Development and computational tests of an undecoupled optimum short-term hydro-thermal schedulling code using network flows

Summary Optimizing the thermal production of electricity in the short term in an integrated power system when a thermal unit commitment has been decided means coordinating hydro and thermal generation in order to obtain the minimum thermal generation costs over the time period under study. Fundamental constraints to be satisfied are the covering of each hourly load and satisfaction of spinning reserve requirements. A nonlinear network flow model with linear side constraints with no decomposition into hydro and thermal subproblems was used to solve the hydrothermal scheduling. Hydrogeneration is linearized with respect to network variables and a novel thermal generation network is introduced. Computational results are reported.     

Some models for water distribution systems

In this paper the results of our investigation of methods and algorithms for operative and dynamical control of water distribution systems are presented. Our investigation was directed to the distribution system equipped with a variety of components—pipes, consumers, valves and the inner water store (a reservoir) as the most important one. The final model of the optimization problem containing all necessary restrictions is so complex that it is impossible to solve it without some special techniques. In the presented study we propose a multilevel approach based on the idea of aggregation of the pipelines network. In the paper the method of determination of aggregated model of the network is presented. The usefulness of this method in the optimization of water supply systems is examined. Based on an aggregated network model one determines optimal strategies for control of pumping stations. The optimization model consists of a linear objective function and quadratic constraints. A nonlinear mixed integer programming problem which is solved by modified branch and bound method is obtained.     

Ant colony optimization for power plant maintenance scheduling optimization—a five-station hydropower system

A number of algorithms have been developed for the optimization of power plant maintenance schedules. However, the true test of such algorithms occurs when they are applied to real systems. In this paper, the application of an Ant Colony Optimization formulation to a hydropower system is presented. The formulation is found to be effective in handling various constraints commonly encountered in practice. Overall, the results obtained using the ACO formulation are better than those given by traditional methods using engineering judgment, which indicates the potential of ACO in solving realistic power plant maintenance scheduling problems.     

Detecting embedded pure network structures in LP problems

Recently, linear programming problems with special structures have assumed growing importance in mathematical programming. It is well known that exploiting network structures within linear programs can lead to considerable improvement of the computational solution of large-scale linear programming problems. A linear program is said to contain an embedded network structure provided that some subset of its constraints can be interpreted as specifying conservation of flow. If a column of the constraint matrix has at most two non-zeros, then it leads to embedded generalized network structure and if these non-zeros are unit elements and of opposite signs, then it leads to embedded pure network structure. In this paper, we are concerned with algorithms for detecting embedded pure network structures within linear programs. The network extraction methods are presented in two groups. The first group covers deletion and addition based algorithms and the second group covers GUB based algorithms. We have extended the GUB based algorithm appearing in the second group by introducing Markowitz merit count approach for exploiting matrix non zeros. A set of well known test problems has been used to carry out computational experiments which show that our extensions to the GUB based algorithms give better results than the algorithms reported earlier.     

Solving nonlinear programming problems with very many constraints

For solving the smooth constrained nonlinear programming problem, sequential quadratic programming (SQP) methods are considered to be the standard tool, as long as they are applicable. However one possible situation preventing the successful solution by a standard SQP-technique, arises if problems with a very large number of constraints are to be solved. Typical applications are semi-infinite or min-max optimization, optimal control or mechanical structural optimization. The proposed technique proceeds from a user defined number of linearized constraints, that is to be used internally to determine the size of the quadratic programming subproblem. Significant constraints are then selected automatically by the algorithm. Details of the numerical implementation and some experimental results are presented     

Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation

The network design problem with relays arises in telecommunications and distribution systems where the payload must be reprocessed at intermediate stations called relays on the route from its origin to its destination. In fiber-optic networks, for example, optical signals may be regenerated several times to overcome signal degradation because of attenuation and other factors. Given a network and a set of commodities, the network design problem with relays involves selecting network edges, determining a route for each commodity, and locating relays to minimize the network design cost. This paper presents a new formulation to the problem based on set covering constraints. The new formulation is used to design a genetic algorithm with a specialized crossover/mutation operator which generates a feasible path for each commodity, and the locations of relays on these paths are determined by solving the corresponding set covering problem. Computational experiments show that the proposed approach can outperform other approaches, particularly on large size problems.     

Thevenin decomposition and large-scale optimization

The Thevenin theorem, one of the most celebrated results of electric circuit theory, provides a two-parameter characterization of the behavior of an arbitrarily large circuit, as seen from two of its terminals. We interpret the theorem as a sensitivity result in an associated minimum energy/network flow problem, and we abstract its main idea to develop a decomposition method for convex quadratic programming problems with linear equality constraints, of the type arising in a variety of contexts such as the Newton method, interior point methods, and least squares estimation. Like the Thevenin theorem, our method is particularly useful in problems involving a system consisting of several subssystems, connected to each other with a small number of coupling variables.This research was supported by NSF under Grant CCR-91-03804.     

Partial differential equations with differential constraints

A geometric setting for constrained exterior differential systems on fibered manifolds with n-dimensional bases is proposed. Constraints given as submanifolds of jet bundles (locally defined by systems of first-order partial differential equations) are shown to carry a natural geometric structure, called the canonical distribution. Systems of second-order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds. As an important particular case, Lagrangian systems subjected to first-order differential constraints are considered. Different kinds of constraints are introduced and investigated (Lagrangian constraints, constraints adapted to the fibered structure, constraints arising from a (co)distribution, semi-holonomic constraints, holonomic constraints).     

Reserve capacity of signal-controlled road network

For a signal control road network subject to equilibrium flows, the maximum possible increase in travel demands is considered in this paper. Using the concept of reserve capacity of signal-controlled junctions, the problem of finding the maximum increase in traffic demands can be formulated as a mathematical program with equilibrium constraints (MPEC). In this paper, we present a projected gradient approach to obtain the maximum increase in travel demands based on the TRANSYT traffic model. Numerical computations are made on a grid network where good results are obtained.     

SOCRATES: A system for scheduling hydroelectric generation under uncertainty

The Pacific Gas and Electric Company, the largest investor-owned energy utility in the United States, obtains a significant fraction of its electric energy and capacity from hydrogeneration. Although hydro provides valuable flexibility, it is subject to usage limits and must be carefully scheduled. In addition, the amount of energy available from hydro varies widely from year to year, depending on precipitation and streamflows. Optimal scheduling of hydrogeneration, in coordination with other energy sources, is a stochastic problem of practical significance to PG&E. SOCRATES is a system for the optimal scheduling of PG&E's various energy sources over a one- to two-year horizon. This paper concentrates on the component of SOCRATES that schedules hydro. The core is a stochastic optimization model, solved using Benders decomposition. Additional components are streamflow forecasting models and a database containing hydrological information. The stochastic hydro scheduling module of SOCRATES is undergoing testing in the user's environment, and we expect PG&E hydrologists and hydro schedulers to place progressively more reliance upon it.     

Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results.     

Exact penalty functions and stability in locally Lipschitz programming

In this paper we extend the theory of exact penalty functions for nonlinear programs whose objective functions and equality and inequality constraints are locally Lipschitz; arbitrary simple constraints are also allowed. Assuming a weak stability condition, we show that for all sufficiently large penalty parameter values an isolated local minimum of the nonlinear program is also an isolated local minimum of the exact penalty function. A tight lower bound on the parameter value is provided when certain first order sufficiency conditions are satisfied. We apply these results to unify and extend some results for convex programming. Since several effective algorithms for solving nonlinear programs with differentiable functions rely on exact penalty functions, our results provide a framework for extending these algorithms to problems with locally Lipschitz functions.     

A capacity scaling heuristic for the multicommodity capacitated network design problem

In this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem.     

A quadratic programming approach to the multi-product newsvendor problem with side constraints

A quadratic programming approach is proposed for solving the newsvendor problem with side constraints. Among its salient features are the facts that it: utilizes familiar packages to solve the problem such as Excel Solver and Lingo, can accommodate lower bounds of product’s demands that are larger than zero, and facilitates the performance of sensitivity analysis tasks.     

Multiqueue System with Non-Exhaustive Cyclic Service Modelled as a Linear-Programming Problem

In modern processor-controlled systems, it is common to find a central processor polling a number of message queues, where at most one message is processed from each queue during one polling cycle. This paper shows how one important parameter can be estimated quickly, namely the cycle-time distribution. This is the distribution of times taken for the cyclic server to perform one complete cycle in its continuous scan of a number of queues. The method of solution is to identify various constraints which will determine the cycle-time distribution, formulate them as linear inequality and equality constraints and, by determining an appropriate objective function, apply the simplex method to find upper and lower bounds on the values taken by the cycle-time distribution itself. A great strength of this technique is its overall simplicity, which enables it to be used to obtain important results very quickly and cheaply.     

An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty

In this work the design of a reverse distribution network is studied. Most of the proposed models on the subject are case based and, for that reason, they lack generality. In this paper we try to overcome this limitation and a generalized model is proposed. It contemplates the design of a generic reverse logistics network where capacity limits, multi-product management and uncertainty on product demands and returns are considered. A mixed integer formulation is developed which is solved using standard B&B techniques. The model is applied to an illustrative case.     

Turbulence modeling from a new perspective

In this work we establish a link between a Reynolds averaged turbulence modeling methodology, containing interactions up to the second order correlations between the velocity fluctuations at various scales, and a multi-objective optimization problem with the constraints expressed in terms of equality and inequality, imposed by the given boundary conditions and the positive semi-definiteness of the Reynolds stress tensor, etc. The information unavailability and uncertainty associated with the boundary conditions for the fluctuation correlations of various orders is delineated, and the information from the Navier–Stokes equations is utilized to the extent allowed by the available input data necessary for simulations; turbulence from the perspective of systems simulation is explored and some objective functions are proposed. Finally, the challenges faced by the formulation and the issues yet to be resolved are discussed.     

Infinite split scheduling: a new lower bound of total weighted completion time on parallel machines with job release dates and unavailability periods

This paper addresses an identical parallel machine scheduling problem with job release dates and unavailability periods to minimize total weighted completion time. This problem is known to be NP-hard in the strong sense. We propose a new lower bound that can be computed in polynomial time. The test on more than 8 400 randomly generated instances shows a very significant improvement with respect to existing results for previously studied special cases: without unavailability constraints, unweighted version, or identical job release dates. For instance, the average improvement for the unweighted problem is as much as 20.43% for 2 machines, 53.03% for 7 machines and 66.70% for 15 machines. For some instances, the improvement can be even as much as 93%.     

Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints

In Ref. 1, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was proposed. At each iteration, this new algorithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of computation required for existing SQP algorithms. Moreover, unlike the quadratic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvable. In Ref. 2, it is shown that the new algorithm can also be used to deal with nonlinear optimization problems having both equality and inequality constraints, by solving an auxiliary problem. But the algorithm of Ref. 2 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve the work of Ref. 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcoming the aforementioned shortcomings. Some numerical results are also reported.     

Optimisation of gravity-fed water distribution network design: A critical review

This paper surveys the literature on the optimisation of water distribution network design. The water distribution network design (WDND) optimisation problem entails finding the material and diameter of each pipe in the network so that the total cost of the network is minimised without violating any hydraulic constraints. This is a difficult combinatorial optimisation problem, in which decision variables are discrete and both cost function and constraints are non-linear. Over the past 30 years, a large number of methods, especially in the field of (meta) heuristics, have been developed to solve this problem, most of which obtain good results on the available benchmark networks. In addition to outlining the basic features of each method, a detailed computational comparison is presented. Based on this comparison, some issues with the current state of the art in this domain are discussed, and some future research directions are suggested. Additionally, the need for an adequate set of benchmark instances is motivated, and the minimal requirements for an instance set generator are discussed.