5,477 research outputs found
A Convergent Approximation of the Pareto Optimal Set for Finite Horizon Multiobjective Optimal Control Problems (MOC) Using Viability Theory
The objective of this paper is to provide a convergent numerical
approximation of the Pareto optimal set for finite-horizon multiobjective
optimal control problems for which the objective space is not necessarily
convex. Our approach is based on Viability Theory. We first introduce the
set-valued return function V and show that the epigraph of V is equal to the
viability kernel of a properly chosen closed set for a properly chosen
dynamics. We then introduce an approximate set-valued return function with
finite set-values as the solution of a multiobjective dynamic programming
equation. The epigraph of this approximate set-valued return function is shown
to be equal to the finite discrete viability kernel resulting from the
convergent numerical approximation of the viability kernel proposed in [4, 5].
As a result, the epigraph of the approximate set-valued return function
converges towards the epigraph of V. The approximate set-valued return function
finally provides the proposed numerical approximation of the Pareto optimal set
for every initial time and state. Several numerical examples are provided
Multiobjective strategies for New Product Development in the pharmaceutical industry
New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems
Multiobjective strategies for New Product Development in the pharmaceutical industry
New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems
A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions
In a general Hilbert framework, we consider continuous gradient-like
dynamical systems for constrained multiobjective optimization involving
non-smooth convex objective functions. Our approach is in the line of a
previous work where was considered the case of convex di erentiable objective
functions. Based on the Yosida regularization of the subdi erential operators
involved in the system, we obtain the existence of strong global trajectories.
We prove a descent property for each objective function, and the convergence of
trajectories to weak Pareto minima. This approach provides a dynamical
endogenous weighting of the objective functions. Applications are given to
cooperative games, inverse problems, and numerical multiobjective optimization
Submodular memetic approximation for multiobjective parallel test paper generation
Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency
On green routing and scheduling problem
The vehicle routing and scheduling problem has been studied with much
interest within the last four decades. In this paper, some of the existing
literature dealing with routing and scheduling problems with environmental
issues is reviewed, and a description is provided of the problems that have
been investigated and how they are treated using combinatorial optimization
tools
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