Showing papers on "Integer programming published in 2002"
08 May 2002
TL;DR: In this article, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance, which can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization.
Abstract: Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization.
791 citations
TL;DR: In this article, a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, such as Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form is presented.
Abstract: This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
625 citations
TL;DR: A distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers that incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term is introduced.
Abstract: We introduce a distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a non-linear integer-programming problem. Model properties are outlined. A Lagrangian relaxation solution algorithm is proposed. By exploiting the structure of the problem we can find a low-order polynomial algorithm for the non-linear integer programming problem that must be solved in solving the Lagrangian relaxation subproblems. A number of heuristics are outlined for finding good feasible solutions. In addition, we describe two variable forcing rules that prove to be very effective at forcing candidate sites into and out of the solution. The algorithms are tested on problems with 88 and 150 retailers. Computation times are consistently below one minute and compare favorably with those of an earlier proposed set partitioning approach for this model (Shen, 2000; Shen, Coullard and Daskin, 2000). Finally, we discuss the sensitivity of the results to changes in key parameters including the fixed cost of placing orders. Significant reductions in these costs might be expected from e-commerce technologies. The model suggests that as these costs decrease it is optimal to locate additional facilities.
591 citations
01 Jan 2002
TL;DR: The GAMS model for Pooling problems as mentioned in this paper is a well-known model for pooling problems, and it has been used extensively in the field of software engineering and computer science.
Abstract: Preface. Acknowledgements. List of Figures. List of Tables. 1. Introduction. 2. Convex Extensions. 3. Project Disaggregation. 4. Relaxations of Factorable Programs. 5. Domain Reduction. 6. Node Partitioning. 7. Implementation. 8. Refrigerant Design Problem. 9. The Pooling Problem. 10. Miscellaneous Problems. 11. GAMS/BARON: A Tutorial. A: GAMS Model for Pooling Problems. Bibliography. Index. Author Index.
562 citations
TL;DR: Computational results demonstrate orders‐of‐magnitude improvements of the decomposition algorithms over direct solution of the MIP and show that SVIs also help solve the original MIP faster.
Abstract: We study the problem of interdicting the arcs in a network in order to maximize the shortest s–t path length. “Interdiction” is an attack on an arc that destroys the arc or increases its effective length; there is a limited interdiction budget. We formulate this bilevel, max–min problem as a mixed-integer program (MIP), which can be solved directly, but we develop more efficient decomposition algorithms. One algorithm enhances Benders decomposition by adding generalized integer cutting planes, called “supervalid inequalities” (SVIs), to the master problem. A second algorithm exploits a unique set-covering master problem. Computational results demonstrate orders-of-magnitude improvements of the decomposition algorithms over direct solution of the MIP and show that SVIs also help solve the original MIP faster. Published 2002 Wiley Periodicals, Inc.
518 citations
TL;DR: The research develops an integrated design methodology based on primal decomposition methods for the mixed integer programming formulation that allows a natural split of the production and transportation decisions and the research identifies the necessary information flows between the subsystems.
511 citations
10 Jun 2002
TL;DR: A two-phase framework that integrates task assignment, ordering and voltage selection together to minimize energy consumption of real-time dependent tasks executing on a given number of variable voltage processors is presented.
Abstract: In this paper, we present a two-phase framework that integrates task assignment, ordering and voltage selection (VS) together to minimize energy consumption of real-time dependent tasks executing on a given number of variable voltage processors. Task assignment and ordering in the first phase strive to maximize the opportunities that can be exploited for lowering voltage levels during the second phase, i.e., voltage selection. In the second phase, we formulate the VS problem as an Integer Programming (IP) problem and solve the IP efficiently. Experimental results demonstrate that our framework is very effective in executing tasks at lower voltage levels under different system configurations.
360 citations
TL;DR: In this article, the authors consider the problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace and propose two different formulations of the multiaircraft conflict avoidance problem as a mixed-integer linear program.
Abstract: This paper considers the problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace. Aircraft can not get closer to each other than a given safety distance in order to avoid possible conflicts between different airplanes. For such system of multiple aircraft, we consider the path planning problem among given waypoints avoiding all possible conflicts. In particular we are interested in optimal paths, i.e., we want to minimize the total flight time. We propose two different formulations of the multiaircraft conflict avoidance problem as a mixed-integer linear program: in the first case only velocity changes are admissible maneuvers, in the second one only heading angle changes are allowed. Due to the linear formulation of the two problems, solutions may be obtained quickly with standard optimization software, allowing our approach to be implemented in real time.
339 citations
08 May 2002
TL;DR: In this article, the authors used Mixed-Integer Linear Programming (MILP) for the optimization of the trajectory of a fixed-wing UAV in large-scale maneuvers.
Abstract: This paper presents a new approach to trajectory optimization for autonomous fixed-wing aerial vehicles performing large-scale maneuvers. The main result is a planner which designs nearly minimum time planar trajectories to a goal, constrained by no-fly zones and the vehicle's maximum speed and turning rate. Mixed-Integer Linear Programming (MILP) is used for the optimization, and is well suited to trajectory optimization because it can incorporate logical constraints, such as no-fly zone avoidance, and continuous constraints, such as aircraft dynamics. MILP is applied over a receding planning horizon to reduce the computational effort of the planner and to incorporate feedback. In this approach, MILP is used to plan short trajectories that extend towards the goal, but do not necessarily reach it. The cost function accounts for decisions beyond the planning horizon by estimating the time to reach the goal from the plan's end point. This time is estimated by searching a graph representation of the environment. This approach is shown to avoid entrapment behind obstacles, to yield near-optimal performance when comparison with the minimum arrival time found using a fixed horizon controller is possible, and to work consistently on large trajectory optimization problems that are intractable for the fixed horizon controller.
310 citations
12 May 2002
TL;DR: Three variants of PSO are compared with the widely used branch and bound technique, on several integer programming test problems and results indicate that PSO handles efficiently such problems, and in most cases it outperforms the branch and Bound technique.
Abstract: The investigation of the performance of the particle swarm optimization (PSO) method in integer programming problems, is the main theme of the present paper. Three variants of PSO are compared with the widely used branch and bound technique, on several integer programming test problems. Results indicate that PSO handles efficiently such problems, and in most cases it outperforms the branch and bound technique.
307 citations
TL;DR: This paper presents a new technique for analyzing a power grid using macromodels that are created for a set of partitions of the grid, and shows that even for a 60 million-node power grid, the approach allows for an efficient analysis, whereas previous approaches have been unable to handle power grids of such size.
Abstract: Careful design and verification of the power distribution network of a chip are of critical importance to ensure its reliable performance. With the increasing number of transistors on a chip, the size of the power network has grown so large as to make the verification task very challenging. The available computational power and memory resources impose limitations on the size of networks that can be analyzed using currently known techniques. Many of today's designs have power networks that are too large to be analyzed in the traditional way as flat networks. In this paper, we propose a hierarchical analysis technique to overcome the aforesaid capacity limitation. We present a new technique for analyzing a power grid using macromodels that are created for a set of partitions of the grid. Efficient numerical techniques for the computation and sparsification of the port admittance matrices of the macromodels are presented. A novel sparsification technique using a 0-1 integer linear programming formulation is proposed to achieve superior sparsification for a specified error. The run-time and memory efficiency of the proposed method are illustrated on industrial designs. It is shown that even for a 60 million-node power grid, our approach allows for an efficient analysis, whereas previous approaches have been unable to handle power grids of such size.
TL;DR: The methodology develops and applies a combination of multi-criteria efficiency models, based on game theory concepts, and linear and integer programming methods for effective supply chain design.
TL;DR: In this paper, an effective method of network reconfiguration to reduce power loss and enhance the voltage profile by the improved mixed-integer hybrid differential evolution (MIHDE) method for distribution systems is proposed.
Abstract: This study proposes an effective method of network reconfiguration to reduce power loss and enhance the voltage profile by the improved mixed-integer hybrid differential evolution (MIHDE) method for distribution systems. This research aims to recognize beneficial load transfers so that the objective function composed of power losses is minimized and the prescribed voltage limits are satisfied. The proposed method determines the proper system topology that reduces the power loss according to a load pattern. Mathematically, the problem of this research is a mixed-integer combinatorial optimization problem well suited to the application of MIHDE.
TL;DR: This work considers a generalization of the maximal cover location problem which allows for partial coverage of customers, with the degree of coverage being a non-increasing step function of the distance to the nearest facility.
TL;DR: This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs and the use of valid inequalities for classes of problems with structure, such as network design, is explored.
TL;DR: In this paper, the authors present fuel/time-optimal control algorithms for a co-ordination and control architecture that was designed for a fleet of spacecraft, including low-level formation-keeping algorithms and a high-level fleet planner that creates trajectories to re-size or re-target the formation.
Abstract: SUMMARY Formation flying of multiple spacecraft is an enabling technology for many future space science missions. However, the co-ordination and control of these instruments poses many difficult design challenges. This paper presents fuel/time-optimal control algorithms for a co-ordination and control architecture that was designed for a fleet of spacecraft. This architecture includes low-level formation-keeping algorithms and a high-level fleet planner that creates trajectories to re-size or re-target the formation. The trajectory and formation-keeping optimization algorithms are based on the solutions of linear and integer programming problems. The result is a very flexible optimization framework that can be used off-line to analyse various aspects of the mission design and in real time as part of an onboard autonomous formation flying control system. The overall control approach is demonstrated using a nonlinear simulation environment that includes realistic measurement noises, disturbances, and actuator nonlinearities. Copyright # 2002 John Wiley & Sons, Ltd.
TL;DR: A survey of algorithms and applications for the nonlinear knapsack problem, a nonlinear optimization problem with just one constraint, bounds on the variables, and a set of specially structured constraints such as generalized upper bounds (GUBs), is presented.
TL;DR: In this paper, a new formulation for reactive power (VAr) planning problem including the allocation of flexible ac transmission systems (FACTS) devices is proposed, which directly takes into account the expected cost for voltage collapse and corrective controls, where the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal VAr planning.
Abstract: This paper proposes a new formulation for reactive power (VAr) planning problem including the allocation of flexible ac transmission systems (FACTS) devices. A new feature of the formulation lies in the treatment of security issues. Different from existing formulations, we directly take into account the expected cost for voltage collapse and corrective controls, where the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal VAr planning. The inclusion of load shedding into the formulation guarantees the feasibility of the problem. The optimal allocation by the proposed method implies that the investment is optimized, taking into account its effects on security in terms of the cost for power system operation under possible events occurring probabilistically. The problem is formulated as a mixed integer nonlinear programming problem of a large dimension. The Benders decomposition technique is tested where the original problem is decomposed into multiple subproblems. The numerical examinations are carried out using AEP-14 bus system to demonstrate the effectiveness of the proposed method.
TL;DR: An integer-programming model and a post-solution heuristic allocates operating room time to the five surgical divisions at Toronto's Mount Sinai Hospital has been used for several years and credits it with both administrative savings and the ability to produce quickly an equitable master surgical schedule.
Abstract: An integer-programming model and a post-solution heuristic allocates operating room time to the five surgical divisions at Toronto's Mount Sinai Hospital. The hospital has used this approach for several years and credits it with both administrative savings and the ability to produce quickly an equitable master surgical schedule.
TL;DR: This work proposes algorithms for the solution of multiparametric quadratic programming (mp-QP) problems and multiparametry mixed-integer quadratics programming (MP-MIQP), with a convex and quadratically objective function and linear constraints, and their application in model predictive and hybrid control problems.
TL;DR: In this paper two strategies are presented to reduce the combinatorial complexity when solving single stage and multistage optimization scheduling problems that involve cost minimization and due dates.
TL;DR: Algorithms underlying the automatic model-building functionality of the ARP/wARP software suite are presented and graph-search algorithms are presented that find solutions to this problem in an efficient manner.
Abstract: Algorithms underlying the automatic model-building functionality of the ARP/wARP software suite are presented. Finding the most likely set of Cα atoms from a given set of atoms is formulated as a constrained integer programming problem. The objective function is a density-weighted score for the match between observed and expected chain conformation. Graph-search algorithms are presented that find solutions to this problem in an efficient manner.
IBM1
TL;DR: A new approximation algorithm for the metric uncapacitated facility location problem is designed, of LP rounding type and is based on a rounding technique developed in [5,6,7].
Abstract: We design a new approximation algorithm for the metric uncapacitated facility location problem. This algorithm is of LP rounding type and is based on a rounding technique developed in [5,6,7].
10 Nov 2002
TL;DR: This work solves instances of the Max-SAT and Max-ONEs optimization problems which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively and shows that specialized 0--1 techniques tend to outperform generic ILP techniques on Boolean optimization problems as well as on general EDA SAT problems.
Abstract: Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, etc. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0--1 variables. Therefore specialized 0--1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" constraints.This work provides an update on the on-going competition between generic ILP techniques and specialized 0--1 ILP techniques. To make a fair comparison, we generalize recent ideas for fast SAT-solving to more general 0--1 ILP problems that may include counting constraints and optimization. Another aspect of our comparison is evaluation on 0--1 ILP benchmarks that originate in Electronic Design Automation (EDA), but that cannot be directly solved by a SAT solver. Specifically, we solve instances of the Max-SAT and Max-ONEs optimization problems which seek to maximize the number of satisfied clauses and the "true" values over all satisfying assignments, respectively. Those problems have straightforward applications to SAT-based routing and are additionally important due to reductions from Max-Cut, Max-Clique, and Min Vertex Cover. Our experimental results show that specialized 0--1 techniques tend to outperform generic ILP techniques on Boolean optimization problems as well as on general EDA SAT problems.
TL;DR: The simultaneous lotsizing and scheduling of several products on non-identical parallel production lines (heterogeneous machines) is addressed by combining the local search metastrategies threshold accepting (TA) and simulated annealing (SA) with dual reoptimization.
TL;DR: New valid inequalities for these mixed integer programming problems with probabilistic constraints involving random variables with discrete distributions are developed using specific properties of stochastic programming problems and bounds on the probability of the union of events.
Abstract: We consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions. They can be reformulated as large scale mixed integer programming problems with knapsack constraints. Using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems. We also develop methods for lifting these inequalities. These procedures are used in a general iterative algorithm for solving probabilistically constrained problems. The results are illustrated with a numerical example.
TL;DR: In this paper, a multi-period electricity auction market tool that explicitly takes into account transmission congestion and losses as well as intertemporal operating constraints such as start-up costs, ramp rates, and minimum up and down times that may be included in any generating unit's composite bid is presented.
Abstract: This paper presents a multiperiod electricity auction market tool that explicitly takes into account transmission congestion and losses as well as intertemporal operating constraints such as start-up costs, ramp rates, and minimum up and down times that may be included in any generating unit's composite bid. This approach, which requires only existing mixed-integer linear solvers, provides the market operator with a valuable tool for scheduling participants in a competitive market where transparency, fairness, and confidentiality of participants' data are of paramount concern. Indeed, under this framework, only network data are of public domain; producers are not required to reveal corporate data, and they have more flexibility in specifying the structure of their composite bid. This paper demonstrates and illustrates, through numerical studies using test systems, that an efficient and fair competitive electricity market can be implemented, taking into account network constraints and losses.
TL;DR: In this article, an exact and computationally efficient mixed-integer linear programming (MILP) formulation of the self-scheduling problem for a price-maker to achieve maximum profit in a pool-based electricity market is presented.
Abstract: This paper addresses the self-scheduling problem faced by a price-maker to achieve maximum profit in a pool-based electricity market. An exact and computationally efficient mixed-integer linear programming (MILP) formulation of this problem is presented. This formulation models precisely the price-maker capability of altering market-clearing prices to its own benefits, through price quota curves. No assumptions are made on the characteristics of the pool and its agents. A realistic case study is presented and the results obtained are analyzed in detail.
TL;DR: A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program and ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities.
Abstract: This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported.
21 Aug 2002
TL;DR: This paper presents the first provably optimal solution for an instance of eight teams of the Travelling Tournament Problem using a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solving the pricing problem.
Abstract: The Travelling Tournament Problem is a sports timetabling problem requiring production of a minimum distance double round-robin tournament for a group of n teams. Even small instances of this problem seem to be very difficult to solve. In this paper, we present the first provably optimal solution for an instance of eight teams. The solution methodology is a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solve the pricing problem. Additionally, constraint programming is used as a primal heuristic.