Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.

The Bangladesh grain model

We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented.

First, this paper presents the results of experiments with algorithmic techniques for efficiently solving medium and large scale linear and mixed integer programming problems. The techniques presented here are either original or recent.

An Application of Interior Point Method to 0-1 Mixed Integer Programing Problems

Future wireless communication systems are expected to provide a broad range of multimedia services that have a significant traffic asymmetry between uplink and downlink. The code division multiple access‐time division duplex (CDMA‐TDD) system is a promising solution to cope with the problem of traffic asymmetry. However, the TDD system is subject to inter‐cell interference compared to frequency division duplex (FDD) system. Since both uplink and downlink share the same frequency in TDD, uplink and downlink may interfere each other especially when neighboring cells require different rates of traffic load. Thus, the resource allocation among cells is an important issue in TDD. In this paper, the resource allocation in the CDMA‐TDD is formulated as a mixed integer programming (MIP) problem. A dynamic resource allocation algorithm (DRAA) is provided that effectively solves the traffic asymmetry problem. The MIP problem is also solved by a well‐known branch and bound procedure. Both the crossed slot and non‐crossed slot allocation are examined and compared to the DRAA. Computational result shows that proposed DRAA gives a good performance as the traffic asymmetry increases between the uplink and downlink. Copyright © 2003 John Wiley & Sons, Ltd.

Coal is one of the main energy sources and the carriage of coals is inevitable in China. How to choose the modes between each cities is one of the key factors that decide the quality of the coal carriage. A model for that problem was formulated to be a mixed integer programming problem at first. Then, a Dynamic Programming algorithm was proposed to obtain the optimal combination strategy of transport modes. The corresponding program was designed based on MATLAB and implemented on a personal computer. Finally, a real life problem was solved to show the feasibility and efficiency of the proposed model and algorithm.

In this paper, we explore a joint subcarrier assignment and power allocation with statistical delay QoS guarantees for full-duplex OFDMA systems. Effective capacity theory which evaluates wireless channel capacity from a novel view of link layer provides a theory basis for modeling the system capacity under the conditions of delay QoS constrains. After modeling the aggregate effective capacity of the system, we formulate joint subcarrier assignment and power allocation problem as a mixed integer programming problem, whose target is to maximize the aggregate effective capacity. To solve this integer programming problem, we allocate initial power on each subcarrier and decompose it into two subproblems, which are subcarrier allocation problem and power allocation problem respectively. Further, we propose an alternative algorithm to achieve joint subcarrier assignment and power allocation, which can meet the “subcarrier continuity” constraint of uplink resource allocation. Simulations have shown that the performance of our proposed scheme is favorite. Additionally, we investigate the effect of the residual selfinterference, inter-node interference (INI) and statistical delay QoS exponent on the performance of systems.

Genetic algorithm for non-linear mixed integer programming problems and its applications

A modification of the branch-and-bound algorithm due to Norman Driebeek for the solution of mixed integer programming problems is discussed. This modification increases the over-all efficiency of the algorithm. In addition, the modified algorithm is capable of solving, without reformulation, the more general problem in which i the allowable values for the restricted variables are not integers or are not evenly spaced. The algorithm has been coded in FORTRAN and tested on a Honeywell H-1800 computer.

Uncapacitated Facility Location (UFL) Problems are, in general, modelled as mixed integer programming problems, which are known as NP-hard problems. In recent years, a few publications have appeared on the metaheuristics for solving UFL problems, discussing the performance of particular implementations of metaheuristics for small and middle size UFL benchmarks. The large-scale problems remain untouched. The approach presented in this paper attempts to tackle them with a metaheuristics combining two well-known approaches. The idea is to enable algorithm searching through solution space by taking advantage of both underlying approaches in order to avoid local minima. The power of simulated annealing (SA) in local search and that of the evolutionary approach in global search have been brought together to obtain the desired solution quality within a shorter time.

An optimization procedure is described that can serve to identify attractive regionalization plans for large wastewater treatment and collection systems. Potential expansion of facilities in Western Suffolk County, Long Island, New York is considered. A mixed integer programming approach is utilized. Each system element cost, taken as a function of wastewater flow, is represented by a linear variable cost plus a fixed cost. The objective is to minimize total cost while ensuring that all wastewater flow generated is treated. Political and administrative feasibility and the location of effluent discharge constrain the model. The Long Island problem is too large to be solved with a standard formulation of wastewater network as a mixed integer programming problem. To improve computational efficiency, additional constraints are introduced on the minimum flow in each pipe and on the number of pipes leaving each node. Network configurations obtained for Western Suffolk County show that limiting development plans to 201 regions is not cost effective. Regional solutions indicate a general trade‐off between lower costs for coastal discharge and increased groundwater recharge.

A heuristic decomposition approach to optimal control in a water supply model

Benders’ partitioning method is a classical method for solving mixed integer programming problems. The basic idea is to partition the problem by dividing the variables into complicating variables, normally the variables that are constrained to be integer valued, and easy variables, normally the continuous variables. By fixing the complicating variables, a convex sub-problem is generated. Solving this convex sub-problem and its dual generates cutting planes that are used to create a master problem, which when solved generates new values for the complicating variables, which have a potential to give a better solution. In this work, we assume that the optimal solution is given, and we present a way in which the partitioning idea can be used to generate a valid inequality that supports the optimal solution. By adding some of the continuous variables to the complicating variables, we generate a valid inequality, which is a supporting hyperplane to the convex hull of the mixed integer program. The relaxed original programming problem with this supporting valid inequality added will produce interpretable prices for the original mixed integer programming problem. The method developed can be used to generate economically interpretable prices for markets with non-convexities. This is an important issue in many of the deregulated electricity markets in which the non-convexities comes from large start up costs or block bids. The generated prices are, in the case when the sub-problem generated by fixing the integer variables to their optimal values has the integrality property, also supported by nonlinear price functions that are the basis for integer programming duality.

Large scale exploitation of Renewable Energy Sources (RES) and their sustainable integration in the power system are important and challenging goals for transmission system operators because of the unpredictability of most of these sources. The aim of this paper is to highlight the advantages, in terms of enhanced RES exploitation and improved system flexibility, deriving from the coordinated management of wind power generation and energy storage systems: in particular, a Residual Unit Commitment procedure is proposed in order to provide the generation resources required to satisfy reserve and transmission network constraints. The resulting model consists in a large scale mixed-integer programming problem which is solved by the CPLEX optimization package. Tests on the IEEE 24 bus system will be presented.