Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.

Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

A Constructive Heuristic Algorithm for Distribution System Planning

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.

Distribution network planning using a constructive heuristic algorithm

An optimization technique to solve distribution network planning (DNP) problem is presented. This is a very complex mixed binary nonlinear programming problem. A constructive heuristic algorithm (CHA) aimed at obtaining an excellent quality solution for this problem is presented. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution network. This sensitivity index is obtained solving the DNP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. A local improvement phase and a branching technique were implemented in the CHA. Results of two tests using a distribution network are presented in the paper in order to show the ability of the proposed algorithm. ©2009 IEEE.

An efficient implementation of tabu search in feeder reconfiguration of distribution systems

This paper presents an efficient tabu search algorithm (TSA) to solve the problem of feeder reconfiguration of distribution systems. The main characteristics that make the proposed TSA particularly efficient are a) the way in which the neighborhood of the current solution was defined; b) the way in which the objective function value was estimated; and c) the reduction of the neighborhood using heuristic criteria. Four electrical systems, described in detail in the specialized literature, were used to test the proposed TSA. The result demonstrate that it is computationally very fast and finds the best solutions known in the specialized literature. © 2012 IEEE.

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

New Rigorous Decomposition Methods for Mixed-integer Linear and Nonlinear Programming

Process systems design, operation and synthesis problems under uncertainty can readily be formulated as two-stage stochastic mixed-integer linear and nonlinear (nonconvex) programming (MILP and MINLP) problems. These problems, with a scenario based formulation, lead to large-scale MILPs/MINLPs that are well structured. The first part of the thesis proposes a new finitely convergent cross decomposition method (CD), where Benders decomposition (BD) and Dantzig-Wolfe decomposition (DWD) are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. A variant of CD, which includes multiple columns per iteration of DW restricted master problem and multiple cuts per iteration of BD relaxed master problem, called multicolumn-multicut CD is then developed to improve solution time. Finally, an extended cross decomposition method (ECD) for solving two-stage stochastic programs with risk constraints is proposed. In this approach, a CD approach at the first level and DWD at a second level is used to solve the original problem to optimality. ECD has a computational advantage over a bilevel decomposition strategy or solving the monolith problem using an MILP solver. The second part of the thesis develops a joint decomposition approach combining Lagrangian decomposition (LD) and generalized Benders decomposition (GBD), to efficiently solve stochastic mixed-integer nonlinear nonconvex programming problems to global optimality, without the need for explicit branch and bound search. In this approach, LD subproblems and GBD subproblems are systematically solved in a single framework. The relaxed master problem obtained from the reformulation of the original problem, is solved only when necessary. A convexification of the relaxed master problem and a domain reduction procedure are integrated into the decomposition framework to improve solution efficiency. Using case studies taken from renewable resource and fossil-fuel based application in process systems engineering, it can be seen that these novel decomposition approaches have significant benefit over classical decomposition methods and state-of-the-art MILP/MINLP global optimization solvers.

Allocation of protective devices in distribution circuits using nonlinear programming models and genetic algorithms

The optimized allocation of protective devices in strategic points of the circuit improves the quality of the energy supply and the system reliability index. This paper presents a nonlinear integer programming (NLIP) model with binary variables, to deal with the problem of protective device allocation in the main feeder and all branches of an overhead distribution circuit, to improve the reliability index and to provide customers with service of high quality and reliability. The constraints considered in the problem take into account technical and economical limitations, such as coordination problems of serial protective devices, available equipment, the importance of the feeder and the circuit topology. The use of genetic algorithms (GAs) is proposed to solve this problem, using a binary representation that does (1) or does not (0) show allocation of protective devices (reclosers, sectionalizers and fuses) in predefined points of the circuit. Results are presented for a real circuit (134 busses), with the possibility of protective device allocation in 29 points. Also the ability of the algorithm in finding good solutions while improving significantly the indicators of reliability is shown. (C) 2003 Elsevier B.V. All rights reserved.

Nonlinear programming solutions for controlling the vibration pattern of stretched strings

The problem of controlling the vibration pattern of a driven string is considered. The basic question dealt with here is to find the control forces which reduce the energy of vibration of a driven string over a prescribed portion of its length while maintaining the energy outside that length above a desired value. The criterion of keeping the response outside the region of energy reduction as close to the original response as possible is introduced as an additional constraint. The slack unconstrained minimization technique (SLUMT) has been successfully applied to solve the above problem. The effect of varying the phase of the control forces (which results in a six-variable control problem) is then studied. The nonlinear programming techniques which have been effectively used to handle problems involving many variables and constraints therefore offer a powerful tool for the solution of vibration control problems.