Search results for: generalized assignment problem

Authors: Eki Ruskartina, Vincent F. Yu, Budi Santosa, A. A. N. Perwira Redi

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This paper introduces symbiotic organism search (SOS) for solving capacitated vehicle routing problem (CVRP). SOS is a new approach in metaheuristics fields and never been used to solve discrete problems. A sophisticated decoding method to deal with a discrete problem setting in CVRP is applied using the basic symbiotic organism search (SOS) framework. The performance of the algorithm was evaluated on a set of benchmark instances and compared results with best known solution. The computational results show that the proposed algorithm can produce good solution as a preliminary testing. These results indicated that the proposed SOS can be applied as an alternative to solve the capacitated vehicle routing problem.

Keywords: symbiotic organism search, capacitated vehicle routing problem, metaheuristic

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Authors: Saeideh Salimpour, Sophie-Charlotte Viaux, Ahmed Azab, Mohammed Fazle Baki

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The Facility Layout Problem (FLP) is key to the efficient and cost-effective operation of a system. This paper presents a hybrid heuristic- and mathematical-programming-based approach that divides the problem conceptually into those of clustering and sequencing. First, clusters of vertically aligned facilities are formed, which are later on sequenced horizontally. The developed methodology provides promising results in comparison to its counterparts in the literature by minimizing the inter-distances for facilities which have more interactions amongst each other and aims at placing the facilities with more interactions at the centroid of the shop.

Keywords: clustering-sequencing approach, mathematical modeling, optimization, unequal facility layout problem

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Authors: Xu LiYun, Briand Florent, Fan GuoLiang

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The loop-layout design problem (LLDP) aims at optimizing the sequence of positioning of the machines around the cyclic production line. Traffic congestion is the usual criteria to minimize in this type of problem, i.e. the number of additional cycles spent by each part in the network until the completion of its required routing sequence of machines. This paper aims at applying several improvements mechanisms such as a positioned-based crossover operator for the Genetic Algorithm (GA) called a Two Points Crossover (TPC) and an offspring selection process. The performance of the improved GA is measured using well-known examples from literature and compared to other evolutionary algorithms. Good results show that GA can still be competitive for this type of problem against more recent evolutionary algorithms.

Keywords: crossover, genetic algorithm, layout design problem, loop-layout, manufacturing optimization

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Abhijith Asok

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This paper presents a generalized approach for the simple linear data transformation, Y=bX, through an integration of multidimensional coordinate geometry, vector space theory and polygonal geometry. The scaling is performed by adding an additional ’Dummy Dimension’ to the n-dimensional data, which helps plot two dimensional component-wise straight lines on pairs of dimensions. The end result is a set of scaled extensions of observations in any of the 2n spatial divisions, where n is the total number of applicable dimensions/dataset variables, created by shifting the n-dimensional plane along the ’Dummy Axis’. The derived scaling factor was found to be dependent on the coordinates of the common point of origin for diverging straight lines and the plane of extension, chosen on and perpendicular to the ’Dummy Axis’, respectively. This result indicates the geometrical interpretation of a linear data transformation and hence, opportunities for a more informed choice of the factor ’b’, based on a better choice of these coordinate values. The paper follows on to identify the effect of this transformation on certain popular distance metrics, wherein for many, the distance metric retained the same scaling factor as that of the features.

Keywords: data transformation, dummy dimension, linear transformation, scaling

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Authors: P. Parthiban, Sonu Rajak, R. Dhanalakshmi

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This paper presents an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the Vehicle Routing Problem (VRP) with environmental considerations, which is well known as Pollution-Routing Problem (PRP). It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. Since VRP is NP-hard problem, so PRP also a NP-hard problem, which requires metaheuristics to solve this type of problems. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage, a SOA is run on the resulting VRPTW solution. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm can provide good solutions within reasonable computational time.

Keywords: ant colony optimization, CO2 emissions, speed optimization, vehicle routing

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Authors: Dávid Csercsik, Péter Kádár

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In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: optimization, MATLAB, quadratic programming, economic dispatch

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Authors: Kyugneun Lee, Ikjin Lee

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Parameter estimation with inverse problem often suffers from unfavorable conditions in the real world. Useless data and many input parameters make the problem complicated or insoluble. Data refinement and reformulation of the problem can solve that kind of difficulties. In this research, a method to solve the rank deficient inverse problem is suggested. A multi-physics system which has rank deficiency caused by response correlation is treated. Impeditive information is removed and the problem is reformulated to sequential estimations using Bayesian network (BN) and subset groups. At first, subset grouping of the responses is performed. Feature selection with singular value decomposition (SVD) is used for the grouping. Next, BN inference is used for sequential conditional estimation according to the group hierarchy. Directed acyclic graph (DAG) structure is organized to maximize the estimation ability. Variance ratio of response to noise is used to pairing the estimable parameters by each response.

Keywords: Bayesian network, feature selection, rank deficiency, statistical inverse analysis

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Authors: Akintunde O. Osibamowo, Abdulrasaq O. Olusanya

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The present study was designed to examine the effect of problem-solving approach as a medium of instruction in teaching and learning of mathematics to improve the achievement of the student. One Hundred (100) students were randomly chosen from five (5) Junior Secondary School in Ijebu-Ode Local Government Area of Ogun State, Nigeria. The data was collected through Mathematics Achievement Test (MAT) on the two groups (experimental and control group). The study confirmed that there is a significant different in the achievement of students exposed to problem-solving approach than those not exposed. The result also indicated that male students, however, had a greater mean-score than the female with no significant difference in their achievement. The result of the study supports the use of problem-solving approach in the teaching and learning of mathematics in secondary schools.

Keywords: problem, achievement, teaching phases, experimental control

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

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Authors: Shaleeza Sohail

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Self, and peer evaluations are some of the main components in almost all group assignments and projects in higher education institutes. These evaluations provide students an opportunity to better understand the learning outcomes of the assignment and/or project. A number of online systems have been developed for this purpose that provides automated assessment and feedback of students’ contribution in a group environment based on self and peer evaluations. All these systems lack a progressive aspect of these assessments and feedbacks which is the most crucial factor for ongoing improvement and life-long learning. In addition, a number of assignments and projects are designed in a manner that smaller or initial assessment components lead to a final assignment or project. In such cases, the evaluation and feedback may provide students an insight into their performance as a group member for a particular component after the submission. Ideally, it should also create an opportunity to improve for next assessment component as well. Self and Peer Progressive Assessment and Feedback System encourages students to perform better in the next assessment by providing a comparative analysis of the individual’s contribution score on an ongoing basis. Hence, the student sees the change in their own contribution scores during the complete project based on smaller assessment components. Self-Assessment Factor is calculated as an indicator of how close the self-perception of the student’s own contribution is to the perceived contribution of that student by other members of the group. Peer-Assessment Factor is calculated to compare the perception of one student’s contribution as compared to the average value of the group. Our system also provides a Group Coherence Factor which shows collectively how group members contribute to the final submission. This feedback is provided for students and teachers to visualize the consistency of members’ contribution perceived by its group members. Teachers can use these factors to judge the individual contributions of the group members in the combined tasks and allocate marks/grades accordingly. This factor is shown to students for all groups undertaking same assessment, so the group members can comparatively analyze the efficiency of their group as compared to other groups. Our System provides flexibility to the instructors for generating their own customized criteria for self and peer evaluations based on the requirements of the assignment. Students evaluate their own and other group members’ contributions on the scale from significantly higher to significantly lower. The preliminary testing of the prototype system is done with a set of predefined cases to explicitly show the relation of system feedback factors to the case studies. The results show that such progressive feedback to students can be used to motivate self-improvement and enhanced team skills. The comparative group coherence can promote a better understanding of the group dynamics in order to improve team unity and fair division of team tasks.

Keywords: effective group work, improvement of team skills, progressive feedback, self and peer assessment system

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Authors: Longqing Li

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The paper addresses the inefficiency of the classical model in measuring the Value-at-Risk (VaR) using a normal distribution or a Student’s t distribution. Specifically, the paper focuses on the one day ahead Value-at-Risk (VaR) of major stock market’s daily returns in US, UK, China and Hong Kong in the most recent ten years under 95% confidence level. To improve the predictable power and search for the best performing model, the paper proposes using two leading alternatives, Extreme Value Theory (EVT) and a family of GARCH models, and compares the relative performance. The main contribution could be summarized in two aspects. First, the paper extends the GARCH family model by incorporating EGARCH and TGARCH to shed light on the difference between each in estimating one day ahead Value-at-Risk (VaR). Second, to account for the non-normality in the distribution of financial markets, the paper applies Generalized Error Distribution (GED), instead of the normal distribution, to govern the innovation term. A dynamic back-testing procedure is employed to assess the performance of each model, a family of GARCH and the conditional EVT. The conclusion is that Exponential GARCH yields the best estimate in out-of-sample one day ahead Value-at-Risk (VaR) forecasting. Moreover, the discrepancy of performance between the GARCH and the conditional EVT is indistinguishable.

Keywords: Value-at-Risk, Extreme Value Theory, conditional EVT, backtesting

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Authors: V. S. Klimash, Ye Min Thu

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Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model

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Authors: Muhammad Faraz, Talat Rafique, Jang Min Park

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In this article, rotational flow above a permeable surface with a variable free stream angular velocity is considered. Main interest is to solve the associated heat/mass transport equations under different situations. Firstly, heat transport phenomena occurring in generalized vortex flow are analyzed under two altered heating processes, namely, the (i) prescribed surface temperature and (ii) prescribed heat flux. The vortex motion imposed at infinity is assumed to follow a power-law form 〖(r/r_0)〗^((2n-1)) where r denotes the radial coordinate, r_0 the disk radius, and n is a power-law parameter. Assuming a similar solution, the governing Navier-Stokes equations transform into a set of coupled ODEs which are treated numerically for the aforementioned thermal conditions. Secondly, mass transport phenomena accompanied by activation energy are incorporated into the generalized vortex flow situation. After finding self-similar equations, a numerical solution is furnished by using MATLAB's built-in function bvp4c.

Keywords: bödewadt flow, vortex flow, rotating flows, prescribed heat flux, permeable surface, activation energy

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Authors: Sergey A. Lurie, Yury O. Solyaev, Dmitry B. Volkov-Bogorodsky, Alexander V. Volkov

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The media with voids is considered and the method of the analytical estimation of the effective mechanical properties in the theory of elastic materials with voids is proposed. The variational model of the porous media is discussed, which is based on the model of the media with fields of conserved dislocations. It is shown that this model is fully consistent with the known model of the linear elastic materials with voids. In the present work, the generalized model of the porous media is proposed in which the specific surface properties are associated with the field of defects-pores in the volume of the deformed body. Unlike typical surface elasticity model, the strain energy density of the considered model includes the special part of the surface energy with the quadratic form of the free distortion tensor. In the result, the non-classical boundary conditions take modified form of the balance equations of volume and surface stresses. The analytical approach is proposed in the present work which allows to receive the simple enough engineering estimations for effective characteristics of the media with free dilatation. In particular, the effective flexural modulus and Poisson's ratio are determined for the problem of a beam pure bending. Here, the known voids elasticity solution was expanded on the generalized model with the surface effects. Received results allow us to compare the deformed state of the porous beam with the equivalent classic beam to introduce effective bending rigidity. Obtained analytical expressions for the effective properties depend on the thickness of the beam as a parameter. It is shown that the flexural modulus of the porous beam is decreased with an increasing of its thickness and the effective Poisson's ratio of the porous beams can take negative values for the certain values of the model parameters. On the other hand, the effective shear modulus is constant under variation of all values of the non-classical model parameters. Solutions received for a beam pure bending and the hydrostatic loading of the porous media are compared. It is shown that an analytical estimation for the bulk modulus of the porous material under hydrostatic compression gives an asymptotic value for the effective bulk modulus of the porous beam in the case of beam thickness increasing. Additionally, it is shown that the scale effects appear due to the surface properties of the porous media. Obtained results allow us to offer the procedure of an experimental identification of the non-classical parameters in the theory of the linear elastic materials with voids based on the bending tests for samples with different thickness. Finally, the problem of implementation of the Saint-Venant hypothesis for the transverse stresses in the porous beam are discussed. These stresses are different from zero in the solution of the voids elasticity theory, but satisfy the integral equilibrium equations. In this work, the exact value of the introduced surface parameter was found, which provides the vanishing of the transverse stresses on the free surfaces of a beam.

Keywords: effective properties, scale effects, surface defects, voids elasticity

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Authors: Çağrı Özgün Kibiroğlu, Zeynep Turgut

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This paper considers a hub location problem where the network service area partitioned into predetermined zones (represented by node clusters is given) and potential hub nodes capacity levels are determined a priori as a selection criteria of hub to investigate congestion effect on network. The objective is to design hub network by determining all required hub locations in the node clusters and also allocate non-hub nodes to hubs such that the total cost including transportation cost, opening cost of hubs and penalty cost for exceed of capacity level at hubs is minimized. A mixed integer linear programming model is developed introducing additional constraints to the traditional model of capacitated multiple allocation hub location problem and empirically tested.

Keywords: hub location problem, p-hub median problem, clustering, congestion

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Authors: Geetha Baskaran, Andrzej Barjiela, Rong Qu

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Motivation: Nurse scheduling is a complex combinatorial optimization problem. It is also known as NP-hard. It needs an efficient re-scheduling to minimize some trade-off of the measures of violation by reducing selected constraints to soft constraints with measurements of their violations. Problem Statement: In this paper, we extend our novel approach to solve the nurse scheduling problem by transforming it through Information Granulation. Approach: This approach satisfies the rules of a typical hospital environment based on a standard benchmark problem. Generating good work schedules has a great influence on nurses' working conditions which are strongly related to the level of a quality health care. Domain transformation that combines the strengths of operation research and artificial intelligence was proposed for the solution of the problem. Compared to conventional methods, our approach involves judicious grouping (information granulation) of shifts types’ that transforms the original problem into a smaller solution domain. Later these schedules from the smaller problem domain are converted back into the original problem domain by taking into account the constraints that could not be represented in the smaller domain. An Integer Programming (IP) package is used to solve the transformed scheduling problem by expending the branch and bound algorithm. We have used the GNU Octave for Windows to solve this problem. Results: The scheduling problem has been solved in the proposed formalism resulting in a high quality schedule. Conclusion: Domain transformation represents departure from a conventional one-shift-at-a-time scheduling approach. It offers an advantage of efficient and easily understandable solutions as well as offering deterministic reproducibility of the results. We note, however, that it does not guarantee the global optimum.

Keywords: domain transformation, nurse scheduling, information granulation, artificial intelligence, simulation

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Authors: Sanam Haseen, Abdul Bari

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In this paper a three stage multivariate programming problem with random survey cost and variances as random variables has been formulated as a non-linear stochastic programming problem. The problem has been converted into an equivalent deterministic form using chance constraint programming and modified E-modeling. An empirical study of the problem has been done at the end of the paper using R-simulation.

Keywords: chance constraint programming, modified E-model, stochastic programming, stratified sample surveys, three stage sample surveys

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Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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Authors: Kehinde Peter Oyeduntan, Kayode Oshinubi

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Nigeria is referred as the ‘Giant of Africa’ due to high population, land mass and large economy. However, it still trails far behind many smaller economies in the continent in terms of maritime operations. As we have seen that the maritime industry is the spark plug for national growth, because it houses the most crucial infrastructure that generates wealth for a nation, it is worrisome that a nation with six seaports lag in maritime activities. In this research, we have studied how the Gross Domestic Product (GDP) of the maritime transport influences the Nigerian economy. To do this, we applied Simple Linear Regression (SLR), Support Vector Machine (SVM), Polynomial Regression Model (PRM), Generalized Additive Model (GAM) and Generalized Linear Mixed Model (GLMM) to model the relationship between the nation’s Total GDP (TGDP) and the Maritime Transport GDP (MGDP) using a time series data of 20 years. The result showed that the MGDP is statistically significant to the Nigerian economy. Amongst the statistical tool applied, the PRM of order 4 describes the relationship better when compared to other methods. The recommendations presented in this study will guide policy makers and help improve the economy of Nigeria in terms of its GDP.

Keywords: maritime transport, economy, GDP, regression, port

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Authors: Abdolsalam Ghaderi

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In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: location-routing problem, robust optimization, stochastic programming, variable neighborhood search

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Authors: Liudmila A.Guzikova

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Being federative state Russia includes more than 80 subjects which are widely diverse by climatic conditions, demographic characteristics, cultural traditions, intensity of migration, economic development and investment attraction and other parameters. Now, in the regions of the country all forms of housing problem are present - housing mismatch to sanitary and hygienic standards, overcrowding, forced residence in financially burdensome housing, homelessness, -although the extent of these symptoms varies widely. Heterogeneity of regional conditions in combination with specifics of regional housing situation requires to concentrate the study of housing problem on the regional level. Traditionally housing market and mortgage are considered as the instruments of housing problem solving. The question arises how the housing market and mortgage market contribute to solving the housing problem in the regions of Russia. Though the purchase of dwelling in ownership should not be regarded as a universal method of the housing problem solving, the purchase of dwelling both by own funds or by use of mortgage can reduce the problem and enhance public satisfaction of living conditions. The aim of the study is to identify differences and similarities in the development of regional housing markets and mortgage lending in the regions of Russia and to evaluate their impact on the status of the housing problem. To achieve the aim of the study the methods of correlation and regression analysis are used. The data of federal statistics constitutes the information base of research. The results of the study contribute to better understanding of the interrelations in housing sphere and can be used to work out social and economic development programs in the regions.

Keywords: housing market, housing problem, mortgage, regional economy

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Authors: Taehan Lee

Abstract:

We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: integer programming, multicommodity network design, routing, shortest path

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Authors: Busaba Phurksaphanrat

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This research proposes a pre-emptive fuzzy goal programming model for multi-objective multi-mode resource constrained project scheduling problem. The objectives of the problem are minimization of the total time and the total cost of the project. Objective in a multi-mode resource-constrained project scheduling problem is often a minimization of make-span. However, both time and cost should be considered at the same time with different level of important priorities. Moreover, all elements of cost functions in a project are not included in the conventional cost objective function. Incomplete total project cost causes an error in finding the project scheduling time. In this research, pre-emptive fuzzy goal programming is presented to solve the multi-objective multi-mode resource constrained project scheduling problem. It can find the compromise solution of the problem. Moreover, it is also flexible in adjusting to find a variety of alternative solutions.

Keywords: multi-mode resource constrained project scheduling problem, fuzzy set, goal programming, pre-emptive fuzzy goal programming

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

Abstract:

A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Mourad Hrizi

Abstract:

In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

Abstract:

Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Wuthichai Wongthatsanekorn, Nuntana Matheekrieangkrai

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This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: bee colony optimization, ready mixed concrete problem, ruck scheduling, multiple construction sites

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Authors: Alaka Padhye, S. P. Kane

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The following study considers some variations made to the secretary problem (SP). In a multiple criteria secretary problem (MCSP), the selection of a unit is based on two independent characteristics. The units that appear before an observer are known say N, the best rank of a unit being N. A unit is selected, if it is better with respect to either first or second or both the characteristics. When the number of units is large and due to constraints like time and cost, the observer might want to stop earlier instead of inspecting all the available units. Let the process terminate at r2th unit where r1Keywords: joint distribution, marginal distribution, real ranks, secretary problem, selection criterion, two tailed secretary problem

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Authors: Thorsten Herrmann, Alexander Laukemann, Hansgeorg Binz, Daniel Roth

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For the analysis of already identified and existing problems, the pertinent literature provides a comprehensive collection of approaches as well as methods in order to analyze the problems in detail. But coming up with problems, which are assets worth pursuing further, is often challenging. However, the importance of well-formulated problem ideas and their influence of subsequent creative processes are incontestable and proven. In order to meet the covered challenges, the Institute for Engineering Design and Industrial Design (IKTD) developed the Emoji Method. This paper presents the Emoji Method, which support designers to generate problem ideas in a structured way. Considering research findings from knowledge management and innovation management, research into emojis and emoticons reveal insights by means of identifying and formulating problem ideas within the early design phase. The simple application and the huge supporting potential of the Emoji Method within the early design phase are only few of the many successful results of the conducted evaluation. The Emoji Method encourages designers to identify problem ideas and describe them in a structured way in order to start focused with generating solution ideas for the revealed problem ideas.

Keywords: emojis, problem ideas, innovation management, knowledge management

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