| 1. |
- Cromvik, Christoffer, 1980, et al.
(författare)
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On the robustness of global optima and stationary solutions to stochastic mathematical programs with equilibrium constraints, Part II: Applications
- 2010
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 144:3, s. 479-500
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Tidskriftsartikel (refereegranskat)abstract
- In a companion paper (Cromvik and Patriksson, Part I, J. Optim. Theory Appl., 2010), the mathematical modeling framework SMPEC was studied; in particular, global optima and stationary solutions to SMPECs were shown to be robust with respect to the underlying probability distribution under certain assumptions. Further, the framework and theory were elaborated to cover extensions of the upper-level objective: minimization of the conditional value-at-risk (CVaR) and treatment of the multiobjective case. In this paper, we consider two applications of these results: a classic traffic network design problem, where travel costs are uncertain, and the optimization of a treatment plan in intensity modulated radiation therapy, where the machine parameters and the position of the organs are uncertain. Owing to the generality of SMPEC, we can model these two very different applications within the same framework. Our findings illustrate the large potential in utilizing the SMPEC formalism for modeling and analysis purposes; in particular, information from scenarios in the lower-level problem may provide very useful additional insights into a particular application.
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| 2. |
- Daneva (Mitradjieva), Maria, et al.
(författare)
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A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
- 2010
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Ingår i: Computational optimization and applications. - : Springer Science and Business Media LLC. - 0926-6003 .- 1573-2894. ; 46:3, s. 451-466
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Tidskriftsartikel (refereegranskat)abstract
- The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.
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| 3. |
- Jakobsson, Stefan, 1970, et al.
(författare)
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A method for simulation based optimization using radial basis functions
- 2010
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Ingår i: Optimization & Engineering. - : Springer Science and Business Media LLC. - 1573-2924 .- 1389-4420. ; 11:4, s. 501-532
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Tidskriftsartikel (refereegranskat)abstract
- We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.
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| 4. |
- Jakobsson, S, et al.
(författare)
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Combustion engine optimization: A multiobjective approach
- 2010
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Ingår i: Optimization & Engineering. - : Springer Science and Business Media LLC. - 1389-4420 .- 1573-2924. ; 11:4, s. 533-554
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Tidskriftsartikel (refereegranskat)abstract
- To simulate the physical and chemical processes inside combustion engines is possible by appropriate software and high performance computers. For combustion engines a good design is such that it combines a low fuel consumption with low emissions of soot and nitrogen oxides. These are however partly conflicting requirements. In this paper we approach this problem in a multi-criteria setting which has the advantage that it is possible to estimate the trade off between the different objectives and the decision of the optimal solution is postponed until all possibilities and limitations are known. The optimization algorithm is based on surrogate models and is here applied to optimize the design of a diesel combustion engine.
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| 5. |
- Lindroth, Peter, 1979, et al.
(författare)
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Approximating the Pareto Optimal Set using a Reduced Set of Objective Functions
- 2010
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Ingår i: European Journal of Operational Research. - : Elsevier BV. - 0377-2217. ; 207:3, s. 1519-1534
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Tidskriftsartikel (refereegranskat)abstract
- Real-world applications of multi-objective optimization often involve numerous objective functions. But while such problems are in general computationally intractable, it is seldom necessary to determine the Pareto optimal set exactly. A significantly smaller computational burden thus motivates the loss of precision if the size of the loss can be estimated. We describe a method for finding an optimal reduction of the set of objectives yielding a smaller problem whose Pareto optimal set w.r.t. a discrete subset of the decision space is as close as possible to that of the original set of objectives. Utilizing a new characterization of Pareto optimality and presuming a finite decision space, we derive a program whose solution represents an optimal reduction. We also propose an approximate, computationally less demanding formulation which utilizes correlations between the objectives and separates into two parts. Numerical results from an industrial instance concerning the configuration of heavy-duty trucks are also reported, demonstrating the usefulness of the method developed. The results show that multi-objective optimization problems can be significantly simplified with an induced error which can be measured.
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| 6. |
- Nilsson, Julia, et al.
(författare)
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An evaluation approach for opportunistic maintenance optimization models for nuclear power plants
- 2010
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Ingår i: Power and Energy Society General Meeting, 2010 IEEE. - : IEEE. - 9781424483570
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Konferensbidrag (refereegranskat)abstract
- Nuclear power constitutes one of the main electricity production sources in several countries, e.g. in Sweden, with about half of today's electricity production. Driving forces for cost-efficiency have pushed the development of new methods for maintenance planning and optimization forward. Reliability Centered Asset Management (RCAM) is one of these new approaches, and maintenance optimization is one way to perform quantitative analysis which is a feature of RCAM. This paper proposes a stochastic framework for evaluating opportunistic maintenance optimization models for the generation of replacement schedules for shaft seals in feed-water pump systems in nuclear power plants. Results show that the extended discounted model has a good overall performance, when compared to other strategies. Moreover, it is shown that it is the best strategy for high values of the constant cost for maintenance and the second best for lower values of the constant cost.
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| 7. |
- Patriksson, Michael, 1964, et al.
(författare)
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On the robustness of global optima and stationary solutions to stochastic mathematical programs with equilibrium constraints, Part 1: Theory
- 2010
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 1573-2878 .- 0022-3239. ; 144:3, s. 461-478
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic mathematical program with equilibrium constraints (SMPEC) and show that, under certain assumptions, global optima and stationary solutions are robust with respect to changes in the underlying probability distribution. In particular, the discretization scheme sample average approximation (SAA), which is convergent for both global optima and stationary solutions, can be combined with the robustness results to motivate the use of SMPECs in practice. We then study two new and natural extensions of the SMPEC model. First, we establish the robustness of global optima and stationary solutions to an SMPEC model where the upper-level objective is the risk measure known as conditional value-at-risk (CVaR). Second, we analyze a multiobjective SMPEC model, establishing the robustness of weakly Pareto optimal and weakly Pareto stationary solutions. In the accompanying paper (Cromvik and Patriksson, Part 2, J. Optim. Theory Appl., 2010, to appear) we present applications of these results to robust traffic network design and robust intensity modulated radiation therapy. © Springer Science+Business Media, LLC 2009.
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| 8. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Optimization of schedules for a multitask production cell
- 2010
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Ingår i: Proceedings of The 22nd NOFOMA Conference in Kolding, Denmark, 10-11th of June 2010.
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Konferensbidrag (refereegranskat)abstract
- Purpose of this paper; To optimize production schedules of a real production cell containing multi-purpose machines working as a job-shop in a complex logistic environment producing aircraft engine components. The planning and control of the production in the so called multitask cell results in a complex combinatorial problem. Design/methodology/approach; A mathematical optimization model of the multitask cell has been developed and tested on real data instances. The current production planning prerequisites have been studied in order to choose an appropriate objective function. Findings; Production plans resulting from the optimization model, are compared with schedules formed by the First in First Out (FIFO) and Earliest Due Date (EDD) priority rules, which are similar to the current manual planning of the multitask cell. Practical implications; The proposed scheduling principle will shorten lead times, and provide a more efficient use of the resources of the multitask cell. The effects are most significant at times with high utilization of the cell. What is original/value of paper; The development of theory and practice of optimization, together with the development of computer hardware during the past decades, enable the utilization of optimization as a tool for computing efficient production schedules in a complex logistic environment.
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