Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the basis of...

Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted $\oplus$ and $\otimes$, respectively). The eigenproblem is the search for a vector $x$ (an eigenvector) and a constant $\lambda$ (an eigenvalue) such that $A\otimes x=\lambda \otimes x$, where $A$ is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation $A\otimes x=\lambda \otimes B\otimes x$ with given matrices $A,B$ and unknown constant $\lambda$ and vector $x$. Generalized eigenvectors have interesting...

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0–1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial...

The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...