses. This paper first develops an exact MILP mathematical formulation for the multiple vehicle time-window-constrained pickup and delivery (MVPDPTW) problem. The approach is able to account for many-to-many transportation requests, pure pickup and delivery tasks, heterogeneous vehicles and multiple depots. Optimal solutions for a variety of benchmark problems with cluster/random distributions of pickup and delivery locations and limited sizes in terms of customer requests and vehicles have been discovered. However, the computational cost exponentially grows with the number of requests. For large-scale m-PDPTW problems, a local search improvement algorithm steadily providing a better solution through two evolutionary steps is also presented. A neighborhood structure around the starting solution is generated by first allowing multiple request exchanges among nearby trips and then permitting the reordering of nodes on every individual route. If a better set of routes is found, both steps are repeated until no improved solution is discovered. Compact MILP mathematical formulations for both sub-problems have been developed and solved through an efficient branch-and-bound algorithm. A significant number of large-scale m-PDPTW benchmark problems, some of them including up to 100 transportation requests, were successfully solved in reasonable CPU times.     

采用虚拟温度法设计换热网络

采用虚拟温度法设计换热网络＊李晖王莉姚平经（大连理工大学化工学院，大连１１６０１２）关键词换热网络综合多温差法虚拟温度１引言随着对换热网络研究的深入，人们越来越重视一些因素对换热网络综合的影响。例如，在以往的设计方法中，设每股物流的传热膜系数和单位换...     

一种改进的顺序型多目的间歇工厂生产调度的MILP模型

分析了顺序型多目的工厂间歇生产的特点,建立了一种新的混合整数线性规划（MILP）模型.该模型以操作活动序列作为建模的依据,将整个间歇生产过程分解成若干个子系统.在对各子系统建模的基础上,实现了顺序型多目的工厂间歇调度的全局性优化.并通过算例验证了该模型求解结果的正确性和可行性.然后将新模型运用到更大规模的调度问题上,均求解出了有效的调度方案.     

Flexible mass transfer model for water minimization in batch plants

This paper presents the least constrained mass transfer mathematical formulation for freshwater minimization in multipurpose batch chemical processes with central reusable water storage. The mathematical formulation is an extension of the model developed by Majozi [T. Majozi, Wastewater minimization using central reusable water storage in batch processes, Computers and Chemical Engineering Journal 29 (7) (2005) 1631–1646]. In the latter model four scenarios were considered with various limitations or constraints. In the scenario presented in this paper only the mass load is fixed, whilst both the quantity of water used in a particular operation and outlet concentration are allowed to vary. In essence, fixing the mass load is more representative of the practical case. A solution procedure for the resultant nonconvex mixed integer nonlinear programming (MINLP) model is also presented. The solution procedure first involves reformulating the MINLP into a relaxed linear model (MILP). The MILP is first solved, the solution of which forms a feasible starting solution for the MINLP. Presented are two illustrative examples.     

批处理过程优化调度研究综述--1.MILP调度方法的描述框架

综述化工批处理过程调度建模研究及其实际应用。计划／调度在企业生产管理中起着承上启下的作用，合理的计划调度不但能提高企业的服务水平、降低存储费用，而且还能提高企业的生产能力、加深对过程机制及关键数据的理解。整数规划方法应用于批处理过程计划调度，具有较好的适用性和扩展性，解的性质良好，在批处理过程调度研究得到广泛的应用。     

Optimal design of reverse-osmosis networks for wastewater treatment

An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case studies to illustrate the proposed solution strategy.     

Simultaneous subtour elimination model for single-stage multiproduct parallel batch scheduling with sequence dependent changeovers

In this paper a mixed-integer linear programming (MILP) model is presented to minimize makespan of single-stage multiproduct parallel batch production with sequence dependent changeovers. The computational inefficiency and suboptimal problems are addressed by the tight and rigorous formulation of the proposed model. Subtours (subcycles) are eliminated simultaneously so that the optimal solution is obtained in one step. The proposed model is tested with two examples. The results show that the model obtains the global optimal solutions with significant improvement in solution time.     

Multiperiod design of azeotropic separation systems. I. An agent based solution

In this paper, the first in a two-part series, we explore an agent based solution approach to the multiperiod design of azeotropic separation systems. Asynchronous Teams (A-Teams), a software organization that has been successfully applied to combinatorial optimization problems in other disciplines, is applied to this chemical process system design problem. A-Teams is a framework in which multiple design techniques can work harmoniously in the solution of a problem too demanding for any one method. We introduce a simple architecture for constructing A-Teams that incorporates the use of persistent data. Several approaches for generating improved multiperiod azeotropic design solutions are developed and are used simultaneously in a large-scale demonstration. The software organization is found to be capable of developing and improving a population of preliminary designs for the multiperiod azeotropic design problem.     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.     

Multi-period design and planning model of shale gas field development

Long-term design and planning of shale gas field development is challenging due to the complex development operations and a wide range of candidate locations. In this work, we focus on the multi-period shale gas field development problem, where the shale gas field has multiple formations and each well can be developed from one of several alternative pads. The decisions in this problem involve the design of the shale gas network and the planning of development operations. A mixed-integer linear programming (MILP) model is proposed to address this problem. Since the proposed model is a large-scale MILP, we propose a solution pool-based bilevel decomposition algorithm to solve it. Results on realistic instances demonstrate the value of the proposed model and the effectiveness of the proposed algorithm.     

Multi-week MILP scheduling for an ice cream processing facility

This paper presents a multi-week mixed integer linear programming (MILP) scheduling model for an ice cream processing facility. The ice cream processing is a typical complex food manufacturing process and a simplified version of this processing has been adapted to investigate scheduling problems in the literature. Most of these models only considered the production scheduling for a week. In this paper, multi-week production scheduling is considered. The problem has been implemented as an MILP model. The model has been tested on a set of cases from the literature, and its results were compared to the results of problems solved using hybrid MILP-heuristics methods in the literature. The inclusion of clean-up session, weekend break and semi-processed product from previous week were also assessed with two additional sets of experiments. The experiments result show that the proposed MILP is able to handle multi-week scheduling efficiently and effectively within a reasonable time limit.     

Comparison of global optimization algorithms for the design of water-using networks

We address a special class of bilinear process network problems with global optimization algorithms iterating between a lower bound provided by a mixed-integer linear programming (MILP) formulation and an upper bound given by the solution of the original nonlinear problem (NLP) with a local solver. Two conceptually different relaxation approaches are tested, piecewise McCormick envelopes and multiparametric disaggregation, each considered in two variants according to the choice of variables to partition/parameterize. The four complete MILP formulations are derived from disjunctive programming models followed by convex hull reformulations. The results on a set of test problems from the literature show that the algorithm relying on multiparametric disaggregation with parameterization of the concentrations is the best performer, primarily due to a logarithmic as opposed to linear increase in problem size with the number of partitions. The algorithms are also compared to the commercial solvers BARON and GloMIQO through performance profiles.     

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

Large scale process optimization techniques applied to chemical and petroleum processes

Some approaches for finding the solution to large scale process optimization problems are discussed. Several popular nonlinear programming algorithms are tested and conclusions reached about their suitability for chemical process optimization. Decomposition procedures are also discussed and numerical studies made to examine the relative merits of decomposition vs. “black box” optimization strategies. Test problems include an oil refinery scheduling problem and a chemical process optimization problem     

New approach for scheduling crude oil operations

Scheduling of crude oil operations is crucial to petroleum refining, which includes determining the times and sequences of crude oil unloading, blending, and CDU feeding. In the last decades, many approaches have been proposed for solving this problem, but they either suffered from composition discrepancy [Lee et al. 1996. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial and Engineering Chemistry Research 35, 1630-1641; Jia et al., 2003. Refinery short-term scheduling using continuous time formulation: crude-oil operations. Industrial and Engineering Chemistry Research 42, 3085-3097; Jia and Ierapetritou, 2004. Efficient short-term scheduling of refinery operations based on a continuous time formulation. Computer and Chemical Engineering 28, 1001-1019] or led to infeasible solutions for some cases [Reddy et al., 2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341]. In this paper, coastal and marine-access refineries with simplified workflow are considered. Unlike existing approaches, the new approach can avoid composition discrepancy without using iterative algorithm and find better solution effectively. In this approach, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules collected from expert experience are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. Thus, crude oil scheduling can be expressed as a complete mixed integer linear programming (MILP) model with fewer binary variables. To illustrate the advantage of the new approach, four typical examples are solved with three models. The new model is compared with the most effective models (RKS(a) and RKS(b) models) presented by Reddy et al. [2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341], which proves that the new approach is valid and feasible in most small-size and medium-size problems.     

化工过程系统综合问题新的模块化求解策略和算法

针对过程系统综合问题中求解混合整数非线性规划（MINLP）问题传统解法的不足提出了在[JP+1]模块化环境中过程系统综合问题新的求解策略,同时提出相对应的算法.实例证明了该策略的正确性和新算法的有效性.     

化工过程系统优化的分布式并行计算

针对大规模化工过程系统优化计算能力不够的情况 ,讨论用机群系统建构成并行优化计算环境 .在分析并行计算的原理和现状后 ,对优化算法的并行化进行探讨 ,并且深入讨论了大规模优化算法SQP的并行化和如何提高机群系统效率的问题 .通过精馏塔优化算例 ,证明利用机群系统开展并行优化是行之有效的