HEURISTICS AND LOWER BOUND FOR ENERGY MANAGEMENT IN HYBRID-ELECTRIC VEHICLES

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A better alternative to dynamic programming for offline energy optimization in hybrid-electric vehicles

International audienceThis article focusses on the well-known problem of energy management for hybrid-electric vehicles. Although researches on this problem have recently intensified. Dynamic programming (DP) is still considered as the reference method because it obtains the best solutions of the literature so far, even though it requires a significant computational time. This article however, describes two heuristic-global-optimization-based algorithms that not only require less computational time than DP, but also produce better solutions, with significantly lower fuel consumption cost

Upper and lower bounding procedures for the optimal management of water pumping and desalination processes

We consider the problem of water production optimization for autonomous water pumping and desalination units supplied by renewable energy sources, designed to be a viable solution to fresh water scarcity for remote areas. Non-linear gyrators as well as the non-linear efficiency of energy and flow transfers model the mechanical-hydraulic power conversion systems involved. We present a generic formulation and resolution algorithms based on piece-wise bounding and integer linear programming to solve to optimality the global optimization problem of finding an optimal energy mangement strategy

Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods.

International audienceVarious optimization problems result from the introduction of nonlinear terms into combinatorial optimization problems. In the context of energy optimization for example, energy sources can have very different characteristics in terms of power range and energy demand/cost function, also known as efficiency function or energy conversion function. Introducing these energy sources characteristics in combinatorial optimization problems, such as energy resource allocation problems or energy-consuming activity scheduling problems may result into mixed integer nonlinear problems neither convex nor concave. Approximations via piecewise linear functions have been proposed in the literature. Non-convex optimization models and heuristics exist to compute optimal breakpoint positions under a bounded absolute error-tolerance. We present an alternative solution method based on the upper and lower bounding of nonlinear terms using non necessarily continuous piecewise linear functions with a relative epsilon-tolerance. Conditions under which such approach yields a pair of mixed integer linear programs with a performance guarantee are analyzed. Models and algorithms to compute the non necessarily continuous piecewise linear functions with absolute and relative tolerances are also presented. Computational evaluations performed on energy optimization problems for hybrid electric vehicles show the efficiency of the method with regards to the state of the art

Heuristiques de linéarisation par morceaux de fonctions à deux variables avec minimisation du nombre de morceaux sous contrainte de tolérance

International audienceHeuristiques de linéarisation par morceaux de fonctions à deux variables avec minimisation du nombre de morceaux sous contrainte de toléranc

On the approximation of separable non-convex optimization programs to an arbitrary numerical precision

We consider the problem of minimizing the sum of a series of univariate (possibly non-convex) functions on a polyhedral domain. We introduce an iterative method with optimality guarantees to approximate this problem to an arbitrary numerical precision. At every iteration, our method replaces the objective by a lower bounding piecewise linear approximation to compute a dual bound. A primal bound is computed by evaluating the cost function on the solution provided by the approximation. If the difference between these two values is deemed as not satisfactory, the approximation is locally tightened and the process repeated. By keeping the scope of the update local, the computational burden is only slightly increased from iteration to iteration. The convergence of the method is assured under very mild assumptions, and no NLP nor MINLP solver/oracle is required to ever be invoked to do so. As a consequence, our method presents very nice scalability properties and is little sensitive to the desired precision. We provide a formal proof of the convergence of our method, and assess its efficiency in approximating the non-linear variants of three problems: the transportation problem, the capacitated facility location problem, and the multi-commodity network design problem. Our results indicate that the overall performance of our method is superior to five state-of-the-art mixed-integer nonlinear solvers by a significant margin, and scales better than a naive variant of the method that avoids performing successive iterations in exchange of solving a much larger mixed-integer linear program

Piecewise linearization of bivariate nonlinear functions: minimizing the number of pieces under a bounded approximation error

This work focuses on the approximation of bivariate functions into piecewise linear ones with a minimal number of pieces and under a bounded approximation error. Applications include the approximation of mixed integer nonlinear optimization problems into mixed integer linear ones that are in general easier to solve. A framework to build dedicated linearization algorithms is introduced, and a comparison to the state of the art heuristics shows their efficiency

Piecewise linearization of bivariate nonlinear functions: minimizing the number of pieces under a bounded approximation error

This work focuses on the approximation of bivariate functions into piecewise linear ones with a minimal number of pieces and under a bounded approximation error. Applications include the approximation of mixed integer nonlinear optimization problems into mixed integer linear ones that are in general easier to solve. A framework to build dedicated linearization algorithms is introduced, and a comparison to the state of the art heuristics shows their efficiency

Approximation à précision numérique prédéfinie d'une classe de problèmes d'optimisation non-linéaires non-convexes séparables

International audienceApproximation à précision numérique prédéfinie d'une classe de problèmes d'optimisation non-linéaires non-convexes séparable

Heuristiques de linéarisation par morceaux de fonctions à deux variables avec minimisation du nombre de morceaux sous contrainte de tolérance

International audienceHeuristiques de linéarisation par morceaux de fonctions à deux variables avec minimisation du nombre de morceaux sous contrainte de toléranc