Search results for: mathematical programming problem

Authors: Qing Lyu, Hang Zhu

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Various flows in the network require to go through different types of middlebox. The improper placement of network middlebox and path assignment for flows could greatly increase the network latency and also decrease the performance of network. Minimizing the total end to end latency of all the ows requires to assign path for the incoming flows. In this paper, the flow path assignment problem in regard to the placement of various kinds of middlebox is studied. The flow path assignment problem is formulated to a linear programming problem, which is very time consuming. On the other hand, a naive greedy algorithm is studied. Which is very fast but causes much more latency than the linear programming algorithm. At last, the paper presents a heuristic algorithm named FPA, which takes bottleneck link information and estimated bandwidth occupancy into consideration, and achieves near optimal latency in much less time. Evaluation results validate the effectiveness of the proposed algorithm.

Keywords: flow path, latency, middlebox, network

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Authors: Y. Smirlis, G. Koronakos, S. Plitsos

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Shipbrokers assist the ship companies in chartering or selling and buying vessels, acting as intermediates between them and the market. They facilitate deals, providing their expertise, negotiating skills, and knowledge about ship market bargains. Their role is very important as it affects the profitability and market position of a shipping company. Due to their significant contribution, the shipping companies have to employ systematic procedures to evaluate the shipbrokers’ services in order to select the best and, consequently, to achieve the best deals. Towards this, in this paper, we consider shipbrokers as financial service providers, and we formulate the problem of evaluating and selecting shipbrokers’ services as a multi-criteria decision making (MCDM) procedure. The proposed methodology comprises a first normalization step to adjust different scales and orientations of the criteria and a second step that includes the mathematical model to evaluate the performance of the shipbrokers’ services involved in the assessment. The criteria along which the shipbrokers are assessed may refer to their size and reputation, the potential efficiency of the services, the terms and conditions imposed, the expenses (e.g., commission – brokerage), the expected time to accomplish a chartering or selling/buying task, etc. and according to our modelling approach these criteria may be assigned different importance. The mathematical programming model performs a comparative assessment and estimates for the shipbrokers involved in the evaluation, a relative score that ranks the shipbrokers in terms of their potential performance. To illustrate the proposed methodology, we present a case study in which a shipping company evaluates and selects the most suitable among a number of sale and purchase (S&P) brokers. Acknowledgment: This study is supported by the OptiShip project, implemented within the framework of the National Recovery Plan and Resilience “Greece 2.0” and funded by the European Union – NextGenerationEU programme.

Keywords: shipbrokers, multi-criteria decision making, mathematical programming, service-provider selection

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Authors: Monica Hoeldtke Pietruchinski, Andrey Ricardo Pimentel

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The teaching of computer programming for beginners has been presented to the community as a not simple or trivial task. Several methodologies and research tools have been developed; however, the problem still remains. This paper aims to present multi-agent system architecture to be incorporated to the educational collaborative game software for teaching programming that monitors, evaluates and encourages collaboration by the participants. A literature review has been made on the concepts of Collaborative Learning, Multi-agents systems, collaborative games and techniques to teach programming using these concepts simultaneously.

Keywords: architecture of multi-agent systems, collaborative evaluation, collaboration assessment, gamifying educational software

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Authors: Yixun Shi

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Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

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Authors: Chechen Liao, Chin Yi Yang

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Although several factors that affect learning to program have been identified over the years, there continues to be no indication of any consensus in understanding why some students learn to program easily and quickly while others have difficulty. Seldom have researchers considered the problem of how to help the students enhance the programming learning outcome. The research had been conducted at a high school in Taiwan. Students participating in the study consist of 330 tenth grade students enrolled in the Basic Computer Concepts course with the same instructor. Two types of training methods-instruction-oriented and exploration-oriented were conducted. The result of this research shows that the instruction-oriented training method has better learning performance than exploration-oriented training method.

Keywords: learning performance, programming learning, TDD, training method

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Authors: Amirreza Kosari, Hossein Maghsoudi, Malahat Givar

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In this study, the three-dimensional optimal path planning of a flying robot for Terrain Following / Terrain Avoidance (TF/TA) purposes using Direct Collocation has been investigated. To this purpose, firstly, the appropriate equations of motion representing the flying robot translational movement have been described. The three-dimensional optimal path planning of the flying vehicle in terrain following/terrain avoidance maneuver is formulated as an optimal control problem. The terrain profile, as the main allowable height constraint has been modeled using Fractal Generation Method. The resulting optimal control problem is discretized by applying Direct Collocation numerical technique, and then transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method is demonstrated by extensive simulations, and in particular, it is verified that this approach could produce a solution satisfying almost all performance and environmental constraints encountering a low-level flying maneuver

Keywords: path planning, terrain following, optimal control, nonlinear programming

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Authors: Nicolás Clavijo Buriticá, Laura Viviana Triana Sanchez

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This research develops a productive context associated with the aquaculture industry in northern Tolima-Colombia, specifically in the town of Lerida. Strategic aspects of chain of fish Production-Distribution, especially those related to supply network design of an association devoted to cultivating, farming, processing and marketing of fish are addressed. This research is addressed from a special approach of Supply Chain Management (SCM) which guides management objectives to the system sustainability; this approach is called Sustainable Supply Chain Management (SSCM). The network design of fish production-distribution system is obtained for the case study by two mathematical programming models that aims to maximize the economic benefits of the chain and minimize total supply chain costs, taking into account restrictions to protect the environment and its implications on system productivity. The results of the mathematical models validated in the productive situation of the partnership under study, called Asopiscinorte shows the variation in the number of open or closed locations in the supply network that determines the final network configuration. This proposed result generates for the case study an increase of 31.5% in the partial productivity of storage and processing, in addition to possible favorable long-term implications, such as attending an agile or not a consumer area, increase or not the level of sales in several areas, to meet in quantity, time and cost of work in progress and finished goods to various actors in the chain.

Keywords: Sustainable Supply Chain, mathematical programming, aquaculture industry, Supply Chain Design, Supply Chain Configuration

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Authors: Alex Contarino

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Professional sports leagues often have a “free agency” period, during which teams may sign players with expiring contracts.To promote parity, many leagues operate under a salary cap that limits the amount teams can spend on player’s salaries in a given year. Similarly, in fantasy sports leagues, salary cap drafts are a popular method for selecting players. In order to sign a free agent in either setting, teams must bid against one another to buy the player’s services while ensuring the sum of their player’s salaries is below the salary cap. This paper models the bidding process for a free agent as a constrained optimization problem that can be solved using linear programming. The objective is to determine the largest bid that a team should offer the player subject to the constraint that the value of signing the player must exceed the value of using the salary cap elsewhere. Iteratively solving this optimization problem for each available free agent provides teams with an effective framework for maximizing the talent on their rosters. The utility of this approach is demonstrated for team sport roster construction and fantasy sport drafts, using recent data sets from both settings.

Keywords: linear programming, optimization, roster management, salary cap

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Authors: Chao Yu, Qing-Guo Wang, Dan Zhang

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The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low-rank, sparse matrices and further recast as a semidefinite programming (SDP) problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered “clean” data from the proposed method can give much better parameter estimation compared with that based on the raw data.

Keywords: outlier detection, system identification, matrix decomposition, low-rank matrix, sparsity, semidefinite programming, interior-point methods, denoising

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Authors: A. Graa, I. Ziane, F. Benhamida, S. Souag

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This paper presents a comparative analysis study of an efficient and reliable quadratic programming (QP) to solve economic load dispatch (ELD) problem with considering transmission losses in a power system. The proposed QP method takes care of different unit and system constraints to find optimal solution. To validate the effectiveness of the proposed QP solution, simulations have been performed using Algerian test system. Results obtained with the QP method have been compared with other existing relevant approaches available in literatures. Experimental results show a proficiency of the QP method over other existing techniques in terms of robustness and its optimal search.

Keywords: economic dispatch, quadratic programming, Algerian network, dynamic load

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Authors: Anusuya Ghosh, Vishnu Narayanan

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The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming.

Keywords: semidefinite programming, semidefinite representable set, compactly semidefinite representable set, approximation

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Authors: Saleem Z. Ramadan

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The material selection problem is concerned with the determination of the right material for a certain product to optimize certain performance indices in that product such as mass, energy density, and power-to-weight ratio. This paper is concerned about optimizing the selection of the manufacturing process along with the material used in the product under performance indices and availability constraints. In this paper, the material selection problem is formulated using binary programming and solved by genetic algorithm. The objective function of the model is to minimize the total manufacturing cost under performance indices and material and manufacturing process availability constraints.

Keywords: optimization, material selection, process selection, genetic algorithm

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Authors: Lidia N. Hernández-Piña, Carlos R. Jaimez-González

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Interoperability in distributed systems is an important feature that refers to the communication of two applications written in different programming languages. This paper presents a serializer and a de-serializer of PHP objects to and from XML, which is an independent library written in the PHP programming language. The XML generated by this serializer is independent of the programming language, and can be used by other existing Web Objects in XML (WOX) serializers and de-serializers, which allow interoperability with other object-oriented programming languages.

Keywords: interoperability, PHP object serialization, PHP to XML, web objects in XML, WOX

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Authors: Saeedeh Ahmadi Basir, Mohammad Mahdavi Mazdeh, Mohammad Namakshenas

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Manufacturers often dispatch jobs in batches to reduce delivery costs. However, sending several jobs in batches can have a negative effect on other scheduling-related objective functions such as minimizing the number of tardy jobs which is often used to rate managers’ performance in many manufacturing environments. This paper aims to minimize the number of weighted tardy jobs and the sum of delivery costs of a two-stage assembly flow-shop problem in a batch delivery system. We present a mixed-integer linear programming (MILP) model to solve the problem. As this is an MILP model, the commercial solver (the CPLEX solver) is not guaranteed to find the optimal solution for large-size problems at a reasonable amount of time. We present several numerical examples to confirm the accuracy of the model.

Keywords: scheduling, two-stage assembly flow-shop, tardy jobs, batched delivery system

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Authors: M. Moradi Dalini, M. R. Talebi

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This research revolves around a technical method according to combines econometric and multiobjective programming to select and obtain optimal solutions to management problems. It is taken for a generation that; it is important to analyze which combination of values of the explanatory variables -in an econometric method- would point to the simultaneous achievement of the best values of the response variables. In this case, if a certain degree of conflict is viewed among the response variables, we suggest a multiobjective method in order to the results obtained from a regression analysis. In fact, with the use of a multiobjective method, we will have the best decision about the conflicting relationship between the response variables and the optimal solution. The combined multiobjective programming and econometrics benefit is an assessment of a balanced “optimal” situation among them because a find of information can hardly be extracted just by econometric techniques.

Keywords: econometrics, multiobjective optimization, management problem, optimization

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Authors: Majid Khalili, Hamed Tayebi

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This paper considers a stochastic flexible job-shop scheduling (SFJSS) problem in the presence of production disruptions, and reactive scheduling is implemented in order to find the optimal solution under uncertainty. In this problem, there are two main disruptions including machine failure which influences operation time, and modification or cancellation of the order delivery date during production. In order to decrease the negative effects of these difficulties, two derived strategies from reactive scheduling are used; the first one is relevant to being able to allocate multiple machine to each job, and the other one is related to being able to select the best alternative process from other job while some disruptions would be created in the processes of a job. For this purpose, a Mixed Integer Linear Programming model is proposed.

Keywords: flexible job-shop scheduling, reactive scheduling, stochastic environment, mixed integer linear programming

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: Raziyeh Shamsi

Abstract:

In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

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Authors: Basil Manos, Parthena Chatzinikolaou, Fedra Kiomourtzi

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This paper presents a Multicriteria Mathematical Programming model for farm planning and sustainable optimization of agricultural production. The model can be used as a tool for the analysis and simulation of agricultural production plans, as well as for the study of impacts of various measures of Common Agriculture Policy in the member states of European Union. The model can achieve the optimum production plan of a farm or an agricultural region combining in one utility function different conflicting criteria as the maximization of gross margin and the minimization of fertilizers used, under a set of constraints for land, labor, available capital, Common Agricultural Policy etc. The proposed model was applied to the region of Larisa in central Greece. The optimum production plan achieves a greater gross return, a less fertilizers use, and a less irrigated water use than the existent production plan.

Keywords: sustainable optimization, multicriteria analysis, agricultural production, farm planning

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Authors: Maxwell Henderson, Tristan Cook, Justin Chan Jin Le, Mark Hodson, YoungJung Chang, John Novak, Daniel Padilha, Nishan Kulatilaka, Ansu Bagchi, Sanjoy Ray, John Kelly

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We present a method of using adiabatic quantum optimization (AQO) to solve a mixed integer nonlinear programming (MINLP) problem instance. The MINLP problem is a general form of a set of NP-hard optimization problems that are critical to many business applications. It requires optimizing a set of discrete and continuous variables with nonlinear and potentially nonconvex constraints. Obtaining an exact, optimal solution for MINLP problem instances of non-trivial size using classical computation methods is currently intractable. Current leading algorithms leverage heuristic and divide-and-conquer methods to determine approximate solutions. Creating more accurate and efficient algorithms is an active area of research. Quantum computing (QC) has several theoretical benefits compared to classical computing, through which QC algorithms could obtain MINLP solutions that are superior to current algorithms. AQO is a particular form of QC that could offer more near-term benefits compared to other forms of QC, as hardware development is in a more mature state and devices are currently commercially available from D-Wave Systems Inc. It is also designed for optimization problems: it uses an effect called quantum tunneling to explore all lowest points of an energy landscape where classical approaches could become stuck in local minima. Our work used a novel algorithm formulated for AQO to solve a special type of MINLP problem. The research focused on determining: 1) if the problem is possible to solve using AQO, 2) if it can be solved by current hardware, 3) what the currently achievable performance is, 4) what the performance will be on projected future hardware, and 5) when AQO is likely to provide a benefit over classical computing methods. Two different methods, integer range and 1-hot encoding, were investigated for transforming the MINLP problem instance constraints into a mathematical structure that can be embedded directly onto the current D-Wave architecture. For testing and validation a D-Wave 2X device was used, as well as QxBranch’s QxLib software library, which includes a QC simulator based on simulated annealing. Our results indicate that it is mathematically possible to formulate the MINLP problem for AQO, but that currently available hardware is unable to solve problems of useful size. Classical general-purpose simulated annealing is currently able to solve larger problem sizes, but does not scale well and such methods would likely be outperformed in the future by improved AQO hardware with higher qubit connectivity and lower temperatures. If larger AQO devices are able to show improvements that trend in this direction, commercially viable solutions to the MINLP for particular applications could be implemented on hardware projected to be available in 5-10 years. Continued investigation into optimal AQO hardware architectures and novel methods for embedding MINLP problem constraints on to those architectures is needed to realize those commercial benefits.

Keywords: adiabatic quantum optimization, mixed integer nonlinear programming, quantum computing, NP-hard

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Authors: Ritu Sharma, Haifeng Shen

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Teaching introductory programming is a challenging task in tertiary education and various factors are believed to have influence on students’ learning of programming. However, these factors were largely studied independently in a chosen context. This paper aims to investigate whether interrelationships exist among the factors and whether the interrelationships are context-dependent. In this empirical study, two universities were chosen from two continents, which represent different cultures, teaching methodologies, assessment criteria and languages used to teach programming in west and east worlds respectively. The results reveal that some interrelationships are common across the two different contexts, while others appear context-dependent.

Keywords: introductory programming, tertiary education, factors, interrelationships, context, empirical study

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Authors: Ayse Ozturk

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The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

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Authors: S. Jayasinghe, R. B. N. Dissanayake

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Optimization modelling together with the Network models and Linear Programming techniques is a powerful tool in problem solving and decision making in real world applications. This study developed a mathematical model to optimize the net profit by minimizing the transportation cost. This model focuses the transportation among decentralized production plants to a centralized distribution centre and then the distribution among island wide agencies considering the customer satisfaction as a requirement. This company produces basically 9 types of food items with 82 different varieties and 4 types of non-food items with 34 different varieties. Among 6 production plants, 4 were located near the city of Mawanella and the other 2 were located in Galewala and Anuradhapura cities which are 80 km and 150 km away from Mawanella respectively. The warehouse located in the Mawanella was the main production plant and also the only distribution plant. This plant distributes manufactured products to 39 agencies island-wide. The average values and average amount of the goods for 6 consecutive months from May 2013 to October 2013 were collected and then average demand values were calculated. The following constraints are used as the necessary requirement to satisfy the optimum condition of the model; there was one source, 39 destinations and supply and demand for all the agencies are equal. Using transport cost for a kilometer, total transport cost was calculated. Then the model was formulated using distance and flow of the distribution. Network optimization and linear programming techniques were used to originate the model while excel solver is used in solving. Results showed that company requires total transport cost of Rs. 146, 943, 034.50 to fulfil the customers’ requirement for a month. This is very much less when compared with data without using the model. Model also proved that company can reduce their transportation cost by 6% when distributing to island-wide customers. Company generally satisfies their customers’ requirements by 85%. This satisfaction can be increased up to 97% by using this model. Therefore this model can be used by other similar companies in order to reduce the transportation cost.

Keywords: mathematical model, network optimization, linear programming

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Authors: Mohammad Pourmohammadi Fallah, Maziar Salahi

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In the literature, a mixed-integer linear programming model for the integrated production planning and warehouse layout problem is proposed. To solve the model, the authors proposed a Lagrangian relax-and-fix heuristic that takes a significant amount of time to stop with gaps above 5$\%$ for large-scale instances. Here, we present two heuristic algorithms to solve the problem. In the first one, we use a greedy approach by allocating warehouse locations with less reservation costs and also less transportation costs from the production area to locations and from locations to the output point to items with higher demands. Then a smaller model is solved. In the second heuristic, first, we sort items in descending order according to the fraction of the sum of the demands for that item in the time horizon plus the maximum demand for that item in the time horizon and the sum of all its demands in the time horizon. Then we categorize the sorted items into groups of 3, 4, or 5 and solve a small-scale optimization problem for each group, hoping to improve the solution of the first heuristic. Our preliminary numerical results show the effectiveness of the proposed heuristics.

Keywords: capacitated lot-sizing, warehouse layout, mixed-integer linear programming, heuristics algorithm

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Authors: Ahmed Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: airport terminal, integer programming, scheduling, simulation

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Authors: Tunjo Perič, Marin Fatović

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In this paper a new methodology for vendor selection and supply quotas determination (VSSQD) is proposed. The problem of VSSQD is solved by the model that combines revised weighting method for determining the objective function coefficients, and a multiple objective linear programming (MOLP) method based on the cooperative game theory for VSSQD. The criteria used for VSSQD are: (1) purchase costs and (2) product quality supplied by individual vendors. The proposed methodology is tested on the example of flour purchase for a bakery with two decision makers.

Keywords: cooperative game theory, multiple objective linear programming, revised weighting method, vendor selection

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Authors: Dao Phuong Nam, Do Trong Tan, Pham Tam Thanh, Le Duy Tung, Tran Hoang Anh

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This paper considers the problem of cascade control system for unmanned aerial vehicles (UAVs). Due to the complicated modelling technique of UAV, it is necessary to separate them into two subsystems. The proposed cascade control structure is a hierarchical scheme including a robust control for inner subsystem based on H infinity theory and trajectory generator using genetic algorithm (GA), outer loop control law based on multi-parametric programming (MPP) technique to overcome the disadvantage of a big amount of calculations. Simulation results are presented to show that the equivalent path has been found and obtained by proposed cascade control scheme.

Keywords: genetic algorithm, GA, H infinity, multi-parametric programming, MPP, unmanned aerial vehicles, UAVs

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Sanaa Rashed Abdallah, Yasser F. Hassan

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The paper will introduce an approach where a rough sets, gene expression programming and rough neural networks are used cooperatively for learning and classification support. The Objective of gene expression programming rough neural networks (GEP-RNN) approach is to obtain new classified data with minimum error in training and testing process. Starting point of gene expression programming rough neural networks (GEP-RNN) approach is an information system and the output from this approach is a structure of rough neural networks which is including the weights and thresholds with minimum classification error.

Keywords: rough sets, gene expression programming, rough neural networks, classification

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