The Experts below are selected from a list of 48 Experts worldwide ranked by ideXlab platform

Parmentier Axel - One of the best experts on this subject based on the ideXlab platform.

  • Integer programming for weakly coupled stochastic dynamic programs with partial information
    2020
    Co-Authors: Cohen Victor, Parmentier Axel
    Abstract:

    This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of the partial observations, and because of the curse of dimensionality that appears when the number of components increases. Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled stochastic dynamic programs address the second. Drawing from these two branches of the literature, we introduce the notion of weakly coupled POMDPs. The objective is to find a policy maximizing the total expected reward over a finite horizon. Our algorithms rely on two ingredients. The first, which can be used independently, is a mixed integer linear formulation for generic POMDPs that computes an optimal memoryless policy. The formulation is strengthened with valid cuts based on a probabilistic interpretation of the dependence between random variables, and its linear relaxation provide a practically tight upper bound on the value of an optimal history-dependent policies. The second is a collection of mathematical programming formulations and algorithms which provide tractable policies and upper bounds for weakly coupled POMDPs. Lagrangian relaxations, fluid approximations, and almost sure constraints relaxations enable to break the curse of dimensionality. We test our generic POMDPs formulations on Benchmark Instance forms the literature, and our weakly coupled POMDP algorithms on a maintenance problem. Numerical experiments show the efficiency of our approach.Comment: 47 pages, 3 figure

  • Integer programming for weakly coupled stochastic dynamic programs with partial information
    HAL CCSD, 2020
    Co-Authors: Cohen Victor, Parmentier Axel
    Abstract:

    47 pages, 3 figuresThis paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of the partial observations, and because of the curse of dimensionality that appears when the number of components increases. Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled stochastic dynamic programs address the second. Drawing from these two branches of the literature, we introduce the notion of weakly coupled POMDPs. The objective is to find a policy maximizing the total expected reward over a finite horizon. Our algorithms rely on two ingredients. The first, which can be used independently, is a mixed integer linear formulation for generic POMDPs that computes an optimal memoryless policy. The formulation is strengthened with valid cuts based on a probabilistic interpretation of the dependence between random variables, and its linear relaxation provide a practically tight upper bound on the value of an optimal history-dependent policies. The second is a collection of mathematical programming formulations and algorithms which provide tractable policies and upper bounds for weakly coupled POMDPs. Lagrangian relaxations, fluid approximations, and almost sure constraints relaxations enable to break the curse of dimensionality. We test our generic POMDPs formulations on Benchmark Instance forms the literature, and our weakly coupled POMDP algorithms on a maintenance problem. Numerical experiments show the efficiency of our approach

Cohen Victor - One of the best experts on this subject based on the ideXlab platform.

  • Integer programming for weakly coupled stochastic dynamic programs with partial information
    2020
    Co-Authors: Cohen Victor, Parmentier Axel
    Abstract:

    This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of the partial observations, and because of the curse of dimensionality that appears when the number of components increases. Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled stochastic dynamic programs address the second. Drawing from these two branches of the literature, we introduce the notion of weakly coupled POMDPs. The objective is to find a policy maximizing the total expected reward over a finite horizon. Our algorithms rely on two ingredients. The first, which can be used independently, is a mixed integer linear formulation for generic POMDPs that computes an optimal memoryless policy. The formulation is strengthened with valid cuts based on a probabilistic interpretation of the dependence between random variables, and its linear relaxation provide a practically tight upper bound on the value of an optimal history-dependent policies. The second is a collection of mathematical programming formulations and algorithms which provide tractable policies and upper bounds for weakly coupled POMDPs. Lagrangian relaxations, fluid approximations, and almost sure constraints relaxations enable to break the curse of dimensionality. We test our generic POMDPs formulations on Benchmark Instance forms the literature, and our weakly coupled POMDP algorithms on a maintenance problem. Numerical experiments show the efficiency of our approach.Comment: 47 pages, 3 figure

  • Integer programming for weakly coupled stochastic dynamic programs with partial information
    HAL CCSD, 2020
    Co-Authors: Cohen Victor, Parmentier Axel
    Abstract:

    47 pages, 3 figuresThis paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of the partial observations, and because of the curse of dimensionality that appears when the number of components increases. Partially observable Markov decision processes (POMDPs) have been introduced to deal with the first challenge, while weakly coupled stochastic dynamic programs address the second. Drawing from these two branches of the literature, we introduce the notion of weakly coupled POMDPs. The objective is to find a policy maximizing the total expected reward over a finite horizon. Our algorithms rely on two ingredients. The first, which can be used independently, is a mixed integer linear formulation for generic POMDPs that computes an optimal memoryless policy. The formulation is strengthened with valid cuts based on a probabilistic interpretation of the dependence between random variables, and its linear relaxation provide a practically tight upper bound on the value of an optimal history-dependent policies. The second is a collection of mathematical programming formulations and algorithms which provide tractable policies and upper bounds for weakly coupled POMDPs. Lagrangian relaxations, fluid approximations, and almost sure constraints relaxations enable to break the curse of dimensionality. We test our generic POMDPs formulations on Benchmark Instance forms the literature, and our weakly coupled POMDP algorithms on a maintenance problem. Numerical experiments show the efficiency of our approach

Maghsoud Amiri - One of the best experts on this subject based on the ideXlab platform.

  • solving binary state multi objective reliability redundancy allocation series parallel problem using efficient epsilon constraint multi start partial bound enumeration algorithm and dea
    Reliability Engineering & System Safety, 2012
    Co-Authors: Kaveh Khalili Damghani, Maghsoud Amiri
    Abstract:

    Abstract In this paper, a procedure based on efficient epsilon-constraint method and data envelopment analysis (DEA) is proposed for solving binary-state multi-objective reliability redundancy allocation series-parallel problem (MORAP). In first module, a set of qualified non-dominated solutions on Pareto front of binary-state MORAP is generated using an efficient epsilon-constraint method. In order to test the quality of generated non-dominated solutions in this module, a multi-start partial bound enumeration algorithm is also proposed for MORAP. The performance of both procedures is compared using different metrics on well-known Benchmark Instance. The statistical analysis represents that not only the proposed efficient epsilon-constraint method outperform the multi-start partial bound enumeration algorithm but also it improves the founded upper bound of Benchmark Instance. Then, in second module, a DEA model is supplied to prune the generated non-dominated solutions of efficient epsilon-constraint method. This helps reduction of non-dominated solutions in a systematic manner and eases the decision making process for practical implementations.

E Lau - One of the best experts on this subject based on the ideXlab platform.

  • the witsenhausen counterexample a hierarchical search approach for nonconvex optimization problems
    IEEE Transactions on Automatic Control, 2001
    Co-Authors: J T Lee, E Lau
    Abstract:

    The Witsenhausens counterexample (1968) is a difficult nonconvex functional optimization problem which has been outstanding for more than 30 years. Considerable amount of literature has been accumulated, but optimal solutions remain elusive. In this paper, we develop a framework that allows one to gain additional new insights to the properties of a better solution for a Benchmark Instance. Through our approach, we are able to zero in on a solution that is 13% better than the previously known best solution, and more than 54% better than previous results obtained by other authors. More importantly, we demonstrate that our approach, called hierarchical search, can be useful in general optimization problems.

Kaveh Khalili Damghani - One of the best experts on this subject based on the ideXlab platform.

  • solving binary state multi objective reliability redundancy allocation series parallel problem using efficient epsilon constraint multi start partial bound enumeration algorithm and dea
    Reliability Engineering & System Safety, 2012
    Co-Authors: Kaveh Khalili Damghani, Maghsoud Amiri
    Abstract:

    Abstract In this paper, a procedure based on efficient epsilon-constraint method and data envelopment analysis (DEA) is proposed for solving binary-state multi-objective reliability redundancy allocation series-parallel problem (MORAP). In first module, a set of qualified non-dominated solutions on Pareto front of binary-state MORAP is generated using an efficient epsilon-constraint method. In order to test the quality of generated non-dominated solutions in this module, a multi-start partial bound enumeration algorithm is also proposed for MORAP. The performance of both procedures is compared using different metrics on well-known Benchmark Instance. The statistical analysis represents that not only the proposed efficient epsilon-constraint method outperform the multi-start partial bound enumeration algorithm but also it improves the founded upper bound of Benchmark Instance. Then, in second module, a DEA model is supplied to prune the generated non-dominated solutions of efficient epsilon-constraint method. This helps reduction of non-dominated solutions in a systematic manner and eases the decision making process for practical implementations.