Search results for: mathematical programming problem

Authors: Shyam Sajan, Kamal Bijlani

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The widespread effects of digital media help people to explore the world more and get entertained with no effort. People became fond of these kind of sedentary life style. The increase in sedentary time and a decrease in physical activities has negative impacts on human health. Even though the addiction to video games has been exploited in exergames, to make people exercise and enjoy game challenges, the contribution is restricted only to physical wellness. This paper proposes creation and implementation of a game with the help of digital media in a virtual environment. The game is designed by collaborating ideas from neural linguistic programming and Stroop effect that can also be used to identify a person’s mental state, to improve concentration and to eliminate various phobias. The multiplayer game is played in a virtual environment created with Kinect sensor, to make the game more motivating and interactive.

Keywords: exergaming, Kinect Sensor, Neural Linguistic Programming, Stroop Effect

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Authors: Siti Indati Mustapa, Hussain Ali Bekhet

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Transportation sector represents more than 40% of total energy consumption in Malaysia. This sector is a major user of fossils based fuels, and it is increasingly being highlighted as the sector which contributes least to CO2 emission reduction targets. Considering this fact, this paper attempts to investigate the problem of reducing CO2 emission using linear programming approach. An optimization model which is used to investigate the optimal level of CO2 emission reduction in the road transport sector is presented. In this paper, scenarios have been used to demonstrate the emission reduction model: (1) utilising alternative fuel scenario, (2) improving fuel efficiency scenario, (3) removing fuel subsidy scenario, (4) reducing demand travel, (5) optimal scenario. This study finds that fuel balancing can contribute to the reduction of the amount of CO2 emission by up to 3%. Beyond 3% emission reductions, more stringent measures that include fuel switching, fuel efficiency improvement, demand travel reduction and combination of mitigation measures have to be employed. The model revealed that the CO2 emission reduction in the road transportation can be reduced by 38.3% in the optimal scenario.

Keywords: CO2 emission, fuel consumption, optimization, linear programming, transportation sector, Malaysia

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Authors: Yu-Jen Chang, Yun Chen, Hei-Lam Wong

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The Economic Lot Scheduling Problem (ELSP) is a valuable mathematical model that can support decision-makers to make scheduling decisions. The basic period approach is effective for solving the ELSP. The assumption for applying the basic period approach is that a product must use its maximum production rate to be produced. However, a product can lower its production rate to reduce the average total cost when a facility has extra idle time. The past researches discussed how a product adjusts its production rate under the common cycle approach. To the best of our knowledge, no studies have addressed how a product lowers its production rate under the basic period approach. This research is the first paper to discuss this topic. The research develops a simple fixed rate approach that adjusts the production rate of a product under the basic period approach to solve the ELSP. Our numerical example shows our approach can find a better solution than the traditional basic period approach. Our mathematical model that applies the fixed rate approach under the basic period approach can serve as a reference for other related researches.

Keywords: economic lot, basic period, genetic algorithm, fixed rate

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Ben Mansour Mouin, Elloumi Abdelkarim

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We will discuss the problem of routing a fleet of different vehicles from a central depot to different types of infrastructure-defaults with dynamic maintenance requests, modified time windows, and control of default maintained. For this reason, we propose a modified metaheuristicto to solve our mathematical model. SVRDP-CMTW is a variant VRP of an optimal vehicle plan that facilitates the maintenance task of different types of infrastructure-defaults. This task will be monitored after the maintenance, based on its priorities, the degree of danger associated with each default, and the neighborhood at the black-spots. We will present, in this paper, a multidimensional genetic algorithm “MGA” by detailing its characteristics, proposed mechanisms, and roles in our work. The coding of this algorithm represents the necessary parameters that characterize each infrastructure-default with the objective of minimizing a combination of cost, distance and maintenance times while satisfying the priority levels of the most urgent defaults. The developed algorithm will allow the dynamic integration of newly detected defaults at the execution time. This result will be displayed in our programmed interactive system at the routing time. This multidimensional genetic algorithm replaces N genetic algorithm to solve P different type problems of infrastructure defaults (instead of N algorithm for P problem we can solve in one multidimensional algorithm simultaneously who can solve all these problemsatonce).

Keywords: mathematical model, VRP, multidimensional genetic algorithm, metaheuristics

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Authors: Darsh N. Patel, Eric Olson

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Fractals can be found everywhere, whether it be the shape of a leaf or a system of blood vessels. Fractals are used to help study and understand different physical and mathematical processes; however, their artistic nature is also beautiful to simply explore. This project explores fractals generated by a cubically convergent extension to Newton's method. With this iteration as a starting point, a complex plane spanning from -2 to 2 is created with a color wheel mapped onto it. Next, the polynomial whose roots the fractal will generate from is established. From the Fundamental Theorem of Algebra, it is known that any polynomial has as many roots (counted by multiplicity) as its degree. When generating the fractals, each root will receive its own color. The complex plane can then be colored to indicate the basins of attraction that converge to each root. From a computational point of view, this project’s code identifies which points converge to which roots and then obtains fractal images. A zoom path into the fractal was implemented to easily visualize the self-similar structure. This path was obtained by selecting keyframes at different magnifications through which a path is then interpolated. Using parallel processing, many images were generated and condensed into a video. This project illustrates how practical techniques used for scientific visualization can also have an artistic side.

Keywords: fractals, cubic method, Julia programming language, basin of attraction

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Authors: V. Pourmostaghimi, M. Zadshakoyan

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Efficiency and productivity of the finish hard turning can be enhanced impressively by utilizing accurate predictive models for cutting tool wear. However, the ability of genetic programming in presenting an accurate analytical model is a notable characteristic which makes it more applicable than other predictive modeling methods. In this paper, the genetic equation for modeling of tool flank wear is developed with the use of the experimentally measured flank wear values and genetic programming during finish turning of hardened AISI D2. Series of tests were conducted over a range of cutting parameters and the values of tool flank wear were measured. On the basis of obtained results, genetic model presenting connection between cutting parameters and tool flank wear were extracted. The accuracy of the genetically obtained model was assessed by using two statistical measures, which were root mean square error (RMSE) and coefficient of determination (R²). Evaluation results revealed that presented genetic model predicted flank wear over the study area accurately (R² = 0.9902 and RMSE = 0.0102). These results allow concluding that the proposed genetic equation corresponds well with experimental data and can be implemented in real industrial applications.

Keywords: cutting parameters, flank wear, genetic programming, hard turning

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Authors: Terence Soule, Tami Al Ghamdi

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To study how the partial knowledge transfer may affect the Genetic Algorithm (GA) performance, we model the Transfer Learning (TL) process using GA as the model solver. The objective of the TL is to transfer the knowledge from one problem to another related problem. This process imitates how humans think in their daily life. In this paper, we proposed to study a case where the knowledge transferred from the S problem has less information than what the T problem needs. We sampled the transferred population using different strategies of TL. The results showed transfer part of the knowledge is helpful and speeds the GA process of finding a solution to the problem.

Keywords: transfer learning, partial transfer, evolutionary computation, genetic algorithm

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Authors: Amirhossein Chambari

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This article proposes a bi-objective model for the facility location problem subject to congestion (overcrowding). Motivated by implementations to locate servers in internet mirror sites, communication networks, one-server-systems, so on. This model consider for situations in which immobile (or fixed) service facilities are congested (or queued) by stochastic demand to behave as M/M/1/K queues. We consider for this problem two simultaneous perspectives; (1) Customers (desire to limit times of accessing and waiting for service) and (2) Service provider (desire to limit average facility idle-time). A bi-objective model is setup for facility location problem with two objective functions; (1) Minimizing sum of expected total traveling and waiting time (customers) and (2) Minimizing the average facility idle-time percentage (service provider). The proposed model belongs to the class of mixed-integer nonlinear programming models and the class of NP-hard problems. In addition, to solve the model, controlled elitist non-dominated sorting genetic algorithms (Controlled NSGA-II) and controlled elitist non-dominated ranking genetic algorithms (NRGA-I) are proposed. Furthermore, the two proposed metaheuristics algorithms are evaluated by establishing standard multiobjective metrics. Finally, the results are analyzed and some conclusions are given.

Keywords: bi-objective, facility location, queueing, controlled NSGA-II, NRGA-I

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Authors: A. Yacob, N. Hj. Ali, M. H. Yusoff, M. Y. MohdSaman, W. M. A. F. W. Hamzah

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Personalized learning becomes increasingly popular which not is restricted by time, place or any other barriers. This study proposes an analysis of Personalized Learning using Item Response Theory which considers course material difficulty and learner ability. The study investigates twenty undergraduate students at TATI University College, who are taking programming subject. By using the IRT, it was found that, finding the most appropriate problem levels to each student include high and low level test items together is not a problem. Thus, the student abilities can be asses more accurately and fairly. Learners who experience more anxiety will affect a heavier cognitive load and receive lower test scores. Instructors are encouraged to provide a supportive learning environment to enhance learning effectiveness because Cognitive Load Theory concerns the limited capacity of the brain to absorb new information.

Keywords: assessment, item response theory, cognitive load theory, learning, motivation, performance

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Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

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In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modeling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: plate heat exchanger, optimization, modeling, simulation

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Mohsen S. Sajadieha, Danyar Molavia

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In this paper, a truck scheduling problem is investigated at a two-touch cross-docking center with due dates for outbound trucks as a hard constraint. The objective is to minimize the total cost comprising penalty and delivery cost of delayed shipments. The sequence of unloading shipments is considered and is assumed that shipments are sent to shipping dock doors immediately after unloading and a First-In-First-Out (FIFO) policy is considered for loading the shipments. A mixed integer programming model is developed for the proposed model. Two meta-heuristic algorithms including genetic algorithm (GA) and variable neighborhood search (VNS) are developed to solve the problem in medium and large sized scales. The numerical results show that increase in due dates for outbound trucks has a crucial impact on the reduction of penalty costs of delayed shipments. In addition, by increase the due dates, the improvement in the objective function arises on average in comparison with the situation that the cross-dock is multi-touch and shipments are sent to shipping dock doors only after unloading the whole inbound truck.

Keywords: cross-docking, truck scheduling, fixed due date, door assignment

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Authors: Ivan Stanev, Maria Koleva

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Described are challenges to the Bulgarian e-Customs (BeC) related to low level of interoperability and standardization, inefficient use of available infrastructure, lack of centralized identification and authorization, extremely low level of software process automation, and insufficient quality of data stored in official registers. The technical requirements for BeC are prepared with a focus on domain independent common platform, specialized customs and excise components, high scalability, flexibility, and reusability. The Knowledge Based Automated Software Engineering (KBASE) Common Platform for Automated Programming (CPAP) is selected as an instrument covering BeC requirements for standardization, programming automation, knowledge interpretation and cloud computing. BeC stage 3 results are presented and analyzed. BeC.S3 development trends are identified.

Keywords: service oriented architecture, cloud computing, knowledge based automated software engineering, common platform for automated programming, e-customs

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Authors: Morteza Khorrami

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The logic as an intellectual infrastructure plays an essential role in the Islamic sciences. Hence, there are a few of the verses of the Holy Quran that their interpretation is not possible due to lack of proper logic. In many verses in the Quran, argument and the respondent has requested from the audience that shows the logic rule is in the Quran. The paper which use a descriptive and analytic method, tries to show the role of logic in understanding of the Quran reasoning methods and display some of Quranic statements with mathematical symbols and point that we can help these symbols for interesting and interpretation and answering to some questions and doubts. In this paper, this problem has been mentioned that the Quran did not use two-valued logic (Aristotelian) in all cases, but the fuzzy logic can also be searched in the Quran.

Keywords: aristotelian logic, fuzzy logic, interpretation, Holy Quran

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Authors: Ismail Karaca, Ridvan Saracoglu, Omer Soner

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Fuzzy Logic, an advanced method to support decision-making, is used by various scientists in many disciplines. Fuzzy programming is a product of fuzzy logic, fuzzy rules, and implication. In marine science, fuzzy programming for ships is dramatically increasing together with autonomous ship studies. In this paper, a program to support the decision-making process for ship navigation has been designed. The program is produced in fuzzy logic and rules, by taking the marine accidents and expert opinions into account. After the program was designed, the program was tested by 46 ship accidents reported by the Transportation Safety Investigation Center of Turkey. Wind speed, sea condition, visibility, day/night ratio have been used as input data. They have been converted into a risk factor within the Fuzzy Logic Designer application and fuzzy rules set by marine experts. Finally, the expert's meteorological risk factor for each accident is compared with the program's risk factor, and the error rate was calculated. The main objective of this study is to improve the navigational safety of ships, by using the advance decision support model. According to the study result, fuzzy programming is a robust model that supports safe navigation.

Keywords: calculation of risk factor, fuzzy logic, fuzzy programming for ship, safety navigation of ships

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Authors: Amjad Nusayr

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Software security is a general term used to any type of software architecture or model in which security aspects are incorporated in this architecture. These aspects are not part of the main logic of the underlying program. Software security can be achieved using a combination of approaches, including but not limited to secure software designs, third part component validation, and secure coding practices. Memory safety is one feature in software security where we ensure that any object in memory has a valid pointer or a reference with a valid type. Aspect-Oriented Programming (AOP) is a paradigm that is concerned with capturing the cross-cutting concerns in code development. AOP is generally used for common cross-cutting concerns like logging and DB transaction managing. In this paper, we introduce the concepts that enable AOP to be used for the purpose of memory and type safety. We also present ideas for extending AOP in software security practices.

Keywords: aspect oriented programming, programming languages, software security, memory and type safety

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Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

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Assigning aircrafts’ activities to appropriate gates is one the most challenging issues in airport authorities’ multiple criteria decision making. The potential financial loss due to imbalances of demand and supply in congested airports, higher occupation rates of gates, and the existing restrictions to expand facilities provide further evidence for the need for an optimal supply allocation. Passengers walking distance, towing movements, extra fuel consumption (as a result of awaiting longer to taxi when taxi conflicts happen at the apron area), etc. are the major traditional components involved in GAP models. In particular, the total cost associated with gate assignment problem highly depends on the airport terminal layout. The study herein presents a well-elaborated literature review on the topic focusing on major concerns, applicable variables and objectives, as well as proposing a three-objective mathematical model for the gate assignment problem. The model has been tested under different concourse layouts in order to check its performance in different scenarios. Results revealed that terminal layout pattern is a significant parameter in airport and that the proposed model is capable of dealing with key constraints and objectives, which supports its practical usability for future decision making tools. Potential solution techniques were also suggested in this study for future works.

Keywords: airport management, terminal layout, gate assignment problem, mathematical modeling

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Mariyam Arif, Ye Liu, Israr Ul Haq, Ahsan Ashfaq

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High cost of fossil fuels and intensifying installations of alternate energy generation sources are intimidating main challenges in power systems. Making accurate load forecasting an important and challenging task for optimal energy planning and management at both distribution and generation side. There are many techniques to forecast load but each technique comes with its own limitation and requires data to accurately predict the forecast load. Artificial Neural Network (ANN) is one such technique to efficiently forecast the load. Comparison between two different ranges of input datasets has been applied to dynamic ANN technique using MATLAB Neural Network Toolbox. It has been observed that selection of input data on training of a network has significant effects on forecasted results. Day-wise input data forecasted the load accurately as compared to year-wise input data. The forecasted load is then distributed among the six generators by using the linear programming to get the optimal point of generation. The algorithm is then verified by comparing the results of each generator with their respective generation limits.

Keywords: artificial neural networks, demand-side management, economic dispatch, linear programming, power generation dispatch

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Authors: Paffrath Meinhard, Zhou Yayun, Guo Yiqing, Ertl Harald

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Winding geometry design is an important part of power transformer electrical design. Conventionally, the winding geometry is designed manually, which is a time-consuming job because it involves many iteration steps in order to meet all cost, manufacturing and electrical requirements. Here a method is presented which automatically generates the winding geometry for given user parameters and allows the user to interactively set and change parameters. To achieve this goal, the winding problem is transferred to a mixed integer nonlinear optimization problem. The relevant geometrical design parameters are defined as optimization variables. The cost and other requirements are modeled as constraints. For the solution, a stochastic ant colony optimization algorithm is applied. It is well-known, that an optimizer can get stuck in a local minimum. For the winding problem, we present efficient strategies to come out of local minima, furthermore a reduced variable search range helps to accelerate the solution process. Numerical examples show that the optimization result is delivered within seconds such that the user can interactively change the variable search area and constraints to improve the design.

Keywords: ant colony optimization, mixed integer nonlinear programming, power transformer, winding design

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Authors: Maria M. Giannakou, Athanasios K. Ziliaskopoulos

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Transmission pipelines carrying natural gas are often routed through populated cities, industrial and environmentally sensitive areas. While the need for these networks is unquestionable, there are serious concerns about the risk these lifeline networks pose to the people, to their habitat and to the critical infrastructures, especially in view of natural disasters such as earthquakes. This work presents an Integrated Pipeline Risk Management methodology (IPRM) for assessing the hazard associated with a natural gas pipeline failure due to natural or manmade disasters. IPRM aims to optimize the allocation of the available resources to countermeasures in order to minimize the impacts of pipeline failure to humans, the environment, the infrastructure and the economic activity. A proposed knapsack mathematical programming formulation is introduced that optimally selects the proper mitigation policies based on the estimated cost – benefit ratios. The proposed model is demonstrated with a small numerical example. The vulnerability analysis of these pipelines and the quantification of consequences from such failures can be useful for natural gas industries on deciding which mitigation measures to implement on the existing pipeline networks with the minimum cost in an acceptable level of hazard.

Keywords: cost benefit analysis, knapsack problem, natural gas distribution network, risk management, risk mitigation

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Authors: Nima Khosravi

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This paper describes an integrated optimization technique with concurrent use of sequential quadratic programming, genetic algorithm, and simulated annealing particle swarm optimization for the design and optimization of a beam column. In this research, the comparison between 4 different types of optimization methods. The comparison is done and it is found out that all the methods meet the required constraints and the lowest value of the objective function is achieved by SQP, which was also the fastest optimizer to produce the results. SQP is a gradient based optimizer hence its results are usually the same after every run. The only thing which affects the results is the initial conditions given. The initial conditions given in the various test run were very large as compared. Hence, the value converged at a different point. Rest of the methods is a heuristic method which provides different values for different runs even if every parameter is kept constant.

Keywords: beam column, genetic algorithm, particle swarm optimization, sequential quadratic programming, simulated annealing

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, José J. Hernández-Flores, Edith Olaco Garcia

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The Project Scheduling Problem (PSP) is a generic name given to a whole class of problems in which the best form, time, resources and costs for project scheduling are necessary. The PSP is an application area related to the project management. This paper aims at being a guide to understand PSP by presenting a survey of the general parameters of PSP: the Resources (those elements that realize the activities of a project), and the Activities (set of operations or own tasks of a person or organization); the mathematical models of the main variants of PSP and the algorithms used to solve the variants of the PSP. The project scheduling is an important task in project management. This paper contains mathematical models, resources, activities, and algorithms of project scheduling problems. The project scheduling problem has attracted researchers of the automotive industry, steel manufacturer, medical research, pharmaceutical research, telecommunication, industry, aviation industry, development of the software, manufacturing management, innovation and technology management, construction industry, government project management, financial services, machine scheduling, transportation management, and others. The project managers need to finish a project with the minimum cost and the maximum quality.

Keywords: PSP, Combinatorial Optimization Problems, Project Management; Manufacturing Management, Technology Management.

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Darwin Castillo Huamaní, Francisco A. M. Gomes

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The aim of the multi-material topology optimization (MTO) is to obtain the optimal topology of structures composed by many materials, according to a given set of constraints and cost criteria. In this work, we seek the optimal distribution of materials in a domain, such that the flexibility of the structure is minimized, under certain boundary conditions and the intervention of external forces. In the case we have only one material, each point of the discretized domain is represented by two values from a function, where the value of the function is 1 if the element belongs to the structure or 0 if the element is empty. A common way to avoid the high computational cost of solving integer variable optimization problems is to adopt the Solid Isotropic Material with Penalization (SIMP) method. This method relies on the continuous interpolation function, power function, where the base variable represents a pseudo density at each point of domain. For proper exponent values, the SIMP method reduces intermediate densities, since values other than 0 or 1 usually does not have a physical meaning for the problem. Several extension of the SIMP method were proposed for the multi-material case. The one that we explore here is the ordered SIMP method, that has the advantage of not being based on the addition of variables to represent material selection, so the computational cost is independent of the number of materials considered. Although the number of variables is not increased by this algorithm, the optimization subproblems that are generated at each iteration cannot be solved by methods that rely on second derivatives, due to the cost of calculating the second derivatives. To overcome this, we apply a globally convergent version of the sequential linear programming method, which solves a linear approximation sequence of optimization problems.

Keywords: globally convergence, multi-material design ordered simp, sequential linear programming, topology optimization

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Authors: Ashwini Umale

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Trajectory planning and optimization is a fundamental problem in articulated robotics. It is often viewed as a two phase problem of initial feasible path planning around obstacles and subsequent optimization of a trajectory satisfying dynamical constraints. An optimized trajectory of multi-axis robot is important and directly influences the Performance of the executing task. Optimal is defined to be the minimum time to transition from the current speed to the set speed. In optimization of trajectory through virtual environment explores the most suitable way to represent robot motion from virtual environment to real environment. This paper aims to review the research of trajectory optimization in virtual environment using simulation software Robcad. Improvements are to be expected in trajectory optimization to generate smooth and collision free trajectories with minimization of overall robot cycle time.

Keywords: trajectory optimization, forward kinematics and reverse kinematics, dynamic constraints, robcad simulation software

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Authors: Miroslav Popelka, Jakub Nožička

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In this paper we deal with using Lego Mindstorms in simulation of robotic systems with respect to cost reduction. Lego Mindstorms kit contains broad variety of hardware components which are required to simulate, program and test the robotics systems in practice. Algorithm programming went in development environment supplied together with Lego kit as in programming language C# as well. Algorithm following the line, which we dealt with in this paper, uses theoretical findings from area of controlling circuits. PID controller has been chosen as controlling circuit whose individual components were experimentally adjusted for optimal motion of robot tracking the line. Data which are determined to process by algorithm are collected by sensors which scan the interface between black and white surfaces followed by robot. Based on discovered facts Lego Mindstorms can be considered for low-cost and capable kit to simulate real robotics systems.

Keywords: LEGO Mindstorms, PID controller, low-cost robotics systems, line follower, sensors, programming language C#, EV3 Home Edition Software

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Authors: Kawser Ahmed, K. Bousson, Milca F. Coelho

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4D flight trajectory optimization is one of the key ingredients to improve flight efficiency and to enhance the air traffic capacity in the current air traffic management (ATM). The present paper explores the iterative dynamic programming (IDP) as a potential numerical optimization method for 4D flight trajectory optimization. IDP is an iterative version of the Dynamic programming (DP) method. Due to the numerical framework, DP is very suitable to deal with nonlinear discrete dynamic systems. The 4D waypoint representation of the flight trajectory is similar to the discretization by a grid system; thus DP is a natural method to deal with the 4D flight trajectory optimization. However, the computational time and space complexity demanded by the DP is enormous due to the immense number of grid points required to find the optimum, which prevents the use of the DP in many practical high dimension problems. On the other hand, the IDP has shown potentials to deal successfully with high dimension optimal control problems even with a few numbers of grid points at each stage, which reduces the computational effort over the traditional DP approach. Although the IDP has been applied successfully in chemical engineering problems, IDP is yet to be validated in 4D flight trajectory optimization problems. In this paper, the IDP has been successfully used to generate minimum length 4D optimal trajectory avoiding any obstacle in its path, such as a no-fly zone or residential areas when flying in low altitude to reduce noise pollution.

Keywords: 4D waypoint navigation, iterative dynamic programming, obstacle avoidance, trajectory optimization

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Authors: Dao Phuong Nam, Tran Van Tuyen, Do Trong Tan, Bui Minh Dinh, Nguyen Van Huong

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In this paper, we investigate the adaptive optimal control law for continuous-time systems with input disturbances and unknown parameters. This paper extends previous works to obtain the robust control law of uncertain systems. Through theoretical analysis, an adaptive dynamic programming (ADP) based optimal control is proposed to stabilize the closed-loop system and ensure the convergence properties of proposed iterative algorithm. Moreover, the global asymptotic stability (GAS) for closed system is also analyzed. The theoretical analysis for continuous-time systems and simulation results demonstrate the performance of the proposed algorithm for an inverted pendulum system.

Keywords: approximate/adaptive dynamic programming, ADP, adaptive optimal control law, input state stability, ISS, inverted pendulum

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