Natural gas system operation: lagrangean optimization techniques

To comply with natural gas demand growth patterns and Europe´s import dependency, the gas industry needs to organize an efficient upstream infrastructure. The best location of Gas Supply Units – GSUs and the alternative transportation mode – by phisical or virtual pipelines, are the key of a successful industry. In this work we study the optimal location of GSUs, as well as determining the most efficient allocation from gas loads to sources, selecting the best transportation mode, observing specific technical restrictions and minimizing system total costs. For the location of GSUs on system we use the P-median problem, for assigning gas demands nodes to source facilities we use the classical transportation problem. The developed model is an optimisation-based approach, based on a Lagrangean heuristic, using Lagrangean relaxation for P-median problems – Simple Lagrangean Heuristic. The solution of this heuristic can be improved by adding a local search procedure - the Lagrangean Reallocation Heuristic. These two heuristics, Simple Lagrangean and Lagrangean Reallocation, were tested on a realistic network - the primary Iberian natural gas network, organized with 65 nodes, connected by physical and virtual pipelines. Computational results are presented for both approaches, showing the location gas sources and allocation loads arrangement, system total costs and gas transportation mode.

An heuristic approach for optimal location of gas supply units in transportation system

The best places to locate the Gas Supply Units (GSUs) on a natural gas systems and their optimal allocation to loads are the key factors to organize an efficient upstream gas infrastructure. The number of GSUs and their optimal location in a gas network is a decision problem that can be formulated as a linear programming problem. Our emphasis is on the formulation and use of a suitable location model, reflecting real-world operations and constraints of a natural gas system. This paper presents a heuristic model, based on lagrangean approach, developed for finding the optimal GSUs location on a natural gas network, minimizing expenses and maximizing throughput and security of supply.The location model is applied to the Iberian high pressure natural gas network, a system modelised with 65 demand nodes. These nodes are linked by physical and virtual pipelines – road trucks with gas in liquefied form. The location model result shows the best places to locate, with the optimal demand allocation and the most economical gas transport mode: by pipeline or by road truck.

Natural Gas location design and operation

A major determinant of the level of effective natural gas supply is the ease to feed customers, minimizing system total costs. The aim of this work is the study of the right number of Gas Supply Units – GSUs - and their optimal location in a gas network. This paper suggests a GSU location heuristic, based on Lagrangean relaxation techniques. The heuristic is tested on the Iberian natural gas network, a system modelized with 65 demand nodes, linked by physical and virtual pipelines. Lagrangean heuristic results along with the allocation of loads to gas sources are presented, using a 2015 forecast gas demand scenario.

Optimization model for medium term natural gas commitment

In this paper we study the optimal natural gas commitment for a known demand scenario. This study implies the best location of GSUs to supply all demands and the optimal allocation from sources to gas loads, through an appropriate transportation mode, in order to minimize total system costs. Our emphasis is on the formulation and use of a suitable optimization model, reflecting real-world operations and the constraints of natural gas systems. The mathematical model is based on a Lagrangean heuristic, using the Lagrangean relaxation, an efficient approach to solve the problem. Computational results are presented for Iberian and American natural gas systems, geographically organized in 65 and 88 load nodes, respectively. The location model results, supported by the computational application GasView, show the optimal location and allocation solution, system total costs and suggest a suitable gas transportation mode, presented in both numerical and graphic supports.

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests. (C) 2009 Elsevier B.V. All rights reserved.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

Polyhedral results for the Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP)

In recent years, there has been studies on the cardinality constrained multi-cycle problems on directed graphs, some of which considered chains co-existing on the same digraph whilst others did not. These studies were inspired by the optimal matching of kidneys known as the Kidney Exchange Problem (KEP). In a KEP, a vertex on the digraph represents a donor-patient pair who are related, though the kidney of the donor is incompatible to the patient. When there are multiple such incompatible pairs in the kidney exchange pool, the kidney of the donor of one incompatible pair may in fact be compatible to the patient of another incompatible pair. If Donor A’s kidney is suitable for Patient B, and vice versa, then there will be arcs in both directions between Vertex A to Vertex B. Such exchanges form a 2-cycle. There may also be cycles involving 3 or more vertices. As all exchanges in a kidney exchange cycle must take place simultaneously, (otherwise a donor can drop out from the program once his/her partner has received a kidney from another donor), due to logistic and human resource reasons, only a limited number of kidney exchanges can occur simultaneously, hence the cardinality of these cycles are constrained. In recent years, kidney exchange programs around the world have altruistic donors in the pool. A sequence of exchanges that starts from an altruistic donor forms a chain instead of a cycle. We therefore have two underlying combinatorial optimization problems: Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP). The objective of the KEP is either to maximize the number of kidney matches, or to maximize a certain weighted function of kidney matches. In a CCMcP, a vertex can be in at most one cycle whereas in a CCCCP, a vertex can be part of (but in no more than) a cycle or a chain. The cardinality of the cycles are constrained in all studies. The cardinality of the chains, however, are considered unconstrained in some studies, constrained but larger than that of cycles, or the same as that of cycles in others. Although the CCMcP has some similarities to the ATSP- and VRP-family of problems, there is a major difference: strong subtour elimination constraints are mostly invalid for the CCMcP, as we do allow smaller subtours as long as they do not exceed the size limit. The CCCCP has its distinctive feature that allows chains as well as cycles on the same directed graph. Hence, both the CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights. Most existing studies focused on solution methodologies, and as far as we aware, there is no polyhedral studies so far. In this paper, we will study the polyhedral structure of the natural arc-based integer programming models of the CCMcP and the CCCCP, both containing exponentially many constraints. We do so to pave the way for studying strong valid cuts we have found that can be applied in a Lagrangean relaxation-based branch-and-bound framework where at each node of the branch-and-bound tree, we may be able to obtain a relaxation that can be solved in polynomial time, with strong valid cuts dualized into the objective function and the dual multipliers optimised by subgradient optimisation.

Lagrangean Approximation for Combinatorial Inverse Problems

Various combinatorial problems are effectively modelled in terms of (0,1) matrices. Origins are coming from n-cube geometry, hypergraph theory, inverse tomography problems, or directly from different models of application problems. Basically these problems are NP-complete. The paper considers a set of such problems and introduces approximation algorithms for their solutions applying Lagragean relaxation and related set of techniques.

Anisotropy of spin relaxation of water protons in cartilage and tendon

Transverse spin relaxation rates of water protons in articular cartilage and tendon depend on the orientation of the tissue relative to the applied static magnetic field. This complicates the interpretation of magnetic resonance images of these tissues. At the same time, relaxation data can provide information about their organisation and microstructure. We present a theoretical analysis of the anisotropy of spin relaxation of water protons observed in fully hydrated cartilage. We demonstrate that the anisotropy of transverse relaxation is due almost entirely to intramolecular dipolar coupling modulated by a specific mode of slow molecular motion: the diffusion of water molecules in the hydration shell of a collagen fibre around the fibre, such that the molecular director remains perpendicular to the fibre. The theoretical anisotropy arising from this mechanism follows the “magic-angle” dependence observed in magnetic-resonance measurements of cartilage and tendon and is in good agreement with the available experimental results. We discuss the implications of the theoretical findings for MRI of ordered collagenous tissues.

Investigation of 'off-line‘ relaxation phenomena in oil filled transformers

Power transformers are one of the most important and costly equipment in power generation, transmission and distribution systems. Current average age of transformers in Australia is around 25 years and there is a strong economical tendency to use them up to 50 years or more. As the transformers operate, they get degraded due to different loading and environmental operating stressed conditions. In today‘s competitive energy market with the penetration of distributed energy sources, the transformers are stressed more with minimum required maintenance. The modern asset management program tries to increase the usage life time of power transformers with prognostic techniques using condition indicators. In the case of oil filled transformers, condition monitoring methods based on dissolved gas analysis, polarization studies, partial discharge studies, frequency response analysis studies to check the mechanical integrity, IR heat monitoring and other vibration monitoring techniques are in use. In the current research program, studies have been initiated to identify the degradation of insulating materials by the electrical relaxation technique known as dielectrometry. Aging leads to main degradation products like moisture and other oxidized products due to fluctuating thermal and electrical loading. By applying repetitive low frequency high voltage sine wave perturbations in the range of 100 to 200 V peak across available terminals of power transformer, the conductive and polarization parameters of insulation aging are identified. An in-house novel digital instrument is developed to record the low leakage response of repetitive polarization currents in three terminals configuration. The technique is tested with known three transformers of rating 5 kVA or more. The effects of stressing polarization voltage level, polarizing wave shapes and various terminal configurations provide characteristic aging relaxation information. By using different analyses, sensitive parameters of aging are identified and it is presented in this thesis.