Solving Mixed Integer Bilinear Problems Using MILP Formulations
نویسندگان
چکیده
In this paper, we examine a mixed integer linear programming (MILP) reformulation for mixed integer bilinear problems where each bilinear term involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resulting product of continuous and binary variables. We present the convex hull of the underlying mixed integer linear set. The effectiveness of this reformulation and associated facet-defining inequalities are computationally evaluated on five classes of instances.
منابع مشابه
On the Solution of Nonconvex Cardinality Boolean Quadratic Programming problems
This paper addresses the solution of a nonlinear boolean quadratic programming problem using three different approaches. The first uses a classic linearization technique to transform the original problem into a Mixed Integer Linear Programming (MILP) problem for which multiple formulations are studied. The second uses the capabilities of current MILP solvers to deal with Mixed Integer Quadratic...
متن کاملPredictive control for baggage handling systems using mixed integer linear programming
State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed integer optimization problem which is usually very expen...
متن کاملPredictive route control for automated baggage handling systems using mixed-integer linear programming
State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed-integer optimization problem, usually very expensive in ...
متن کاملEvent-based MILP models for resource-constrained project scheduling problems
In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose MILP formulations for the RCPSP base...
متن کاملMixed Integer Linear Programming Formulation Techniques
A wide range of problems can be modeled as Mixed Integer Linear Programming (MILP) problems using standard formulation techniques. However, in some cases the resulting MILP can be either too weak or to large to be effectively solved by state of the art solvers. In this survey we review advanced MILP formulation techniques that result in stronger and/or smaller formulations for a wide class of p...
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:
- SIAM Journal on Optimization
دوره 23 شماره
صفحات -
تاریخ انتشار 2013