The Thirteen Spheres: A New Proof

The multi-objective linear fractional programming is an interesting topic with many applications in different fields. Until now, various algorithms have been proposed in order to solve the multi-objective linear fractional programming (MOLFP) problem. An important point in most of them is the use of non-linear programming with a high computational complexity or the use of linear programming with preferences of the objective functions which are assigned by the decision maker. The current paper, through combining goal programming and data envelopment analysis (DEA), proposes an iterative method to solve MOLFP problems using only linear programming. Moreover, the proposed method provides an efficient solution which fairly optimizes each objective function when the decision maker has no information about the preferences of the objective functions. In fact, along with normalization of the objective functions, their relative preferences are fairly determined using the DEA. The implementation of the proposed method is demonstrated using numerical examples.

Low-Cost, Ready-to-Use Therapeutic Foods Can Be Designed Using Locally Available Commodities with the Aid of Linear Programming ,

It is necessary to select appropriate active parameters to ensure both the accuracy and computation efficiency before the global analysis of chemical kinetic model. This paper proposes a new method for selecting the active parameters on the base of the combination of sensitivity analysis and linear programming. Compared with the usual methods for selecting active parameters, such as the local sensitive analysis, the characteristics of the proposed method is preliminary visualization of the possible influence of the selected active parameters on the model outputs in the process of parameter selection, ensuring the reliability of the selected active parameters. Considering the computation efficiency, the number of selected active parameters can be controlled in a suitable size through combining with dichotomy or other screening techniques. In the study, the pre-exponential factors of the Arrhenius equations in the USC-Mech II model were considered as the candidate parameters and the uncertainties of the pre-exponential factors were set. Taking the ignition of ethylene for example, the 10 reactions that can increase the ignition time of ethylene under a wide range of conditions with equivalence ratio of 1, 0.1 ~ 1 MPa and 1000 K ~ 1500 K were successfully selected using the proposed method. Then, the 10 active parameters were tested in each condition. The results showed that the selected active parameters can make the ignition delay time close to the target for each condition, which reflects the reliability of active parameter selection.

The next generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five control surfaces, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude of the aircraft. Next generation aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship no longer exists between the required control surface deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands to attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples the sensitivity of the solutions provided by the linear programming and quadratic programming methods.

Manufacturing system effectiveness depends on several factors which include qualitative as well as quantitative factors. In the present paper, the management of the case company has to take a decision about the prioritisation of manufacturing systems on the basis of their effectiveness and has to decide about their production capacity. In the available literature, approaches like linear programming and AHP, mixed integer linear programming, and goal programming have been applied by some authors to tackle similar type of problems. These techniques are mathematical in nature and also consider qualitative factors which are crucial in determining the effectiveness of any manufacturing system, particularly when manufacturing systems are to be prioritised. The result from the research work with AHP framework indicates higher manufacturing effectiveness to leagile manufacturing system followed by agile manufacturing system, lean manufacturing system and flexible manufacturing system.

This study presents an improved technique for obtaining the collapse loads for any geotechnical stability problem with the application of the lower bound finite elements limit analysis in combination with linear programming. In the proposed method, a lower order polygon is initially used throughout the problem domain to model the Mohr–Coulomb yield function; the order of the polygon refers to its total number of sides. After obtaining the initial solution, the problem domain is then discretized into a number of zones in which a different order polygon is used to model the yield surface. It is noted that a higher order polygon needs to be chosen only in a region, not everywhere, where the stress state approaches towards the yield. The total memory usage as well as the computational time needed to solve the problem with the proposed technique becomes significantly smaller. In order to check the validity of the method, the bearing capacity factor Nγ was computed for smooth as well as rough strip footing and the obtained computational results were found to be quite encouraging.

The increased water demand and the increased capital construction costs of water resource development projects force engineers and water planners to utilize efficiently the existing and proposed water resources systems. Hence, it is considered necessary to find the optimum real time operating rules for systems of multiple reservoirs.Stochastic dynamic programming (SDP) has been used as the tool for deriving the real time operating rules for a system of multiple reservoirs, in preference to simulation analysis and linear programming. This is because the operation of the storages is considered as a sequential decision problem and dynamic programming is well suited to handle sequential, multi-period type decision problems. Further, the stochastic nature of streamflow is considered explicitly through a multivariate distribution for streamflow. The method theoretically produces the global optimum solution.The computational difficulties in terms of computer time and memory space have prohibited the realistic application of this method to systems of multiple reservoirs in the past. In this study, two methods have been introduced to reduce the computational difficulties of the method, thus making SDP more attractive to use in the derivation of the real time operating rules for a system of multiple reservoirs.The first method, the assumption of cross correlation of streamflow, reduces the number of states in the SDP method which reduces computer time and memory space. Further, it reduces the number of conditional probability estimates of streamflow which are used in recursive relation of the SDP algorithm. The second method, the “corridor” approach, reduces computer time involved in the SDP method by eliminating the computation of infeasible and/or inferior (suboptimal) solutions. These two methods have resulted in significant savings in the computer effort of the SDP method.The conditional probabilities of streamflow are computed by considering the hypervolume under the conditional probability density function between the integration limits using the computationally efficient Gaussian Legendre quadrature method. The conditional probability density function is derived from the historical streamflow data.Real time operating rules are expressed as a function of the storage volume(s) at the beginning of the current time interval and the forecast inflow into the storage(s) during the current time interval.The Melbourne water supply system is used as the example. The derived operating rules have been tested by operating a simulation model and the conclusion is made that the SDP method is a satisfactory technique for objectively deriving real time operating rules for a system of multiple reservoirs.Finally, a combined stochastic dynamic programming – statistical disaggregation approach is introduced to determine the real time operating rules for a system of multiple reservoirs where operational data are available. Releases from individual storages are a function of the total system storage volume and inflow. The method uses SDP to determine the release rules from the equivalent single reservoir of the multiple reservoir system; these releases are then disaggregated to individual releases using the statistical release disaggregation model whose parameters are derived from the historical operational data. The approach was used to derive real time operating rules for the Melbourne water supply system and the operating rules were validated using a simulation model of the system.

A large number of operational tools exist to help researchers determine business solutions for their customers. Each individual tool serves a distinct purpose for specific types of problems. Deciding which tool to use requires knowledge and experience. Sometimes, the researcher should integrate several tools because each tool may get too complex or not form a complete solution. This paper discusses how simulation, linear programming and spreadsheet analysis were integrated to help a new hospital determine ideal space assignments, schedule configurations and throughput targets for numerous clinic services.

The very large bandwidth available in the 60 GHz band allows, in principle, to design highly accurate positioning systems. Integrating such systems with standard protocols (e.g., IEEE 802.11ad) is crucial for the deployment of location-based services, but it is also challenging and limits the design choices. Another key problem is that consumer-grade 60 GHz hardware only provides coarse channel state information, and has highly irregular beam shapes due to its cost-efficient design. In this paper, we explore the location accuracy that can be achieved using such hardware, without modifying the 802.11ad standard. We consider a typical 802.11ad indoor network with multiple access points (APs). Each AP collects the coarse signal-to-noise ratio of the directional beacons that clients transmit periodically. Given the irregular beam shapes, the challenge is to relate each beacon to a set of transmission angles that allows to triangulate a user. We design a location system based on particle filters along with linear programming and Fourier analysis. We implement and evaluate our algorithm on commercial off-the-shelf 802.11ad hardware in an office scenario with mobile human blockage. Despite the strong limitations of the hardware, our system operates in real-time and achieves sub-meter accuracy in 70% of the cases.

Space Information Flow (SIF) is a new promising research area that studies network coding in geometric space, such as Euclidean space. The design of algorithms that compute the optimal SIF solutions remains one of the key open problems in SIF. This work proposes the first exact SIF algorithm and a heuristic SIF algorithm that compute min-cost multicast network coding for N (N ≥ 3) given terminal nodes in 2-D Euclidean space. Furthermore, we find that the Butterfly network in Euclidean space is the second example besides the Pentagram network where SIF is strictly better than Euclidean Steiner minimal tree. The exact algorithm design is based on two key techniques: Delaunay triangulation and linear programming. Delaunay triangulation technique helps to find practically good candidate relay nodes, after which a min-cost multicast linear programming model is solved over the terminal nodes and the candidate relay nodes, to compute the optimal multicast network topology, including the optimal relay nodes selected by linear programming from all the candidate relay nodes and the flow rates on the connection links. The heuristic algorithm design is also based on Delaunay triangulation and linear programming techniques. The exact algorithm can achieve the optimal SIF solution with an exponential computational complexity, while the heuristic algorithm can achieve the sub-optimal SIF solution with a polynomial computational complexity. We prove the correctness of the exact SIF algorithm. The simulation results show the effectiveness of the heuristic SIF algorithm.

Inter-parametric Tolerance Analysis of a Multiobjective Linear Programming

We introduce the notion of factoraggregation,which is a special construction of general aggregation operators, and apply it for an analysis of optimal solution parameters for bilevel linear programming problems. The aggregation observes lower level objective functions considering the classes of equivalence generated by an objective function on the upper level. The proposed method is illustrated with numerical and graphical examples.KeywordsMembership FunctionLinear Programming ProblemAggregation OperatorLower Level ObjectiveBilevel Linear Programming ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Application of mixed-integer linear programming in multiterm expansion planning under multiobjectives

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

Removing underground, unexploded bombs, mortars, cannon-shells and other ordnance (MEC or UXO) from former military ranges is difficult and expensive. The principal difficulty is discriminating intact, underground ordnance from other metallic items such as fragments of exploded ordnance (Clutter), magnetic rocks, and historic items such as horseshoes, barbed-wire, and refrigerators. This study represents the first, large-scale, blind-test of MEC discrimination technology on production-grade, survey-mode data from the cleanup of a real impact site. The results reported here significantly advance the state-of-the-art in MEC discrimination over alternative forward-modeling/inversion approaches to performing MEC discrimination. We combined Linear Genetic Programming (LGP) and statistical analysis to process data from the cleanup of 600 acres of the F.E.Warren Air Force Base. That data contained almost 30,000 targets of interest identified by geophysicists, including three-hundred thirty-two 75mm projectiles (75mm) and 37mm projectiles (37mm). A little under one-third of the groundtruth was held back by the customer for blind-testing. Our task was to discriminate intact 37mm's and 75mm's from the clutter by ordering the targets from most-likely to be MEC to least-likely to be MEC in what is referred to as a dig-list. We identified all 75mm's by 28.2% of the way through our prioritized dig-list and all 37mm's by 64.2% of the way through the prioritized dig list. Thus, depending on ordnance type, we reduced the number of targets that had to be excavated (false alarms) to clear the entire site by between 35% and 72%.