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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 9 (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 6 (5 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.
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 5 (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.
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 4 (3 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
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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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