A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm

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.

Real-time power optimization for application server clusters based on Mixed-Integer Programming

In this paper, we consider simultaneous wireless information and energy transfer in an orthogonal-frequency-division-multiple-access decode-and-forward relay network, in which an energy-constrained relay node harvests energy from a source node and uses the harvested energy to forward information to multiple destination nodes. Our objective is to maximize the end-to-end sum rate by resource allocation, subject to transmit power constraint at the source and energy-harvesting (EH) constraint at the relay. A non-convex and mixed-integer programming (MIP) problem is formulated to optimize time-switching (TS) ratios of EH and information decoding at the relay, TS ratio of information transmission from relay to destinations, subcarrier allocation as well as power allocation (PA) over all subcarriers at source and relay. We propose to decouple this problem into a convex problem and an MIP problem in fractional form. To solve the MIP problem, we transform it into an equivalent optimization problem in subtractive form which has a tractable solution. As a result, we propose a novel scheme to achieve jointly optimal TS ratios, subcarrier allocation and PA. Simulation results verify the optimality of our proposed resource allocation scheme.

Path planning is key research topic in the field of robotics research, transportation, bioinformatics, virtual prototype designing, gaming, computer aided designs, and virtual reality estimation. In optimal path planning, it is important to determine the collision free optimal and shortest path. There may be various aspects to determine the optimal path based on workspace environment and obstacle types. In this research work, optimal path is determined based on the workspace environment having static obstacles and unknown environment area. A hybrid approach of meta-heuristic algorithm of Bat Algorithm (BA) and Cuckoo Search (CS) is used to determine the optimal path from defined source to destination. For experimentation, case study area of Alwar region, Rajasthan is considered which consist of urban and vegetation area. The reason for the selection of BA and CS for the path planning is the wide application and success of implementation of these concepts in the field of robotics and path planning. The consideration of individual BA for path planning can lead to problem of trapping between local optima. This obligates us to hybridize the concept of BA with some other efficient problem solving concept like CS. The hybridized concept of BA and CS is initially tested with standard benchmarks functions, after that considered for the application of path planning. Results of hybrid path planning concept are compared with individual CS and BA concepts in terms of simulation time and minimum number of iteration required to achieve the optimal path from defined source to destination. The evaluated results comparison of hybrid approach with individual concepts indicates the dominance of proposed hybrid concept in terms of standard benchmarks functions and other parameters as well.

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 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.

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.

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.

Introduction: Moringa oleifera root is the most underutilized part of the plant and it is rich in many phytochemicals.
 Aim of the Study: This study was carried out to evaluate the effect of Standardized and characterized aqueous root extract of Moringa oleifera following the administration of alcohol-induced liver damage in albino wistar rats.
 Materials and Methods: Thirty (30) experimental rats weighing 100-120 g were randomly divided into 6 groups of 5 rats each. Group 1, the normal control group was given just rat feed and water, group 2, negative control was administered alcohol only (1.5 ml/kg body weight), rats in group 3, 4 and 5 received combined administration of alcohol 1.5 ml/kg body weight and 200, 400 and 600 mg/kg body weight of characterized aqueous root extract of Moringa oleifera respectively, group 6 rats were administered 250mg/body weight of extract only. At the end of fourteen days (14) the experimental rats were then sacrificed and the serum liver enzymes were then assayed.
 Results: The results obtained from the laboratory was analyzed using one-way ANOVA and post-hoc test was done afterwards. Rats fed alcohol only produced significant increase in the levels of enzyme markers of tissue damage (AST, ALT and ALP) compared to normal control rats. Rats in group 3, 4 and 5 that were post treated with 200, 400 and 600 mg/kg body weight of extract and they had significant decrease (P<0.05) in the levels of these enzyme markers in a dose-dependent manner compared to the negative control. The extract control group had no significant increase (P<0.05) in the levels of the enzyme markers when compared to the normal control; however, there was a significant increase in the serum activity of ALP of the extract control group when compared with the normal control.
 Conclusion: The present study exhibited a potent hepatoprotective effect against liver injury caused by alcohol administration. This suppository effect could be related to the antioxidant’s properties of Moringa oleifera that is rich in flavonoids and phenolic constituents of the extracts may contribute to their enzyme action.

In the wireless sensor networks, deploying a small amount of heterogeneous nodes which directly communicate with the Sink node, can form shortcuts. The shortcuts can make the network to have small-world properties, which can save energy and improve network performance. In the large-scale networks, the optimal deployment of heterogeneous nodes is a NP-hard problem. Considering the total energy consumption of the network and the uniformity of each node energy consumption, this paper presents a clustering heterogeneous network routing algorithm which based on mixed integer programming (CHNMIP). Firstly, the algorithm supposes that the heterogeneous nodes can only be placed in the position of the common nodes and converts the optimal deployment of heterogeneous nodes into a mixed integer programming problem, and finds out the approximate optimal solution using Lagrangian relaxation and Benders decomposition algorithm. Then, it dynamically divides common nodes into clusters, and sets the appropriate transmission. Finally, it theoretically analyzes the performance of CHNMIP routing algorithm, and the simulation results also show that CHNMIP routing algorithm can better improve the network performance in different simulation environment.

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.

Semi-supervised support vector machines arise in machine learning as a model of mixed integer programming problem for classification. In this paper, we propose two convex conic relaxations for the original mixed integer programming problem. The first one is a new semi-definite relaxation, and its possibly maximal ratio of the optimal value is estimated approximately. The second one is a doubly nonnegative relaxation, which is relaxed from a well-known conic programming problem called completely positive programming problem that is equivalent to the original problem. Furthermore, we prove that the doubly nonnegative relaxation is tighter than the semi-definite relaxation. Finally, the numerical results show that two proposed relaxations not only generate proper classifiers but also outperform some existing methods in classification accuracy.