Mixed-integer nonlinear programming techniques for process systems engineering

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.

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.

Mixed-integer nonlinear programming techniques for process systems engineering

<div class="htmlview paragraph">Recently, the control of traffic flow has been proposed using several types of criteria (e.g. minimum-time control, minimum fuel control and so on). Most recently, an environmental noise pollution problem caused by the road traffic is being aggravated more and more by the consolidation and expansion of roadway system particularly in urban areas. However, the objective of this paper is to control road traffic flow by regulating traffic noise propagation in an urban area in Cairo city. The results of traffic noise prediction obtained by trending of the experimental data collecting by systematic noise measurement and the evaluation of the traffic noise which is in close connection with physical parameters of traffic flow and noise propagation characteristics is presented. The analysis of road traffic flow noise control is based on the mixed integer non-linear programming technique, where the optimal control strategy is used. The results indicate that significant information gained for controlling road traffic in urban areas.</div>

A nonlinear programming approach to kinematic shakedown analysis of frictional materials

Recently, in structural engineering, many main elements in structural systems such as columns or girders are designed with variable cross-section for certain purposes. In addition, in order to determine the appropriate sizes or suitable shapes of structural elements for optimal volume of material under the effect of certain loading or with the given sizes of elements the structures can be subjected maximum loading, it is required to studied the optimization problem. This paper presents the non-linear weight optimization problem of frames with variable section stiffness of columns according to the strength, stiffness and stability criteria with the help of finite element method. The non-linear optimization problem is solved by the Genetic Algorithm. The calculation procedure of non-linear optimization of plane frames with variable section stiffness of columns is established and implemented using Matlab calculation programming software. From the results of numerical examples, the conclusions and recommendations will be proposed.

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).

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.

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 this paper we present a Lagrange-multiplier formulation of discrete constrained optimization problems, the associated discrete-space first-order necessary and sufficient conditions for saddle points, and an efficient first-order search procedure that looks for saddle points in discrete space. Our new theory provides a strong mathematical foundation for solving general nonlinear discrete optimization problems. Specifically, we propose a new vector-based definition of descent directions in discrete space and show that the new definition does not obey the rules of calculus in continuous space. Starting from the concept of saddle points and using only vector calculus, we then prove the discrete-space first-order necessary and sufficient conditions for saddle points. Using well-defined transformations on the constraint functions, we further prove that the set of discrete-space saddle points is the same as the set of constrained local minima, leading to the first-order necessary and sufficient conditions for constrained local minima. Based on the first-order conditions, we propose a local-search method to look for saddle points that satisfy the first-order conditions.KeywordsLocal MinimumLagrange MultiplierSaddle PointLagrangian MethodFeasible PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Reliability constrained generation expansion planning by a modified shuffled frog leaping algorithm

The utilization of wind energy sources in autonomous power systems can significantly reduce the system fuel costs but increase the investment costs and have adverse effect on the system safety and reliability, therefore there is a need to study rational capacity expansion planning. This paper proposes the model of the optimal expansion planning of wind-diesel energy system based on improved genetic algorithm (IGA) due to its application to the highly constrained nonlinear discrete dynamic optimization problem. The main advantage of IGA approach is that "the curse of dimensionality" in the mathematical method can be overcame. In this paper the planning objective costs take into account unserved energy costs besides investment costs and operation costs. The evaluation of probability cost and reliability in the model is performed by using Monte-Carlo method for representing the uncertainty for wind speed and loads, forced outage rate of the units, the correlation of wind speed and load series, wind generation operational constraints. The example indicates that the model and algorithm that puts forward in this paper is feasible and provides the important reference value for the planning and design of wind generation system.

In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.

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.