An Integrated Solver for Optimization Problems

Abstract

One of the central trends in the optimization community over the past several years has been the steady improvement of general-purpose solvers. A logical next step in this evolution is to combine mixed-integer linear programming, constraint programming, and global optimization in a single system. Recent research in the area of integrated problem solving suggests that the right combination of different technologies can simplify modeling and speed up computation substantially. Nevertheless, integration often requires special-purpose coding, which is time consuming and error prone. We present a general-purpose solver, SIMPL, that allows its user to replicate (and sometimes improve on) the results of custom implementations with concise models written in a high-level language. We apply SIMPL to production planning, product configuration, machine scheduling, and truss structure design problems on which customized integrated methods have shown significant computational advantage. We obtain results that either match or surpass the original codes at a fraction of the implementation effort.

Approches hybrides pour la résolution d'un problème d'ordonnancement industriel /

“…Plusieurs expérimentations et recherches ont montré que l'ordonnancement des variables a un impact subséquent sur la complexité du retour en arrière [Freuder, 1982;Dechter et Meiri, 1994;Freuder et al, 1995;Frost et Dechter, 1998;Dechter et Frost, 2002 [Freuder, 1982], qui choisit un ordre minimisant la largeur du graphe ou Maxdeg [Dechter et Meiri, 1994] Il est bien évident que l'écart entre la PC et l'optimisation tend à diminuer de plus en plus et qu'une technique peut en intégrer une autre [Baptiste et al, 2001;Yunes et al, 2010]. C'est ce que nous explorons dans la prochaine section en adaptant la PC aux problèmes d'ordonnancement.…”

“…En effet, les deux domaines de recherche ont longuement été rivaux en cherchant à prouver leur supériorité respective. De plus, dans la dernière décennie, l'utilisation des méthodes exactes a été fortement encouragée avec l'apparition de nombreux solveurs commerciaux [Freuder et Wallace, 2000;Yunes et al, 2010]. Cependant, les chercheurs et décideurs en entreprises ont émis plusieurs difficultés quant à l'interaction entre ces solveurs et les applications connexes [Hnich et al, 2004;Yunes et al, 2010].…”

Dantzig-Wolfe decomposition and branch-and-price solving in G12

“…A system based on similar ideas such as annotating high-level models is SIMPL [34], allowing various types of hybrid solving. The focus of SIMPL is on instances of a branch-infer-relax model of solving which naturally fits with Benders decomposition and branch-and-bound search.…”

“…The focus of SIMPL is on instances of a branch-infer-relax model of solving which naturally fits with Benders decomposition and branch-and-bound search. The paper [34] allows a bp search specification indicating branch-and-price search, but there are no details of how this is supported, nor any examples making use of it.…”

Analyzing the impact of in-rack sprinklers in a warehouse fire: A demonstration of the role optimization has in mitigating damage

“…Such problems often involve a system of equations or inequalities that implicitly characterize all feasible solutions, together with means to evaluate the quality of any given solution satisfying that system. In the context of engineering design, optimization and simulation optimization has proven useful in a wide variety of applications, including improving the designs of truss structures [2,3], Stirling engines [4,5], aircraft fuselage panels [6], water pumping systems [7], the built environment [8], and gas detector spacing [9], among others [10]. For more information on simulation optimization we refer to [11].…”