Search results for: convex feasibility problem

Authors: Felix Damilola Ajibade, Opeyemi O. Enoch, Taiwo Paul Fajusigbe

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This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results.

Keywords: stability, F* -iterative algorithm, pseudo-contractive mappings, uniformly convex Banach space, mixed-type Volterra-Fredholm integral equation

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Authors: Michael Dreyfuss, Yahel Giat

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Limited battery range and long recharging times are the greatest obstacles to the successful adoption of electric cars. One of the suggestions to overcome these problems is that carmakers retain ownership of batteries and provide battery swapping service so that customers exchange their depleted batteries for recharged batteries. Motivated by this example, we consider the problem of optimal spares allocation in an exchangeable-item, multi-location repair system. We generalize the standard service measures of fill rate and average waiting time to reflect the fact that customers penalize the service provider only if they have to wait more than a ‘tolerable’ time window. These measures are denoted as the window fill rate and the truncated waiting time, respectively. We find that the truncated waiting time is convex and therefore a greedy algorithm solves the spares allocation problem efficiently. We show that the window fill rate is generally S-shaped and describe an efficient algorithm to find a near-optimal solution and detail a priori and a posteriori upper bounds to the distance from optimum. The theory is complemented with a large scale numerical example demonstrating the spare battery allocation in battery swapping stations.

Keywords: convex-concave optimization, exchangeable item, M/G/infinity, multiple location, repair system, spares allocation, window fill rate

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Authors: Ali Shareef, Aliha Shareef, Yifeng Zhu

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Energy minimization is of great importance in wireless sensor networks in extending the battery lifetime. One of the key activities of nodes in a WSN is communication and the routing of their data to a centralized base-station or sink. Routing using the shortest path to the sink is not the best solution since it will cause nodes along this path to fail prematurely. We propose a cross-layer energy efficient routing protocol Optrix that utilizes a convex formulation to maximize the lifetime of the network as a whole. We further propose, Optrix-BW, a novel convex formulation with bandwidth constraint that allows the channel conditions to be accounted for in routing. By considering this key channel parameter we demonstrate that Optrix-BW is capable of congestion control. Optrix is implemented in TinyOS, and we demonstrate that a relatively large topology of 40 nodes can converge to within 91% of the optimal routing solution. We describe the pitfalls and issues related with utilizing a continuous form technique such as convex optimization with discrete packet based communication systems as found in WSNs. We propose a routing controller mechanism that allows for this transformation. We compare Optrix against the Collection Tree Protocol (CTP) and we found that Optrix performs better in terms of convergence to an optimal routing solution, for load balancing and network lifetime maximization than CTP.

Keywords: wireless sensor network, Energy Efficient Routing

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Authors: Sima Hassankhali, Ildar Sadeqi

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In the theory of Pareto efficient points, the existence of a bounded base for a cone K of a normed space X is so important. In this article, we study the geometric structure of a nonzero closed convex cone K with a bounded base. For this aim, we study the structure of the polar cone K# of K. Furthermore, we obtain a necessary and sufficient condition for a nonempty closed convex set C so that its recession cone C∞ has a bounded base.

Keywords: solid cones, recession cones, polar cones, bounded base

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Authors: Amira M. Attia, Karim H. Youssef, Nabil H. Abbasi

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Demand Side Management (DSM) is an essential characteristic of current and future smart grid systems. As one of DSM functions, load management aims to control customers’ total electric consumption and utility’s load factor by using various load shaping techniques. However, applying load shaping techniques such as load shifting, peak clipping, or strategic conservation individually does not provide the desired level of improvement for load factor increment and/or customer’s bill reduction. In this paper, two load shaping techniques will be simulated as constrained optimization problems. The purpose is to reflect the application of combined load shifting and strategic conservation model together at the same time, and the application of combined load shifting and peak clipping model as well. The problem will be formulated and solved by using disciplined convex programming (CVX) based MATLAB® R2013b. Simulation results will be evaluated and compared for studying the most impactful multi-techniques model in improving load curve.

Keywords: convex programing, demand side management, load shaping, multiple, building energy optimization

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Authors: Rabeeya Raoof, Abrar Ul-Haq, Muhammad Arshad

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The current study is trying to explain the relationship between entrepreneurial education and entrepreneurial passion. This study introduces multiple mechanisms by which entrepreneurial education may induce entrepreneurial passion in business graduates. With the help of expectancy theory, we proposed that entrepreneurial education develops entrepreneurial passion through the mediation of desirability and feasibility. Furthermore, desirability is also influencing feasibility. Therefore, desirability and feasibility may also play their role as double mediators in the relationship between entrepreneurial education and passion. The role of gender has become very vital in entrepreneurship studies. Therefore, we also incorporated the role of gender as a moderator while studying the indirect effect of entrepreneurial education on entrepreneurial passion via desirability and feasibility. We proposed that entrepreneurial education may influence the passion of male individuals primarily through feasibility. On the other hand, entrepreneurial education may impact on the entrepreneurial passion of female individuals primarily through the mediation of desirability. Learning orientation may increase the direct effect of entrepreneurial education on entrepreneurial passion.

Keywords: entrepreneurial passion, perceived desirability, perceived feasibility, entrepreneurial intention

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Authors: Shao-Yuan Huang

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We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

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Authors: Alexander Vaninsky

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The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO2 emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO2 emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO2 emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications.

Keywords: economic restructuring, input-output analysis, divisia index, factorial decomposition, E3 models

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Authors: Hande Yesil, Seda Aycan Altan, M. Vehbi Bal, Alper Uyar, O. Cumhur Sipahi

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Purpose: Fixed partial dentures (FPDs) must fulfill functional requirements such as phonetics, chewing efficiency and esthetics especially in the anterior region. A convex type tissue surface is usually recommended for pontics of FPDs. That pontic design also provides suitable oral hygiene and ease of cleaning. However, high esthetic requirements and correct emergence profile are not always achievable because of the convex shape of adjacent soft tissues. Therefore, the ovate type pontic which fulfills the high esthetic demands of the patients may be a good alternative to the modified ridge lap pontic design. Clinical Report: A female patient referred with the complaint of anterior upper edentulousness. In the oral examination it was determined that teeth 11, 12, 21, 22 were deficient. A thick and convex gingival tissue that may cause aesthetic problems was also observed.. Periodontal augmentation surgery was performed to ensure proper papillary configuration and gingival contour. An interim removable partial denture (IRPD) which applied pressure to operated gingival tissues was fabricated postoperatively. The IRPD was used for 4 weeks and after completion of tissue sculpting, the permanent FPD with an ovate pontic was fabricated and cemented. After a follow-up period of 6 months, not any esthetical and hygienic problem was detected and the patient was satisfied with her prosthesis. Conclusion: It was concluded that shaping of gingival contours with IRPD and use of a FPD with ovate pontic fulfills all esthetic and hygienic requirements.

Keywords: interim appliance, ovate pontic, tissue sculpturing, fixed partial denture

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Authors: Shuwen Hu, Yuancheng Lou, Dongxu Ji

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Photovoltaic (PV) power generation, as one of the most commercialized methods to utilize solar power, can only convert a limited range of solar spectrum into electricity, whereas the majority of the solar energy is dissipated as heat. To address this problem, thermoelectric (TE) module is often integrated with the concentrated PV module for waste heat recovery and regeneration. In this research, a feasibility analysis is conducted for the tandem concentrated photovoltaic-thermoelectric (CPV-TE) hybrid system considering various operational parameters as well as TE material properties. Furthermore, the power output density of the CPV-TE hybrid system is maximized by selecting the optimal TE material with application of a systematic assessment methodology. In the feasibility analysis, CPV-TE is found to be more advantageous than sole CPV system except under high optical concentration ratio with low cold side convective coefficient. It is also shown that the effects of the TE material properties, including Seebeck coefficient, thermal conductivity, and electrical resistivity, on the feasibility of CPV-TE are interacted with each other and might have opposite effect on the system performance under different operational conditions. In addition, the optimal TE material selected by the proposed assessment methodology can improve the system power output density by 227 W/m2 under highly concentrated solar irradiance hence broaden the feasible range of CPV-TE considering optical concentration ratio.

Keywords: feasibility analysis, material assessment methodology, photovoltaic waste heat recovery, tandem photovoltaic-thermoelectric

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Authors: Malte Schilling, Mahmoud M. Rabah, Sven Liebisch

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Wave run-up and overtopping are the relevant parameters for the dimensioning of the crest height of dikes. Various experimental as well as numerical studies have investigated these parameters under different boundary conditions (e.g. wave conditions, structure type). Particularly for the dike design in Europe, a common approach is formulated where wave and structure properties are parameterized. However, this approach assumes equal run-up heights and overtopping discharges along the longitudinal axis. However, convex dikes have a heterogeneous crest by definition. Hence, local differences in a convex dike line are expected to cause wave-structure interactions different to a straight dike. This study aims to assess both run-up and overtopping at convexly curved dikes. To cast light on the relevance of curved dikes for the design approach mentioned above, physical model tests were conducted in a 3D wave basin of the Ludwig-Franzius-Institute Hannover. A dike of a slope of 1:6 (height over length) was tested under both regular waves and TMA wave spectra. Significant wave heights ranged from 7 to 10 cm and peak periods from 1.06 to 1.79 s. Both run-up and overtopping was assessed behind the curved and straight sections of the dike. Both measurements were compared to a dike with a straight line. It was observed that convex curvatures in the longitudinal dike line cause a redirection of incident waves leading to a concentration around the center point. Measurements prove that both run-up heights and overtopping rates are higher than on the straight dike. It can be concluded that deviations from a straight longitudinal dike line have an impact on design parameters and imply uncertainties within the design approach in force. Therefore, it is recommended to consider these influencing factors for such cases.

Keywords: convex dike, longitudinal curvature, overtopping, run-up

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Authors: Kenneth O. Otasowie, Matthew Ikuabe, Clinton Aigbavboa, Ayodeji Oke

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The practice of feasibility studies plays a huge role in the success of construction projects. Feasibility studies according to several research should be the reason for embarking on any project. However, it has been discovered that in South Africa (SA), feasibility studies are mainly done in the private sector construction but skipped in the construction of most public projects. Hence, this study aims to evaluate the barriers to feasibility studies practice in public projects and the implications. A survey design was adopted. A total number of One hundred and fifty (150) questionnaires were administered to Quantity Surveyors, Construction managers, Construction project managers, Project managers, Architects and Civil and Structural engineers in Guateng Province, SA and ninety (90) were returned and found suitable for analysis. Collected data was analysed using percentage, mean item score, standard deviation, one-sample t-test. The findings show that political interference and corruption are the most significant barriers to feasibility studies practice in the public construction projects in SA, while late project completion, poor quality infrastructure are among the implication of not conducting feasibility studies in SA public projects. Therefore, the study recommends the development of a framework for public projects execution that will reduce the interference of the political class in the country, that way the risk of late project completion and poor quality infrastructure will be mitigated.

Keywords: arriers, feasibility studies, public construction, South Africa.

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Authors: Christo Februanto Putra

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This paper presents risk identification that affects investment feasibility on toll road infrastructure in Indonesia using qualitative methods survey based on the expert practitioner in investor, contractor, and state officials. The problems on infrastructure investment in Indonesia, especially on KPBU model contract, is many risk factors in the investment plan is not calculated in detail thoroughly. Risk factor is a value used to provide an overview of the risk level assessment of an event which is a function of the probability of the occurrence and the consequences of the risks that arise. As results of the survey which is to show which risk factors impacts directly to the investment feasibility and rank them by their impacts on the investment.

Keywords: risk identification, indonesia toll road, investment feasibility

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Authors: Abraham Castellanos, Christophe Durville, Sophie Echenim

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In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling.

Keywords: financial risk, numerical optimization, portfolio management, solvency capital requirement

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Authors: Maryam Safarirad

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Fast and increasing growth of electronic commerce (e-commerce) in developed countries and its resulting competitive advantages mean that those countries should revise dramatically their trade and commercial strategies and policies. Regarding the importance of food industry in Iran, the current paper studies the feasibility of implementing the e-commerce system in Shiraz’s petrochemical unit. The statistical population of the study includes 29 senior managers and experts of the food industries. In the present Feasibility study of implementing electronic commerce 249 research, senior managers and experts’ opinions on feasibility have been examined and some feedbacks have resulted in from the opinions. The current research concludes that the organization under study does not have favorable state either in software or in hardware. Implementation of the e-commerce system in food industries would reduce the average value of the transaction costs.

Keywords: electronic trading, electronic commerce, electronic exchange of information, feasibility study, information technology, virtual shopping, computer networks, electronic commerce laws, food industry

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Authors: Mardi Falck, André Theron

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Traffic congestion on the Northern side of Table Bay is a major problem. In Gauteng, the implementation of the Gautrain between Pretoria and Johannesburg, solved their traffic congestion. In 2002 two entrepreneurs endeavoured to implement a hovercraft ferry service across the bay from Table View to the Port of Cape Town. However, the EIA process proved that disgruntled residents from the area did not agree with their location for a launch site. 17 years later the traffic problem has not gone away, but instead the congestion has increased. While property prices in the City Bowl of Cape Town are ever increasing, people tend to live more on the outskirts of the CBD and commute to work. This means more vehicles on the road every day and the public transport services cannot keep up with the demand. For this reason, the study area of the previous hovercraft plans is being extended further North. The study’s aim is thus to determine the feasibility of a launch site North of Bloubergstrand to launch and receive a public transport ferry across Table Bay. The feasibility is being established by researching ferry services across the world and on what makes them successful. Different types of ferries and their operational capacities in terms of weather and waves are researched and by establishing the offshore and nearshore wind and wave climate for the area, an appropriate protected launch site is determined. It was concluded that travel time could potentially be halved. A hovercraft proved to be the most feasible ferry type, because it does not require a conventional harbour. Other types of vessels require a protected launch site because of the wave climate. This means large breakwaters that influence the cost substantially. The Melkbos Cultural Centre proved to be the most viable option for the location of the launch site, because it already has buildings and infrastructure. It is recommended that, if a harbour is chosen for the proposed ferry service, it could be used for more services like fishing, eco-tourism and leisure. Further studies are recommended to optimise the feasibility of such a harbour.

Keywords: Cape Town, ferry, public, Table Bay

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Authors: Yang Zhou, Kangfeng Zheng, Wei Ni, Ren Ping Liu

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Software-defined networking (SDN) provides a solution for scalable network framework with decoupled control and data plane. However, this architecture also induces a particular distributed denial-of-service (DDoS) attack that can affect or even overwhelm the SDN network. DDoS attack detection problem has to date been mostly researched as entropy comparison problem. However, this problem lacks the utilization of SDN, and the results are not accurate. In this paper, we propose a DDoS attack detection method, which interprets DDoS detection as a signature matching problem and is formulated as Earth Mover’s Distance (EMD) model. Considering the feasibility and accuracy, we further propose to define the cost function of EMD to be a generalized Kullback-Leibler divergence. Simulation results show that our proposed method can detect DDoS attacks by comparing EMD values with the ones computed in the case without attacks. Moreover, our method can significantly increase the true positive rate of detection.

Keywords: DDoS detection, EMD, relative entropy, SDN

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Authors: Oleg Vlasovets, Fabian Schaipp, Christian L. Mueller

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we conduct a network analysis and predict the sex of 1000 participants based on ”connectome” - pairwise Pearson’s correlation across 436 brain parcels. We solve the non-smooth convex optimization problem, known under the name of Graphical Lasso, where the solution includes a low-rank component. With this solution and machine learning model for a sex prediction, we explain the brain parcels-sex connectivity patterns.

Keywords: network analysis, neuroscience, machine learning, optimization

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Authors: Fernando L. P. Santos, Luiz G. Lyra, Helenice O. Florentino, Daniela R. Cantane

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Dengue is a febrile infectious disease caused by a virus of the family Flaviridae. It is transmitted by the bite of mosquitoes, usually of the genus Aedes aegypti. It occurs in tropical and subtropical areas of the world. This disease has been a major public health problem worldwide, especially in tropical countries such as Brazil, and its incidence has increased in recent years. Dengue is a subject of intense research. Efficient forms of mosquito control must be considered. In this work, the mono-objective optimal control problem was solved for analysing the dengue disease problem. Chemical and biological controls were considered in the mathematical aspect. This model describes the dynamics of mosquitoes in water and winged phases. We applied the genetic algorithms (GA) to obtain optimal strategies for the control of dengue. Numerical simulations have been performed to verify the versatility and the applicability of this algorithm. On the basis of the present results we may recommend the GA to solve optimal control problem with a large region of feasibility.

Keywords: genetic algorithm, dengue, Aedes aegypti, biological control, chemical control

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Authors: Susanta Kumar Gachhayat, S. K. Dash

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Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances.

Keywords: economic load dispatch, ELD, biogeography-based optimization, BBO, ramp rate biogeography-based optimization, RRBBO, valve-point loading, VPL

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Authors: Antonin Jolly, Bertrand Aubry, Corentin Michel, Rebecca Freva

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Wind energy depends on wind strength and varies largely in time. When it is above the demand, it generates a loss while in the opposite case; energy needs are not fully satisfied. To overcome this problem specific to irregular energies, the process of pumped-storage hydroelectricity (PSH) is studied in present paper. A combination of wind turbine and pumped storage system is more predictable and is more compliant to provide electricity supply according to daily demand. PSH system is already used in several countries to accumulate electricity by pumping water during off-peak times into a storage reservoir, and to use it during peak times to produce energy. Present work discusses a feasibility study on size and financial productivity of PSH system actuated with wind turbines specific power.

Keywords: wind turbine, hydroelectricity, energy storage, pumped-storage hydroelectricity

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Authors: A. A. Behroozpoor, M. M. Mazarei

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In this paper, a fuzzy recurrent neural network is proposed for solving the classical quadratic control problem subject to linear equality and bound constraints. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed.

Keywords: REFERENCES [1] Xia, Y, A new neural network for solving linear and quadratic programming problems. IEEE Transactions on Neural Networks, 7(6), 1996, pp.1544–1548. [2] Xia, Y., & Wang, J, A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Transactions on Neural Networks, 16(2), 2005, pp. 379–386. [3] Xia, Y., H, Leung, & J, Wang, A projection neural network and its application to constrained optimization problems. IEEE Transactions Circuits and Systems-I, 49(4), 2002, pp.447–458.B. [4] Q. Liu, Z. Guo, J. Wang, A one-layer recurrent neural network for constrained seudoconvex optimization and its application for dynamic portfolio optimization. Neural Networks, 26, 2012, pp. 99-109.

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Authors: Shunichi Ohmori, Sirawadee Arunyanart, Kazuho Yoshimoto

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We consider a periodic review inventory control problem of minimizing production cost, inventory cost, and lost-sales under demand uncertainty, in which product demands are not specified exactly and it is only known to belong to a given uncertainty set, yet the constraints must hold for possible values of the data from the uncertainty set. We propose a robust optimization formulation for obtaining lowest cost possible and guaranteeing the feasibility with respect to range of order quantity and inventory level under demand uncertainty. Our formulation is based on the adaptive robust counterpart, which suppose order quantity is affine function of past demands. We derive certainty equivalent problem via second-order cone programming, which gives 'not too pessimistic' worst-case.

Keywords: robust optimization, inventory control, supply chain managment, second-order programming

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: Stojan Kravanja, Andrej Ivanič, Tomaž Žula

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This contribution focuses on structural optimization in civil engineering using mixed integer non-linear programming (MINLP). MINLP is characterized as a versatile method that can handle both continuous and discrete optimization variables simultaneously. Continuous variables are used to optimize parameters such as dimensions, stresses, masses, or costs, while discrete variables represent binary decisions to determine the presence or absence of structural elements within a structure while also calculating discrete materials and standard sections. The optimization process is divided into three main steps. First, a mechanical superstructure with a variety of different topology-, material- and dimensional alternatives. Next, a MINLP model is formulated to encapsulate the optimization problem. Finally, an optimal solution is searched in the direction of the defined objective function while respecting the structural constraints. The economic or mass objective function of the material and labor costs of a structure is subjected to the constraints known from structural analysis. These constraints include equations for the calculation of internal forces and deflections, as well as equations for the dimensioning of structural components (in accordance with the Eurocode standards). Given the complex, non-convex and highly non-linear nature of optimization problems in civil engineering, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is applied. This algorithm alternately solves subproblems of non-linear programming (NLP) and main problems of mixed-integer linear programming (MILP), in this way gradually refines the solution space up to the optimal solution. The NLP corresponds to the continuous optimization of parameters (with fixed topology, discrete materials and standard dimensions, all determined in the previous MILP), while the MILP involves a global approximation to the superstructure of alternatives, where a new topology, materials, standard dimensions are determined. The optimization of a convex problem is stopped when the MILP solution becomes better than the best NLP solution. Otherwise, it is terminated when the NLP solution can no longer be improved. While the OA/ER algorithm, like all other algorithms, does not guarantee global optimality due to the presence of non-convex functions, various modifications, including convexity tests, are implemented in OA/ER to mitigate these difficulties. The effectiveness of the proposed MINLP approach is demonstrated by its application to various structural optimization tasks, such as mass optimization of steel buildings, cost optimization of timber halls, composite floor systems, etc. Special optimization models have been developed for the optimization of these structures. The MINLP optimizations, facilitated by the user-friendly software package MIPSYN, provide insights into a mass or cost-optimal solutions, optimal structural topologies, optimal material and standard cross-section choices, confirming MINLP as a valuable method for the optimization of structures in civil engineering.

Keywords: MINLP, mixed-integer non-linear programming, optimization, structures

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Authors: Kourosh Modarresi

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The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry.

Keywords: convex optimization, LASSO, regression, recommender systems, singular value decomposition, low rank approximation

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Authors: Eylem Koç, Hasan Arda Burhan

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Location selection presents a crucial decision problem in today’s business world where strategic decision making processes have critical importance. Thus, location selection has strategic importance for companies in boosting their strength regarding competition, increasing corporate performances and efficiency in addition to lowering production and transportation costs. A right choice in location selection has a direct impact on companies’ commercial success. In this study, a store location selection problem of Carglass Turkey which operates in vehicle glass branch is handled. As this problem includes both tangible and intangible criteria, Analytic Network Process (ANP) was accepted as the main methodology. The model consists of control hierarchy and BOCR subnetworks which include clusters of actors, alternatives and criteria. In accordance with the management’s choices, five different locations were selected. In addition to the literature review, a strict cooperation with the actor group was ensured and maintained while determining the criteria and during whole process. Obtained results were presented to the management as a report and its feasibility was confirmed accordingly.

Keywords: analytic network process (ANP), BOCR, multi-actor decision making, multi-criteria decision making, real-life problem, location selection

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Authors: Bezhan Ghvaberidze

Abstract:

A multiple criteria optimization approach for the solution of the Fuzzy Vehicle Routing Problem (FVRP) is proposed. For the possibility environment the levels of movements between customers are calculated by the constructed simulation interactive algorithm. The first criterion of the bi-criteria optimization problem - minimization of the expectation of total fuzzy travel time on closed routes is constructed for the FVRP. A new, second criterion – maximization of feasibility of movement on the closed routes is constructed by the Choquet finite averaging operator. The FVRP is reduced to the bi-criteria partitioning problem for the so called “promising” routes which were selected from the all admissible closed routes. The convenient selection of the “promising” routes allows us to solve the reduced problem in the real-time computing. For the numerical solution of the bi-criteria partitioning problem the -constraint approach is used. An exact algorithm is implemented based on D. Knuth’s Dancing Links technique and the algorithm DLX. The Main objective was to present the new approach for FVRP, when there are some difficulties while moving on the roads. This approach is called FVRP for extreme conditions (FVRP-EC) on the roads. Also, the aim of this paper was to construct the solving model of the constructed FVRP. Results are illustrated on the numerical example where all Pareto-optimal solutions are found. Also, an approach for more complex model FVRP with time windows was developed. A numerical example is presented in which optimal routes are constructed for extreme conditions on the roads.

Keywords: combinatorial optimization, Fuzzy Vehicle routing problem, multiple objective programming, possibility theory

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Authors: K.Ishii, T. Furuichi, A. Fujiyama, S. Hariya

Abstract:

Rice straw pellets are a promising fuel as a renewable energy source. Financial analysis is needed to make a utilization system using rise straw pellets financially feasible, considering all regional conditions including stakeholders related to the collection and storage, production, transportation and heat utilization. We conducted the financial analysis of feasibility for a heat utilization system using rice straw pellets which has been developed for the first time in Nanporo, Hokkaido, Japan. Especially, we attempted to clarify the effect of factors required for the system to be financial feasibility, such as the heating energy demand and collection and storage method of rice straw. The financial feasibility was found to improve when increasing the heating energy demand and collecting wheat straw in August separately from collection of rice straw in November because the costs of storing rice straw and producing pellets were reduced. However, the system remained financially unfeasible. This study proposed a contractor program funded by a subsidy from Nanporo local government where a contracted company, instead of farmers, collects and transports rice straw in order to ensure the financial feasibility of the system, contributing to job creation in the region.

Keywords: rice straw, pellets, heating energy demand, collection, storage

Procedia PDF Downloads 384