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  1. No Access

    Article

    An algorithmic approach to multiobjective optimization with decision uncertainty

    In real life applications, optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties conc...

    Gabriele Eichfelder, Julia Niebling, Stefan Rocktäschel in Journal of Global Optimization (2020)

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    Book

    A Branch-and-Bound Algorithm for Multiobjective Mixed-integer Convex Optimization

    Stefan Rocktäschel in BestMasters (2020)

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    Chapter

    Introduction

    Mixed-integer optimization problems (MIP) appear in a variety of applications like in economics or engineering. One example is the uncapacitated facility location problem studied by Günlük, Lee, Weismantel [9]...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

  4. Chapter

    Conclusion

    In this book, we have considered multiobjective mixed-integer convex optimization problems. We introduced basic definitions and concepts of multiobjective optimization. We derived a basic Branch-and-Bound algo...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

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    Chapter

    Outlook and further possible improvements

    In this Chapter, we discuss an extension of the proposed algorithm to the nonconvex case. Therefore, we introduce the concept of convex underestimators. As we have seen in Example 2.13, the assumption of conve...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

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    Chapter

    A basic Branch-and-Bound algorithm for (MOMICP)

    In this chapter, we introduce a basic algorithm for computing a ’good’ cover of the efficient set of (MOMICP). The algorithm illustrates the basic procedure that we use. The idea of this Branch-and-Bound algor...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

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    Chapter

    Test instances and numerical results

    We have implemented Algorithm 7 in MATLAB for p = 2. All tests have been run on an Intel(R) Core (TM) i7-6700K CPU @ 4.00GHz with 32GB RAM (2x DDR4-2399/16GB) on the operating system Microsoft Windows 10 Pro vers...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

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    Chapter

    Theoretical Basics

    In this chapter, we introduce the basic concepts of multiobjective optimization. We introduce basic definitions and derive a concept of optimality for multiobjective optimization problems. Based on this, we fo...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)

  9. No Access

    Chapter

    Enhancing Algorithm 1

    In this chapter, we introduce modifications that enhance the basic Branch-and-Bound algorithm for (MOMICP), we introduced in Chapter 3. We follow different goals with these modifications. We would like to redu...

    Stefan Rocktäschel in A Branch-and-Bound Algorithm for Multiobje… (2020)