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Optimization models for operative planning in drinking water networks
 IN PREPARATION
, 2004
"... The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed m ..."
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Cited by 15 (3 self)
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The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradientbased optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory nearoptimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.
Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control
 Journal of Process Control
"... In modelbased nonlinear optimal control switching decisions that can be optimized often play an important role. Prominent examples of such hybrid systems are gear switches for transport vehicles or on/off valves in chemical engineering. Optimization algorithms need to take the discrete nature of th ..."
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Cited by 12 (7 self)
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In modelbased nonlinear optimal control switching decisions that can be optimized often play an important role. Prominent examples of such hybrid systems are gear switches for transport vehicles or on/off valves in chemical engineering. Optimization algorithms need to take the discrete nature of the variables that model these switching decisions into account. Unnecessarily, for many applications still an equidistant time discretization and either rounding or standard mixed–integer solvers are used. In this article we survey recent progress in theoretical bounds, reformulations, and algorithms for this problem class and show how process control can benefit from them. We propose a comprehensive algorithm based on the solution of a sequence of purely continuous problems and simulations, and provide a new and more compact proof for its wellposedness. Instead of focusing on a particular application, we classify different solution behaviors in the applications section. We provide references to respective case studies with prototype character and cite newly emerging benchmark libraries. We conclude by pointing out future challenges for process control with switching decisions. Key words: hybrid systems, optimal control, integer programming, MINLP 1.
The Integer Approximation Error in MixedInteger Optimal Control
"... Summary. We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixedinteger optimal control problems, MIOCP). We improve a theorem [25] that states that the solution of a relaxed and convexified problem can be approximated with arbit ..."
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Cited by 8 (6 self)
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Summary. We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixedinteger optimal control problems, MIOCP). We improve a theorem [25] that states that the solution of a relaxed and convexified problem can be approximated with arbitrary precision by a solution fulfilling the integer requirements. Unlike in previous publications the new proof avoids the usage of the KreinMilman theorem, which is undesirable as it only states the existence of a solution that may switch infinitely often. We present a constructive way to obtain an integer solution with a guaranteed bound on the performance loss in polynomial time. We prove that this bound depends linearly on the control discretization grid. A numerical benchmark example illustrates the procedure. As a byproduct, we obtain an estimate of the Hausdorff distance between reachable sets. We improve the approximation order to linear grid size h instead of the previously known result with order √ h [14]. We are able to include a Special Ordered Set condition which will allow for a transfer of the results to a more general, multidimensional and nonlinear case compared to the Theorems in [20]. 1
On PDE solution in transient optimization of gas networks
 J. COMPUT. APPL. MATH. ACCEPTED
, 2004
"... Operative planning in gas distribution networks leads to largescale mixedinteger optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions—or as relaxation in a branch and bound framework, addressing in particular the ..."
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Cited by 7 (2 self)
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Operative planning in gas distribution networks leads to largescale mixedinteger optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions—or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primaldual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems ’ structural properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided.
A BENCHMARK LIBRARY OF MIXEDINTEGER OPTIMAL CONTROL PROBLEMS
"... Abstract. Numerical algorithm developers need standardized test instances for empirical studies and proofs of concept. There are several libraries available for finitedimensional optimization, such as the netlib or the miplib. However, for mixedinteger optimal control problems (MIOCP) this is not y ..."
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Cited by 6 (1 self)
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Abstract. Numerical algorithm developers need standardized test instances for empirical studies and proofs of concept. There are several libraries available for finitedimensional optimization, such as the netlib or the miplib. However, for mixedinteger optimal control problems (MIOCP) this is not yet the case. One explanation for this is the fact that no dominant standard format has been established yet. In many cases instances are used in a discretized form, but without proper descriptions on the modeling assumptions and discretizations that have been applied. In many publications crucial values, such as initial values, parameters, or a concise definition of all constraints are missing. In this contribution we intend to establish the basis for a benchmark library of mixedinteger optimal control problems that is meant to be continuously extended online on the open community web page
KnowledgeBased Verification of Service Compositions – An SMT Approach
 in Engineering of Complex Computer Systems (ICECCS), 2013 18th International Conference on, July 2013. doi: 10.1109/ICECCS.2013.14
"... Abstract—In the Semantic (Web) Services area, services are considered black boxes with a semantic description of their interfaces as to allow for precise service selection and configuration. The semantic description is usually grounded on domainspecific concepts as modeled in ontologies. This acco ..."
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Cited by 2 (2 self)
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Abstract—In the Semantic (Web) Services area, services are considered black boxes with a semantic description of their interfaces as to allow for precise service selection and configuration. The semantic description is usually grounded on domainspecific concepts as modeled in ontologies. This accounts to types used in service signatures, but also to predicates occurring in preconditions and effects of services. Ontologies, in particular those enhanced with rules, capture the knowledge of domain experts on properties of and relations between domain concepts. In this paper, we present a verification technique for service compositions which makes use of this domain knowledge. We consider a service composition to be an assembly of services of which we just know signatures, preconditions, and effects. We aim at proving that a composition satisfies a (userdefined) requirement, specified in terms of guaranteed preconditions and required postconditions. As an underlying verification engine we use an SMT solver. To take advantage of the domain knowledge (and often, to enable verification at all), the knowledge is fed into the solver in the form of sorts, uninterpreted functions and in particular assertions as to enhance the solver’s reasoning capabilities. Thereby, we allow for deductions within a domain previously unknown to the solver. We exemplify our technique on a case study from the area of water network optimization software. I.
ABOUT ONE APPROACH TO SOLVE THE PROBLEM OF MANAGEMENT OF THE DEVELOPMENT AND OPERATION OF CENTRALIZED WATERSUPPLY SYSTEMS
, 2014
"... A b s t r a c t. One of the approaches to solve the problem of resource and energy saving in centralized watersupply systems by reducing the total excess pressure in watersupply nodes is examined in the present work. The implementation of this approach is provided due to reengineering of watersu ..."
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A b s t r a c t. One of the approaches to solve the problem of resource and energy saving in centralized watersupply systems by reducing the total excess pressure in watersupply nodes is examined in the present work. The implementation of this approach is provided due to reengineering of watersupplies by their zoning and optimal fluxdistribution in the watersupplies. Mathematical formulations of the problems to be examined and efficient algorithms of their solving are presented. K e y w o r d s: resource and energy saving, zoning, pressure regulators, pump station, adjustable drive.
On Perspective Functions and Vanishing Constraints in MixedInteger Nonlinear Optimal Control
"... Abstract Logical implications appear in a number of important mixedinteger nonlinear optimal control problems (MIOCPs). Mathematical optimization offers a variety of different formulations that are equivalent for boolean variables, but result in different relaxations. In this article we give an o ..."
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Abstract Logical implications appear in a number of important mixedinteger nonlinear optimal control problems (MIOCPs). Mathematical optimization offers a variety of different formulations that are equivalent for boolean variables, but result in different relaxations. In this article we give an overview over a variety of different modeling approaches, including outer versus inner convexification, generalized disjunctive programming, and vanishing constraints. In addition to the tightness of the respective relaxations, we also address the issue of constraint qualification and the behavior of computational methods for some formulations. As a benchmark, we formulate a truck cruise control problem with logical implications resulting from gearchoice specific constraints. We provide this benchmark problem in AMPL format along with different realistic scenarios. Computational results for this benchmark are used to investigate feasibility gaps, integer feasibility gaps, quality of local solutions, and wellbehavedness of numerical methods for the presented reformulations of the benchmark problem. Vanishing constraints give the most satisfactory results. 1