| 1. |
- Almgren, Torgny, 1962, et al.
(författare)
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Optimization of opportunistic replacement activities: A case study in the aircraft industry
- 2007
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In the aircraft industry maximizing availability is essential. Maintenance schedules must therefore be opportunistic, incorporating preventive maintenance activities within the scheduled as well as the unplanned ones. At the same time, the maintenance contractor should utilize opportunistic maintenance to enable the minimization of the total expected cost to have a functional aircraft engine and thus to provide attractive service contracts. This paper provides an opportunistic maintenance optimization model which has been constructed and tested together with Volvo Aero Corporation in Trollhättan, Sweden for the maintenance of the RM12 engine. The model incorporates components with deterministic as well as with stochastic lives. The replacement model is shown to have favourable properties; in particular, when the maintenance occasions are fixed the remaining problem has the integrality property, the replacement polytope corresponding to the convex hull of feasible solutions is full-dimensional, and all the necessary constraints for its definition are facet-inducing. We present an empirical crack growth model that estimates the remaining life and also a case study that indicates that a non-stationary renewal process with Weibull distributed lives is a good model for the recurring maintenance occasions. Using one point of support for the distribution yields a deterministic replacement model; it is evaluated against classic maintenance policies from the literature through stochastic simulations. The deterministic model provides maintenance schedules over a finite time period that induce fewer maintenance occasions as well as fewer components replaced.
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| 2. |
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| 3. |
- Almgren, Torgny, 1962, et al.
(författare)
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The replacement problem: A polyhedral and complexity analysis. The complete version
- 2009
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We consider an optimization model for determining optimal opportunistic maintenance (that is, component replacement) schedules when data is deterministic. This problem, which generalizes that of Dickman et al., is a natural starting point for the modelling of replacement schedules when component lives are non-deterministic, whence a mathematical study of the model is of large interest. We show that the convex hull of the set of feasible replacement schedules is full-dimensional, and that all the necessary inequalities are facet-inducing. Additional facets are then provided through Chvatal-Gomory rounding. We show that when maintenance occasions are fixed, the remaining problem reduces to a linear program; in some cases the latter is solvable through a greedy procedure. We further show that this basic replacement problem is NP-hard.
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| 4. |
- Besnard, Francois, et al.
(författare)
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An Optimization Framework for Opportunistic Maintenance of Offshore Wind Power System
- 2009
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Ingår i: 2009 IEEE BUCHAREST POWERTECH, VOLS 1-5. - NEW YORK : IEEE. - 9781424422340 ; , s. 2970-2976
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Konferensbidrag (refereegranskat)abstract
- A sound maintenance planning is of crucial importance for wind power farms, and especially for offshore locations. There is a large potential in cost savings by maintenance optimization to make the projects more cost-efficient. This paper presents an opportunistic maintenance optimization model for offshore wind power system. The model takes advantage of wind forecasts and corrective maintenance activities in order to perform preventive maintenance tasks at low costs. The approach is illustrated with an example to demonstrate the value of the optimization. In this example 43% of the cost to perform preventive maintenance could be saved using the proposed method.
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| 5. |
- Daneva (Mitradjieva), Maria, et al.
(författare)
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A Sequential Linear Programming Algorithm with Multi-dimensional Search : Derivation and Convergence
- 2007
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We present a sequential linear programming, SLP, algorithm in which the traditional line-search step is replaced by a multi-dimensional search. The algorithm is based on inner approximations of both the primal and dual spaces, which yields a method which in the primal space combines column and constraint generation. The algorithm does not use a merit function, and the linear programming subproblem of the algorithm differs from the one obtained in traditional methods of this type, in the respect that linearized constraints are taken into account only implicitly in a Lagrangiandual fashion. Convergence to a point that satisfies the Karush-Kuhn-Tucker conditions is established. We apply the new method to a selection of the Hoch-Schittkowski’s nonlinear test problems and report a preliminary computational study in a Matlab environment. Since the proposed algorithmcombines column and constraint generation, it should be advantageous with large numbers of variables and constraints.
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| 6. |
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| 7. |
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| 8. |
- Larsson, Torbjörn, et al.
(författare)
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Convergent Lagrangian heuristics for nonlinear minimum cost network flows
- 2008
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Ingår i: European Journal of Operational Research. - : Elsevier BV. - 0377-2217 .- 1872-6860. ; 189:2, s. 324-346
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Tidskriftsartikel (refereegranskat)abstract
- We consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector, this is referred to as "early primal recovery". It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme, such a vector is not available from a Lagrangian dual vector unless it is optimal. The scheme is constructed such that if we apply it from a sequence of Lagrangian dual vectors that converge to an optimal one, then the resulting primal (feasible) vectors converge to the unique optimal primal flow vector. It is therefore also a convergent Lagrangian heuristic, akin to those primarily devised within the field of combinatorial optimization but with the contrasting and striking advantage that it is guaranteed to yield a primal optimal solution in the limit. Thereby we also gain access to a new stopping criterion for any Lagrangian dual algorithm for the problem, which is of interest in particular if the SSCNFP arises as a subproblem in a more complex model. We construct instances of convergent Lagrangian heuristics that are based on graph searches within the residual graph, and therefore are efficiently implementable, in particular we consider two shortest path based heuristics that are based on the optimality conditions of the original problem. Numerical experiments report on the relative efficiency and accuracy of the various schemes. © 2007 Elsevier B.V. All rights reserved.
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| 9. |
- Larsson, Torbjörn, 1957-, et al.
(författare)
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Global optimality conditions for discrete and nonconvex optimization-with applications to Lagrangian heuristics and column generation
- 2006
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Ingår i: Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0030-364X .- 1526-5463. ; 54:3, s. 436-453
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Tidskriftsartikel (refereegranskat)abstract
- The well-known and established global optimality conditions based on the Lagrangian formulation of an optimization problem are consistent if and only if the duality gap is zero. We develop a set of global optimality conditions that are structurally similar but are consistent for any size of the duality gap. This system characterizes a primal-dual optimal solution by means of primal and dual feasibility, primal Lagrangian ε-optimality, and, in the presence of inequality constraints, a relaxed complementarity condition analogously called δ-complementarity. The total size ε + δ of those two perturbations equals the size of the duality gap at an optimal solution. Further, the characterization is equivalent to a near-saddle point condition which generalizes the classic saddle point characterization of a primal-dual optimal solution in convex programming. The system developed can be used to explain, to a large degree, when and why Lagrangian heuristics for discrete optimization are successful in reaching near-optimal solutions. Further, experiments on a set-covering problem illustrate how the new optimality conditions can be utilized as a foundation for the construction of new Lagrangian heuristics. Finally, we outline possible uses of the optimality conditions in column generation algorithms and in the construction of core problems. © 2006 INFORMS.
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| 10. |
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| 11. |
- Nilsson, Julia, et al.
(författare)
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An Opportunistic Maintenance Optimization Model for Shaft Seals in Feed-Water Pump Systems in Nuclear Power Plants
- 2009
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Ingår i: 2009 IEEE Bucharest PowerTech. - New York : IEEE. - 9781424422340 ; , s. 2962-2969
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Konferensbidrag (refereegranskat)abstract
- Nuclear power is one of the main electricity production sources in Sweden today. Maintenance management is one tool for reducing the costs for operation of a power plant. Driving forces for cost-efficiency has 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 model for opportunistic maintenance optimization where replacement schedules for shaft seals in feed-water pump systems in nuclear power plants are constructed. The feed-water pump system is important for the availability of the entire nuclear power plant. Results show that the optimization model is dependent on e.g. the discount interest and a limit for when the optimal solution goes from non-opportunistic to opportunistic is calculated. The circumstances for which opportunistic maintenance could be used have been investigated given different values of discount rates and remaining life at start of the planning period.
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| 12. |
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| 13. |
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| 14. |
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| 15. |
- Patriksson, Michael, 1964
(författare)
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A survey on the continuous nonlinear resource allocation problem
- 2008
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Ingår i: European Journal of Operational Research. - : Elsevier BV. - 0377-2217. ; 185:1, s. 1-46
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Tidskriftsartikel (refereegranskat)abstract
- Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. © 2006 Elsevier B.V. All rights reserved.
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| 16. |
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| 17. |
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| 18. |
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| 19. |
- Patriksson, Michael, 1964
(författare)
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On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints
- 2008
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Ingår i: Transportation Research Part B. - : Elsevier BV. - 0191-2615. ; 42:10, s. 843-860
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Tidskriftsartikel (refereegranskat)abstract
- Bilevel optimization models, and more generally MPEC (mathematical program with equilibrium constraints) models, constitute important modelling tools in transportation science and network games, as they place the classic ``what-if'' analysis in a proper mathematical framework. The MPEC model is also becoming a standard for the computation of optimal design solutions, where ``design'' may include either or both of network infrastructure investments and various types of tolls. At the same time, it does normally not sufficiently well take into account possible uncertainties and/or perturbations in problem data (travel costs and demands), and thus may not a priori guarantee robust designs under varying conditions. We consider natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty. In stochastic programming terminology, we consider ``here-and-now'' models where decisions on the design must be made before observing the uncertain parameter values and the responses of the network users, and the design is chosen to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed link pricing scheme that provides the best revenue for a given network over a given time period, where the varying traffic conditions are described by distributions of parameters in the link travel time and OD demand functions. For a general such SMPEC network model we establish not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution. We also provide convergence results for general algorithmic schemes based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution, the latter enabling the utilization of standard MPEC algorithms. Especially the latter part utilizes relations between the traffic application of SMPEC and stochastic structural topology optimization problems.
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| 20. |
- Patriksson, Michael, 1964
(författare)
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On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of solutions to SMPEC models
- 2007
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Bilevel optimization models, and more generally MPEC (mathematical program with equilibrium constraints) models, constitute important modelling tools in transportation science and network games, as they place the classic ``what-if'' analysis in a proper mathematical framework. The MPEC model is also becoming a standard for the computation of optimal design solutions, where ``design'' may include either or both of network infrastructure investments and various types of tolls. At the same time, it does normally not sufficiently well take into account possible uncertainties and/or perturbations in problem data (travel costs and demands), and thus may not a priori guarantee robust designs under varying conditions. We consider natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty. In stochastic programming terminology, we consider ``here-and-now'' models where decisions on the design must be made before observing the uncertain parameter values and the responses of the network users, and the design is chosen to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed link pricing scheme that provides the best revenue for a given network over a given time period, where the varying traffic conditions are described by distributions of parameters in the link travel time and OD demand functions. For a general such SMPEC network model we establish not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution. We also provide convergence results for general algorithmic schemes based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution, the latter enabling the utilization of standard MPEC algorithms. Especially the latter part utilizes relations between the traffic application of SMPEC and stochastic structural topology optimization problems.
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| 21. |
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| 22. |
- Patriksson, Michael, 1964
(författare)
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Robust bilevel optimization models in transportation science
- 2008
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Ingår i: Philosophical Transactions of the Royal Society, A. ; 366:1872, s. 1989-2004
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical programs with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper mathematical framework. We consider a class of stochastic MPEC traffic models which explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now' models where decisions must be made before observing the uncertain parameter values and the responses of the network users; the objective is to minimize the expectation of the upper-level objective function. Such a model could, for example, be used to derive a fixed toll pricing scheme that provides the best revenue for a given network over a time period, where variations in traffic conditions and demand elasticities are described by distributions of parameters in the travel time and demand functions. We present new results on the stability of optimal solutions to perturbations in the probability distribution, establishing the robustness of the model. We also provide convergence results for algorithms based on the penalization of the equilibrium conditions or possible joint upper-level constraints, as well as for algorithms based on the discretization of the probability distribution; the latter enables the utilization of standard MPEC algorithms.
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| 23. |
- Patriksson, Michael, 1964, et al.
(författare)
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Traffic Equilibrium
- 2007
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Ingår i: Handbooks in Operations Research and Management Science.
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 24. |
- Svensson, Elin, 1980, et al.
(författare)
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A Scenario-Based Stochastic Programming Model for the Optimization of Process Integration Opportunities in a Pulp Mill
- 2008
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Several studies show that substantial industrial energy savings can be achieved through process integration. The returns on such investments are, however, uncertain because of uncertainties in future energy prices and policies. This article presents a stochastic mixed-integer programming approach which enables the identification of robust process integration investments under uncertainty. The proposed approach is applied to the case of a pulp mill for which the complete optimization model is presented. The model is a scenario-based multistage stochastic programming model with the objective of maximizing the net present value of the investments. The model also enables the optimization of investment timing. We show as one important result that the probability distribution can be varied rather much without a change in the optimal solution. This implies that the stochastic programming approach is a valuable tool although the true probabilities for the future scenarios are not known.
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| 25. |
- Svensson, Elin, 1980, et al.
(författare)
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An optimization methodology for identifying robust process integration investments under uncertainty
- 2009
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Ingår i: Energy Policy. - : Elsevier BV. - 0301-4215. ; 37:2, s. 680-685
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Tidskriftsartikel (refereegranskat)abstract
- Uncertainties in future energy prices and policies strongly affect decisions on investments in process integration measures in industry. In this paper, we present a five-step methodology for the identification of robust investment alternatives incorporating explicitly such uncertainties in the optimization model. Methods for optimization under uncertainty (or, stochastic programming) are thus combined with a deep understanding of process integration and process technology in order to achieve a framework for decision-making concerning the investment planning of process integration measures under uncertainty. The proposed methodology enables the optimization of investments in energy efficiency with respect to their net present value or an environmental objective. In particular, as a result of the optimization approach, complex investment alternatives, allowing for combinations of energy efficiency measures, can be analyzed. Uncertainties as well as time-dependent parameters, such as energy prices and policies, are modelled using a scenario-based approach, enabling the identification of robust investment solutions. The methodology is primarily an aid for decision-makers in industry, but it will also provide insight for policy-makers into how uncertainties regarding future price levels and policy instruments affect the decisions on investments in energy efficiency measures.
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