39 research outputs found
An SDP approach for multiperiod mixed 0-1 linear programming models with stochastic dominance constraints for risk management *
Abstract In this paper we consider multiperiod mixed 0-1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact the cross-scenario constraints, due to SDC, have on the decomposability of the model. In our computational experience we compare our SDP against a commercial optimization package, in terms of solution accuracy and elapsed time. We use supply chain planning instances, where procurement, production, inventory, and distribution decisions need to be made under demand uncertainty. We confirm the hardness of the testbed, where the benchmark cannot find a feasible solution for half of the test instances while we always find one, and show the appealing tradeoff of SDP, in terms of solution accuracy and elapsed time, when solving medium-to-large instances
On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management
A new scheme for dealing with uncertainty in scenario trees is presented for dynamic mixed 0–1 optimization problems with strategic and operational stochastic parameters. Let us generically name this type of problems as capacity expansion planning (CEP) in a given system, e.g., supply chain, production, rapid transit network, energy generation and transmission network, etc. The strategic scenario tree is usually a multistage one, and the replicas of the strategic nodes root structures in the form of either a special scenario graph or a two-stage scenario tree, depending on the type of operational activity in the system. Those operational scenario structures impact in the constraints of the model and, thus, in the decomposition methodology for solving usually large-scale problems. This work presents the modeling framework for some of the risk neutral and risk averse measures to consider for CEP problem solving. Two types of risk averse measures are considered. The first one is a time-inconsistent mixture of the chance-constrained and second-order stochastic dominance (SSD) functionals of the value of a given set of functions up to the strategic nodes in selected stages along the time horizon, The second type is a strategic node-based time-consistent SSD functional for the set of operational scenarios in the strategic nodes at selected stages. A specialization of the nested stochastic decomposition methodology for that problem solving is outlined. Its advantages and drawbacks as well as the framework for some schemes to, at least, partially avoid those drawbacks are also presentedThis research has been partially supported by the projects: MTM2015-63710 and MTM2016-79765 from the Spanish Ministry of Economy and Competitiveness. The authors like to thank the positive criticism of their colleagues Antonio Alonso-Ayuso, Luis Cadarso, F. Javier MartĂn-Campo and Angel MarĂn that helped to improve the presentation of the wor
Distributionally Robust Optimization: A Review
The concepts of risk-aversion, chance-constrained optimization, and robust
optimization have developed significantly over the last decade. Statistical
learning community has also witnessed a rapid theoretical and applied growth by
relying on these concepts. A modeling framework, called distributionally robust
optimization (DRO), has recently received significant attention in both the
operations research and statistical learning communities. This paper surveys
main concepts and contributions to DRO, and its relationships with robust
optimization, risk-aversion, chance-constrained optimization, and function
regularization
A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0-1 problems
A parallel matheuristic algorithm is presented as a spin-off from the exact Branch-and-Fix Coordination
(BFC) algorithm for solving multistage stochastic mixed 0-1 problems. Some steps to guarantee the
solution’s optimality are relaxed in the BFC algorithm, such that an incomplete backward branching scheme
is considered for solving large sized problems. Additionally, a new branching criterion is considered, based
on dynamically-guided and stage-wise ordering schemes, such that fewer Twin Node Families are expected
to be visited during the execution of the so-called H-DBFC algorithm. The inner parallelization IH-DBFC
of the new approach, allows to solve in parallel scenario clusters MIP submodels at different steps of the
algorithm. The outer parallel version, OH-DBFC, considers independent paths and allows iterative incumbent
solution values exchanges to obtain tighter bounds of the solution value of the original problem. A broad
computational experience is reported for assessing the quality of the matheuristic solution for large sized
instances. The instances dimensions that are considered are up to two orders of magnitude larger than in some
other works that we are aware of. The optimality gap of the H-DBFC solution value versus the one obtained
by a state-of-the-artMIP solver is very small, if any. The new approach frequently outperforms it in terms of
solution’s quality and computing time. A comparison with our Stochastic Dynamic Programming algorithm
is also reported. The use of parallel computing provides, on one hand, a perspective for solving very large
sized instances and, on the other hand, an expected large reduction in elapsed time.MTM2015-65317-P, MTM2015-63710-P, IT928-16; UFI BETS 2011; IZO-SGI SGIke
A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming
Despite methodological advances for modeling decision problems under
uncertainty, faithfully representing endogenous uncertainty still proves
challenging, both in terms of modeling capabilities and computational
requirements. A novel framework called Decision Programming provides an
approach for solving such decision problems using off-the-shelf mathematical
optimization solvers. This is made possible by using influence diagrams to
represent a given decision problem, which is then formulated as a mixed-integer
linear programming problem.
In this paper, we focus on the type of endogenous uncertainty that received
less attention in the introduction of Decision Programming: conditionally
observed information. Multi-stage stochastic programming (MSSP) models use
conditional non-anticipativity constraints (C-NACs) to represent such
uncertainties, and we show how such constraints can be incorporated into
Decision Programming models. This allows us to consider the two main types of
endogenous uncertainty simultaneously, namely decision-dependent information
structure and decision-dependent probability distribution. Additionally, we
present a decomposition approach that provides significant computational
savings and also enables considering continuous decision variables in certain
parts of the problem, whereas the original formulation was restricted to
discrete variables only.
The extended framework is illustrated with two example problems. The first
considers an illustrative multiperiod game and the second is a large-scale
cost-benefit problem regarding climate change mitigation. Neither of these
example problems could be solved with existing frameworks.Comment: 26 pages, 10 figure
On modelling planning under uncertainty in manufacturing
We present a modelling framework for two-stage and multi-stage mixed 0-1 problems under uncertainty for strategic Supply Chain Management, tactical production planning and operations assignment and scheduling. A scenario tree based scheme is used to represent the uncertainty. We present the Deterministic Equivalent Model of the stochastic mixed 0-1 programs with complete recourse that we study. The constraints are modelled by compact and splitting variable representations via scenarios
Mathematical Optimization for Routing and Logistic Problems
In this thesis, we focus on mathematical optimization models and algorithms for solving routing and logistic problems. The first contribution regards a path and mission planning problem, called Carrier-Vehicle Traveling Salesman Problem (CVTSP), for a system of heterogeneous vehicles. A Mixed-Integer Second Order Conic Programming (MISOCP) model and a Benders-like enumeration algorithm are presented for solving CVTSP. The second work concerns a class of routing problems, referred to as Interceptor Vehicle Routing Problems (IVRPs). They generalize VRPs in the sense that target points are allowed to move from their initial location according to a known motion. We present a novel MISOCP formulation and a Branch-and-Price algorithm based on a Lagrangian Relaxation of the vehicle-assignment constraints. Other two contributions focus on waste flow management problems: the former considers a deterministic setting in which a Mixed-Integer Linear Programming (MILP) formulation is used as a Decision Support System for a real-world waste operator, whereas the latter deals with the uncertainty of the waste generation amounts by means of Two-Stage Multiperiod Stochastic Mixed-Integer Programming formulations. Finally, we give an overview on the optimization challenges arising in electric car-sharing systems, both at strategic and tactical planning level
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more