Krzysztof Malinowski

Predictive Methods for Real-Time Control of Flood Operation of a Multireservoir System: Methodology and Comparative Study

Predictive methods for real-time flood operation of water systems consisting of reservoirs located in parallel on tributaries to the main river are presented and discussed. The aspect of conflicting individual goals of the local decision units and other objectives important from an overall point of view is taken into account. The particular attention is focused on hierarchical control structure which provides framework for organization of an on-line reservoir management problem. The important factor involved in flood control the uncertainty with respect to future inflows is taken into consideration. A case study of the upper Vistula river basin system in the southern part of Poland is presented. Simulation results based on 11 historical floods are briefly described and discussed.

A hybrid analytic/rule-based approach to reservoir system management during flood

The article presents an approach to real-time operation of a water retention reservoir during flood. Water releases are calculated repetitively on the basis of two-variant inflow forecasts and some expert knowledge. During every intervention of the control algorithm, an optimization problem with the expected value type performance index is solved. In the paper, the basic characteristics of trajectories of outflows resulting from the application of this control method are analyzed. Afterwards, the results of the series of simulation experiments based on a large set of historical data concerning a big Polish reservoir are presented.

Optimization network flow control and price coordination with feedback: proposal of a new distributed algorithm

The usage of price instruments was found to offer an interesting opportunity for reactive congestion flow control in communication or computer networks where the objective is to maximize the total utility of all traffic sources over their transmission rates. The proposed control mechanisms were, amongst others, based on the Price Method-known also as the Interaction Balance Method-and both synchronous and asynchronous versions were developed. It was, however, so far assumed that the transmission network model was known exactly and that no traffic was lost and the traffic routes were fixed and known to the transmitting sources. In this paper, we formulate the flow control problem in a modified form, allowing in particular for the routing decisions to be hidden from the sources, and recall the concept of the Price Coordination with Feedback (known also under the name of the Interaction Balance Method with Feedback-IBMF). It is then shown that the use of this approach allows for proposing the new distributed algorithm for pricing of network services. The existence of an optimal solution in steady state is proved under reasonable assumptions and the convergence issues are discussed. Two examples are provided to illustrate the operation of the proposed algorithm and to compare its performance with the usage of classical price coordination.

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods

Object Library of Algorithms for Dynamic Optimization Problems: Benchmarking SQP and Nonlinear Interior Point Methods The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.

On formulation of a network energy saving optimization problem

Possible formulations of mathematical programing problem concerning energy aware network are presented. Two main possibilities of reducing problem complexity are analysed: allocation of predefined paths and reformulation of task using continuous variables. Properties of both methods are analysed and hybrid formulation is proposed. Comparison of complexity is provided.

Characterization of scalar strategy mechanisms for efficient resource allocation: Supply side case

We give a characterization of scalar strategy mechanisms that efficiently allocate production among strategically interdependent agents. We establish necessary and sufficient conditions for the mechanisms to yield allocations that maximize aggregate surplus of the market under constraints given by the market-clearing equation setting a price at which the total output supplied equals demand. Efficient Nash equilibria of games induced by the proposed class of mechanisms are proved to be asymptotically stable and reachable in a dynamical bidding process. A distributed bidding algorithm is given as well.

On Efficient Resource Allocation in Communication Networks

We study the problem of allocating a single divisible resource to strategic agents in communication networks. For the setting of inelastic supply we formulate conditions for the efficiency of Nash equilibria in a resulting resource allocation game. Then we answer the question how to design a mechanism which yields efficient allocations and analyze revenues generated by the proposed class of mechanisms. Finally, we propose a distributed resource allocation algorithm and prove its convergence.

An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems

This paper considers two main topics.The first one is a new interval global optimization algorithm, using some symbolic transformations of the optimality conditions. The theory of Groebner bases and the idea of componentwise interval Newton method are used.The second topic is the description of an optimization problem connected with access control to a computer server. This optimization problem is solved by using a new algorithm and, for comparison, by using a classical interval branch-and-bound algorithm.

FC-VS: a decision support system for flood control in multireservoir systems

Abstract The paper presents a software package FC-VS (Flood Control - Vistula System) designed as a real-time Decision Support System for the control centre of multireservoir water system in Southern Poland. This is an implementation of a two-level control structure for the optimal flood operation of river - reservoir systems. The natural hierarchy of the decision units, i.e., the control centre and operators of the reservoirs is preserved. The FC-VS system helps the central dispatcher by proposing him the values of special coordinating parameters for modifying release decisions of local reservoirs operators. The aim of the structure is to minimize damages created by a flood wave passing through a river-basin. FC-VS can be also used for training purposes using historical data. Some simulation results in the final part of the article.

Hierarchical Control Under Uncertainty; Formal and Practical Aspects

Abstract The paper is concerned with coordination in hierarchical control of large scale systems under uncertainty. The main objective is to present important methodological and theoretical issues related to design and operation of hierarchical control structures and to discuss possible practical approaches to the design of such structures.