Thorsten Ederer

Experimental Validation of an Enhanced System Synthesis Approach

Planning the layout and operation of a technical system is a common task for an engineer. Typically, the workflow is divided into consecutive stages: First, the engineer designs the layout of the system, with the help of his experience or of heuristic methods. Secondly, he finds a control strategy which is often optimized by simulation. This usually results in a good operating of an unquestioned system topology. In contrast, we apply Operations Research (OR) methods to find a cost-optimal solution for both stages simultaneously via mixed integer programming (MILP). Technical Operations Research (TOR) allows one to find a provable global optimal solution within the model formulation. However, the modeling error due to the abstraction of physical reality remains unknown. We address this ubiquitous problem of OR methods by comparing our computational results with measurements in a test rig. For a practical test case we compute a topology and control strategy via MILP and verify that the objectives are met up to a deviation of 8.7 %.

Quantified linear programs: a computational study

Quantified linear programs (QLPs) are linear programs with variables being either existentially or universally quantified. The integer variant (QIP) is PSPACE-complete, and the problem is similar to games like chess, where an existential and a universal player have to play a two-person-zero-sum game. At the same time, a QLP with n variables is a variant of a linear program living in Rn, and it has strong similarities with multi-stage stochastic linear programs with variable right-hand side. Our interest in QLPs stems from the fact that they are LP-relaxations of QIPs, which themselves are mighty modeling tools. In order to solve QLPs, we apply a nested decomposition algorithm. In a detailed computational study, we examine, how different structural properties like the number of universal variables, the number of universal variable blocks as well as their positions in the QLP influence the solution process.

Modeling Games with the Help of Quantified Integer Linear Programs

Quantified linear programs (QLPs) are linear programs with mathematical variables being either existentially or universally quantified. The integer variant (Quantified linear integer program, QIP) is PSPACE-complete, and can be interpreted as a two-person zero-sum game. Additionally, it demonstrates remarkable flexibility in polynomial reduction, such that many interesting practical problems can be elegantly modeled as QIPs. Indeed, the PSPACE-completeness guarantees that all PSPACE-complete problems such as games like Othello, Go-Moku, and Amazons, can be described with the help of QIPs, with only moderate overhead. In this paper, we present the Dynamic Graph Reliability (DGR) optimization problem and the game Go-Moku as examples.

A Mixed-Integer Nonlinear Program for the Design of Gearboxes

Gearboxes are mechanical transmission systems that provide speed and torque conversions from a rotating power source. Being a central element of the drive train, they are relevant for the efficiency and durability of motor vehicles. In this work, we present a new approach for gearbox design: Modeling the design problem as a mixed-integer nonlinear program (MINLP) allows us to create gearbox designs from scratch for arbitrary requirements and—given enough time—to compute provably globally optimal designs for a given objective. We show how different degrees of freedom influence the runtime and present an exemplary solution.

A Comparison of MILP and MINLP Solver Performance on the Example of a Drinking Water Supply System Design Problem

Finding a good system topology with more than a handful of components is a highly non-trivial task. The system needs to be able to fulfil all expected load cases, but at the same time the components should interact in an energy-efficient way. An example for a system design problem is the layout of the drinking water supply of a residential building. It may be reasonable to choose a design of spatially distributed pumps which are connected by pipes in at least two dimensions. This leads to a large variety of possible system topologies. To solve such problems in a reasonable time frame, the nonlinear technical characteristics must be modelled as simple as possible, while still achieving a sufficiently good representation of reality. The aim of this paper is to compare the speed and reliability of a selection of leading mathematical programming solvers on a set of varying model formulations. This gives us empirical evidence on what combinations of model formulations and solver packages are the means of choice with the current state of the art. Lea Rausch, Philipp Leise, Thorsten Ederer, Lena C. Altherr and Peter F. Pelz

Multicriterial Optimization of Technical Systems Considering Multiple Load and Availability Scenarios

Cheap does not imply cost-effective -- this is rule number one of zeitgeisty system design. The initial investment accounts only for a small portion of the lifecycle costs of a technical system. In fluid systems, about ninety percent of the total costs are caused by other factors like power consumption and maintenance. With modern optimization methods, it is already possible to plan an optimal technical system considering multiple objectives. In this paper, we focus on an often neglected contribution to the lifecycle costs: downtime costs due to spontaneous failures. Consequently, availability becomes an issue.

Developing a Control Strategy for Booster Stations under Uncertain Load

Booster stations can fulfill a varying pressure demand with high energy-efficiency, because individual pumps can be deactivated at smaller loads. Although this is a seemingly simple approach, it is not easy to decide precisely when to activate or deactivate pumps. Contemporary activation controls derive the switching points from the current volume flow through the system. However, it is not measured directly for various reasons. Instead, the controller estimates the flow based on other system properties. This causes further uncertainty for the switching decision. In this paper, we present a method to find a robust, yet energy-efficient activation strategy.

Analysis of Market Demand Parameters for the Evaluation of Flexibility in Forming Technology

The production planning of forming companies is regularly confronted with a large market power of the costumers. Hence, unexpected variations in demand can heavily affect the predefined selection of production technologies. In this paper a taxonomy is developed that allows the categorisation of demand data depending on the time level and the consideration of uncertainty. Discrete modelling is employed to identify the optimal technology selection considering flexible and dedicated manufacturing systems. Therefore, parameters describing deterministic and stochastic demand scenarios are examined providing an assessment of their informative value. Further, the influence of external, technology-independent model parameters is investigated. To validate the discrete model the manufacturing of a sample is analysed considering multiple production technologies.

Quantified Integer Programs with Polyhedral Uncertainty Set

Quantified Integer Programs (QIPs) are integer programs with variables being either existentially or universally quantified. They can be interpreted as a two-person zero-sum game with an existential and a universal player where the existential player tries to meet all constraints and the universal player intends to force at least one constraint to be not satisfied.

Multistage Optimization with the Help of Quantified Linear Programming

Quantified linear integer programs (QIPs) are linear integer programs (IPs) with variables being either existentially or universally quantified. They can be interpreted as two-person zero-sum games between an existential and a universal player on the one side, or multistage optimization problems under uncertainty on the other side. Solutions of feasible QIPs are so called winning strategies for the existential player that specify how to react on moves—certain fixations of universally quantified variables—of the universal player to certainly win the game. In order to solve the QIP optimization problem, where the task is to find an especially attractive winning strategy, we examine the problem’s hybrid nature and combine linear programming techniques with solution techniques from game-tree search.