Solving chance-constrained combinatorial problems to optimality
نویسنده
چکیده
The aim of this paper is to provide new efficient methods for solving general chance-constrained integer linear programs to optimality. Valid linear inequalities are given for these problems. They are proved to characterize properly the set of solutions. They are based on a specific scenario, whose definition impacts strongly on the quality of the linear relaxation built. A branch-and-cut algorithm is described to solve chance-constrained combinatorial problems to optimality. Numerical tests validate the theoretical analysis and illustrate the practical efficiency of the proposed approach. keywords: chance-constrained programming, integer linear programming
منابع مشابه
Solving Chance-Constrained Stochastic Programs via Sampling and Integer Programming
Various applications in reliability and risk management give rise to optimization problems with constraints involving random parameters, which are required to be satisfied with a pre-specified probability threshold. There are two main difficulties with such chance-constrained problems. First, checking feasibility of a given candidate solution exactly is, in general, impossible since this requir...
متن کاملA robust approach to the chance-constrained knapsack problem
Chance-constrained programming is a relevant model for many concrete problems. However, it is known to be very hard to tackle directly. In this paper, the chance-constrained knapsack problem (CKP) is addressed. Relying on the recent advances in robust optimization, a tractable combinatorial algorithm is proposed to solve CKP. It always provides feasible solutions for CKP. Moreover, for two spec...
متن کاملDecomposition algorithms for two-stage chance-constrained programs
We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility...
متن کاملTractable algorithms for chance-constrained combinatorial problems
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 op...
متن کاملThe Minmax Multidimensional Knapsack Problem with Application to a Chance-Constrained Problem
In this paper we present a new combinatorial problem, called minmax multidimensional knapsack problem (MKP), motivated by a military logistics problem. The logistics problem is a two-period, two-level, chance-constrained problem with recourse. We show that the MKP is NP-hard and develop a practically efficient combinatorial algorithm for solving it. We also show that under some reasonable assum...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comp. Opt. and Appl.
دوره 45 شماره
صفحات -
تاریخ انتشار 2010