Mixed-integer nonlinear programming techniques for process systems engineering

Mixed-integer nonlinear programming techniques for process systems engineering

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.

Development of transportation cost functions and optimization of transportation networks for solar-aided utilization of CO2

ABSTRACTThe main objectives in the management of energy systems are to reduce the operation costs and simultaneously increase the reliability indices. The achievement of these aims is among the key challenges that network operators encounter. To overcome this challenge, the current study presents a model in which the reliability criterion is calculated in addition to the well-established technical constraints for an energy hub. In this strategy, reliability evaluations are added to the classical model as new constraints. In other words, the energy hubs can be more appropriately and realistically operated by imposing these limitations. Moreover, in addition to the costs of different energy carriers, the objective function also includes the costs of “energy not supplied” (ENS) for different loads. This approach demonstrates a mixed-integer nonlinear programming (MINLP) technique implemented using the LINDOGlobal solver in GAMS. To examine the efficiency of the proposed method, modeling is performed on a sample energy hub, and the results assessed.

In this paper a general framework is discussed within which a municipal authority can assess future needs for certain public services within its area and can develop a programme for land purchase within a fixed budget. Concentration is on developing an optimising model, using mixed integer programming techniques, to identify available plots of land and to earmark them for specific land uses. A range of constraints is discussed, and a set of subsidies and penalties arising out of a solution method due to Balas, explained with reference to the local municipality of Coimbra in central Portugal, is presented.

This article presents an overview and a flavour of almost two decades of MARKAL model developments and selected applications. The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s. Under the auspices of the International Energy Agency’s (IEA) Energy Technology Systems Analysis Programme (ETSAP) the model started as a linear programming (LP) application focused strictly on the integrated assessment of energy systems. It was followed by a non-linear programming (NLP) formulation which combines the ‘bottom-up’ technology model with a ‘top-down’ simplified macro-economic model. In recent years, the family was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, to model endogenous technology learning using mixed integer programming (MIP) techniques, and to model multiple regions (NLP/LP).

We provide the methods for searching for the unique Nash equilibrium using mixed integer programming techniques. We also simulate the model parameters using this technique and derive the numerical solution to show the characteristics of a key player providing both public goods as suggested by Bergstrom et al. (1986). We present two key results. First, when the number of players decreases, the appearance rate of the unique equilibrium accompanying a key player increases. Second, when the variance of the preference or price parameters decreases, the appearance rate of the unique equilibrium accompanying a key player increases.

This paper proposes a real time price based optimal scheduling mechanism for centralized air conditioning load. In residential context, air conditioners are the main reason for peak load in summers. The proposed mechanism aims to determine optimal operation of air conditioner such that it results in reduction in consumer's electricity bills. Mixed Integer Programming technique is used for obtaining optimal schedule. The results obtained are compared with a previously established Linear Sequential Algorithm for evaluating the effectiveness of the scheme. The results show that Mixed Integer Programming technique provides higher reduction in electricity bill as compared to Linear Sequential technique.

In a recent paper by Prodan et al. (J. Optim. Theory Appl. 154:549---572, 2012), a technique was presented to reduce the number of binary variables needed to represent not convex constraints in a mixed-integer programming (MIP) problem. The proposed technique employs tuples of binary variables, which are associated with feasible regions of the feature space. However, since the number of all possible tuples with a given number of bits is a power of two, there may be several unallocated tuples that must be rendered infeasible by imposing suitable constraints. We show in this paper that it is always possible to partition the tuples so that only one inequality is necessary to render all the unallocated tuples and only them infeasible. Moreover, we develop a systematic procedure to perform this partition and write the referred inequality.

We present a method based on mean field theory to cope with the mixed nonlinear integer programming, especially with optimal power flow problems involving both continuous and discrete variables, in a more exact manner. That is, we first formulate OPF as a mixed integer programming, and then derive its mean field equations as well as the annealing algorithm, by taking advantage of the characteristics of the original problems. Numerical simulations have verified effectiveness of this approach for small power systems.

Integration of distributed generation (DG) in a distribution network is a key for power loss mitigation and improvement in the voltage profile. In this paper, a mixed-integer nonlinear programming (MINLP) based optimization technique has been used to determine the optimal sizes and corresponding locations of DGs to be placed in a distribution network for reduction of power loss and improvement in the voltage profile. The MINLP technique considered in this paper, utilizes the sequential quadratic programming (SQP) through ‘fmincon’ function available in the MATLAB optimization toolbox. The MINLP technique has been applied for solving the problem of optimal DG placement in IEEE 33-Bus and 69-Bus distribution systems. For the purpose of load flow, a well-known direct load flow technique has been used. After the analysis of the results obtained for the two test systems, it can be concluded that MINLP is an effective approach for minimizing the distribution network losses and improving the system voltage profile by optimally placing the DGs of suitable sizes at appropriate locations.

A nonlinear programming approach to kinematic shakedown analysis of frictional materials

We examine various aspects of modeling and solution via mixed-integer nonlinear programming (MINLP). MINLP has much to offer as a powerful modeling paradigm. Recently, significant advances have been made in MINLP solution software. To fully realize the power of MINLP to solve complex business optimization problems, we need to develop knowledge and expertise concerning MINLP modeling and solution methods. Some of this can be drawn from conventional wisdom of mixed-integer linear programming (MILP) and nonlinear programming (NLP), but theoretical and practical issues exist that are specific to MINLP. This paper discusses some of these, concentrating on an aspect of a classical facility location problem that is well-known in the MILP literature, although here we consider a nonlinear objective function.

Mixed-integer programming and multi-objective optimization techniques for the design of control augmented structures

The sugarcane transport system is very complex and uses a daily schedule, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Producing efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. In this paper, the sugarcane rail operations are formulated as a blocking job shop scheduling problem. A mixed integer programming approach is used to formulate the shop job scheduling problem. Mixed integer programming and constraint programming search techniques are integrated for solving the problem. A case study is solved to test the approach.