Search results for: symmetric traveling salesman problem

Authors: Tin Lai Win, Nant Christina Kyaw

Abstract:

This paper is taken into consideration the problem of cryptanalysis of stream ciphers. There is some attempts need to improve the existing attacks on stream cipher and to make an attempt to distinguish the portions of cipher text obtained by the encryption of plain text in which some parts of the text are random and the rest are non-random. This paper presents a tutorial introduction to symmetric cryptography. The basic information theoretic and computational properties of classic and modern cryptographic systems are presented, followed by an examination of the application of cryptography to the security of VoIP system in computer networks using LFSR algorithm. The implementation program will be developed Java 2. LFSR algorithm is appropriate for the encryption and decryption of online streaming data, e.g. VoIP (voice chatting over IP). This paper is implemented the encryption module of speech signals to cipher text and decryption module of cipher text to speech signals.

Keywords: Linear Feedback Shift Register.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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Authors: I. Mahdavi, A. Jazayeri, M. Jahromi, R. Jafari, H. Iranmanesh

Abstract:

One of the most important problems in production planning of flexible manufacturing system (FMS) is machine tool selection and operation allocation problem that directly influences the production costs and times .In this paper minimizing machining cost, set-up cost and material handling cost as a multi-objective problem in flexible manufacturing systems environment are considered. We present a 0-1 integer linear programming model for the multiobjective machine tool selection and operation allocation problem and due to the large scale nature of the problem, solving the problem to obtain optimal solution in a reasonable time is infeasible, Paretoant colony optimization (P-ACO) approach for solving the multiobjective problem in reasonable time is developed. Experimental results indicate effectiveness of the proposed algorithm for solving the problem.

Keywords: Flexible manufacturing system, Production planning, Machine tool selection, Operation allocation, Multiobjective optimization, Metaheuristic.

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Authors: Tao Zhang, Nan Yan

Abstract:

In recent years, the Chaoshan area, a special place located in the southeast of Guangdong province in China, actively protects religious heritage and is developing religious tourism, which is attracting many expatriate Chinese who are coming back for travel and to worship. This paper discussed three questions. Firstly, what is the current situation about the different social background of tourists’ motivation, satisfaction and behavioral intention? Secondly, is there a relationship between the motivation, satisfaction and behavioral intention and the different social backgrounds of tourists? Thirdly, what is the relationship between religious tourists’ motivation, satisfaction and behavioral intention? The research methods use a combination of qualitative analysis and quantitative analysis. Qualitative analysis uses the method of observation and interviews. Convenient sampling technique was used for quantitative analysis. The study showed that the different social backgrounds of tourists’ forms diverse cognition and experiences about religious tourism, and their motivations, satisfaction and behavioral intention as tourists vary. Tourists’ motivation and satisfaction has a positive phase relation. Tourists’ motivation with satisfaction as the intervening variable also has a positive phase effect on tourists’ behavior intention. The result shows that religious tourists’ motivations include experiencing a religious atmosphere, and having a rest and recreation. The result also shows that religious tourists want to travel with their family members and friends. While traveling, religious tourists like to talk with Buddhist monks or nuns. Compared to other tourism types, religious tourists have higher expectations about temple environment, traveling experience, peripheral service and temple management.

Keywords: Behavioral intension, motivation, religious tourism, satisfaction.

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Authors: Jindřiška Šedová, Miloš Šeda

Abstract:

This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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Authors: Tami Alghamdi, Terence Soule

Abstract:

To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed that combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: Transfer Learning, Multiple Sources, Knowledge Transfer, Domain Adaptation, Source, Target.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

Abstract:

A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: S. Nasri, H. Bouziri

Abstract:

Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: Dynamic network flow, Load dependent transit time, Evacuation strategy, Earliest arrival flow problem.

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Authors: M. Dinakaran, P. Balasubramanie

Abstract:

With the demand of mobility by users, wireless technologies have become the hotspot developing arena. Internet Engineering Task Force (IETF) working group has developed Mobile IP to support node mobility. The concept of node mobility indicates that in spite of the movement of the node, it is still connected to the internet and all the data transactions are preserved. It provides location-independent access to Internet. After the incorporation of host mobility, network mobility has undergone intense research. There are several intricacies faced in the real world implementation of network mobility significantly the problem of nested networks and their consequences. This article is concerned regarding a problem of nested network called pinball route problem and proposes a solution to eliminate the above problem. The proposed mechanism is implemented using NS2 simulation tool and it is found that the proposed mechanism efficiently reduces the overload caused by the pinball route problem.

Keywords: Mobile IP, Pinball routing problem, NEMO

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Authors: E. Dabbour, S. M. Easa

Abstract:

Most of the collision warning systems currently available in the automotive market are mainly designed to warn against imminent rear-end and lane-changing collisions. No collision warning system is commercially available to warn against imminent turning collisions at intersections, especially for left-turn collisions when a driver attempts to make a left-turn at either a signalized or non-signalized intersection, conflicting with the path of other approaching vehicles traveling on the opposite-direction traffic stream. One of the major factors that lead to left-turn collisions is the human error and misjudgment of the driver of the turning vehicle when perceiving the speed and acceleration of other vehicles traveling on the opposite-direction traffic stream; therefore, using a properly-designed collision warning system will likely reduce, or even eliminate, this type of collisions by reducing human error. This paper introduces perceptual framework for a proposed collision warning system that can detect imminent left-turn collisions at intersections. The system utilizes a commercially-available detection sensor (either a radar sensor or a laser detector) to detect approaching vehicles traveling on the opposite-direction traffic stream and calculate their speeds and acceleration rates to estimate the time-tocollision and compare that time to the time required for the turning vehicle to clear the intersection. When calculating the time required for the turning vehicle to clear the intersection, consideration is given to the perception-reaction time of the driver of the turning vehicle, which is the time required by the driver to perceive the message given by the warning system and react to it by engaging the throttle. A regression model was developed to estimate perception-reaction time based on age and gender of the driver of the host vehicle. Desired acceleration rate selected by the driver of the turning vehicle, when making the left-turn movement, is another human factor that is considered by the system. Another regression model was developed to estimate the acceleration rate selected by the driver of the turning vehicle based on driver-s age and gender as well as on the location and speed of the nearest approaching vehicle along with the maximum acceleration rate provided by the mechanical characteristics of the turning vehicle. By comparing time-to-collision with the time required for the turning vehicle to clear the intersection, the system displays a message to the driver of the turning vehicle when departure is safe. An application example is provided to illustrate the logic algorithm of the proposed system.

Keywords: Collision warning systems, intelligent transportationsystems, vehicle safety.

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

Abstract:

Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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Authors: Divyesh Patel, Tanuja Srivastava

Abstract:

This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: Discrete Tomography, exactly-1-4-adjacency, simulated annealing.

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Authors: R. Hashemi, M.H.Kargarnovin

Abstract:

This paper presents the identification of the impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and the genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness vs. the measurement noise and sensor location.

Keywords: Genetic Algorithm, Inverse problem, Optimization, Vibration.

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

Abstract:

In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: Binary cat swarm optimization, set covering problem, metaheuristic, binarization methods.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: Halizah Awang, Ishak Ramly

Abstract:

Problem-based learning (PBL) is one of the student centered approaches and has been considered by a number of higher educational institutions in many parts of the world as a method of delivery. This paper presents a creative thinking approach for implementing Problem-based Learning in Mechanics of Structure within a Malaysian Polytechnics environment. In the learning process, students learn how to analyze the problem given among the students and sharing classroom knowledge into practice. Further, through this course-s emphasis on problem-based learning, students acquire creative thinking skills and professional skills as they tackle complex, interdisciplinary and real-situation problems. Once the creative ideas are generated, there are useful additional techniques for tender ideas that will grow into a productive concept or solution. The combination of creative skills and technical abilities will enable the students to be ready to “hit-the-ground-running" and produce in industry when they graduate.

Keywords: Creative Thinking Skills, Problem-based Learning, Problem Solving.

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Authors: Ching-Shoei Chiang

Abstract:

The Malfatti’s problem solves the problem of fitting three circles into a right triangle such that these three circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s problem). Furthermore, the problem has been extended to have 1 + 2 + … + n circles inside the triangle with special tangency properties among circles and triangle sides; it is called the extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for the Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving the Tri(Tn) problem, n > 2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary as in Tri(Tn) problems. We call these problems the Carc(Tn) problems. The algorithm is a mO(Tn) algorithm, where m is the number of iterations in the loop. It takes less than 1000 iterations and less than 1 second for the Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties. This algorithm gives a solution for circle packing problem inside convex circular triangle with arbitrarily-sized circles. Many applications concerning circle packing may come from the result of the algorithm, such as logo design, architecture design, etc.

Keywords: Circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem.

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Authors: Hosein Faramarzpour

Abstract:

This work presents the optimum operational conditions for a hydrogen-based micro-scale power source, using a verified mathematical model including fluid dynamics and reaction kinetics. Thereafter, the stable operational flame regime is pursued as a key factor in optimizing the design of micro-combustors. The results show that with increasing velocities, four H2 flame regimes develop in the micro-combustor, namely: 1) periodic ignition-extinction regime, 2) steady symmetric regime, 3) pulsating asymmetric regime, and 4) steady asymmetric regime. The first regime that appears in 0.8 m/s inlet velocity is a periodic ignition-extinction regime which is characterized by counter flows and tulip-shape flames. For flow velocity above 0.2 m/s, the flame shifts downstream, and the combustion regime switches to a steady symmetric flame where temperature increases considerably due to the increased rate of incoming energy. Further elevation in flow velocity up to 1 m/s leads to the pulsating asymmetric flame formation, which is associated with pulses in various flame properties such as temperature and species concentration. Further elevation in flow velocity up to 1 m/s leads to the pulsating asymmetric flame formation, which is associated with pulses in various flame properties such as temperature and species concentration. Ultimately, when the inlet velocity reached 1.2 m/s, the last regime was observed, and a steady asymmetric regime appeared.

Keywords: Thermophotovoltaic generator, micro combustor, micro power generator, combustion regimes, flame dynamic.

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Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

Abstract:

Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

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Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.

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Authors: Ei Phyo Wai, Nay Min Tun

Abstract:

Computation of facility location problem for every location in the country is not easy simultaneously. Solving the problem is described by using cluster computing. A technique is to design parallel algorithm by using local search with single swap method in order to solve that problem on clusters. Parallel implementation is done by the use of portable parallel programming, Message Passing Interface (MPI), on Microsoft Windows Compute Cluster. In this paper, it presents the algorithm that used local search with single swap method and implementation of the system of a facility to be opened by using MPI on cluster. If large datasets are considered, the process of calculating a reasonable cost for a facility becomes time consuming. The result shows parallel computation of facility location problem on cluster speedups and scales well as problem size increases.

Keywords: cluster, cost, demand, facility location

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Authors: Tsuyoshi Okita

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach in order to make a solver quickly. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem. It is noted that our formal modeling language is not intend for providing an efficient notation for data mining application, but for facilitating a designer who develops solvers in machine learning.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: Supriya Arya, Sunita Dhingra

Abstract:

Multiprocessor task scheduling problem for dependent and independent tasks is computationally complex problem. Many methods are proposed to achieve optimal running time. As the multiprocessor task scheduling is NP hard in nature, therefore, many heuristics are proposed which have improved the makespan of the problem. But due to problem specific nature, the heuristic method which provide best results for one problem, might not provide good results for another problem. So, Simulated Annealing which is meta heuristic approach is considered. It can be applied on all types of problems. However, due to many runs, meta heuristic approach takes large computation time. Hence, the hybrid approach is proposed by combining the Duplication Scheduling Heuristic and Simulated Annealing (SA) and the makespan results of Simple Simulated Annealing and Hybrid approach are analyzed.

Keywords: Multiprocessor task scheduling Problem, Makespan, Duplication Scheduling Heuristic, Simulated Annealing, Hybrid Approach.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

Abstract:

The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal openshop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Keywords: Integer programming, open shop problem, optimal staffing.

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Authors: Neda Shahidi, Hadi Esmaeilzadeh, Marziye Abdollahi, Caro Lucas

Abstract:

In this paper, the problem of finding the optimal collision free path for a mobile robot, the path planning problem, is solved using an advanced evolutionary algorithm called memetic algorithm. What is new in this work is a novel representation of solutions for evolutionary algorithms that is efficient, simple and also compatible with memetic algorithm. The new representation makes it possible to solve the problem with a small population and in a few generations. It also makes the genetic operator simple and allows using an efficient local search operator within the evolutionary algorithm. The proposed algorithm is applied to two instances of path planning problem and the results are available.

Keywords: Path planning problem, Memetic Algorithm, Representation.

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

Abstract:

In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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Authors: Deepak Chhabra, Gian Bhushan, Pankaj Chandna

Abstract:

The present work deals with the optimal placement of piezoelectric actuators on a thin plate using Modified Control Matrix and Singular Value Decomposition (MCSVD) approach. The problem has been formulated using the finite element method using ten piezoelectric actuators on simply supported plate to suppress first six modes. The sizes of ten actuators are combined to outline one actuator by adding the ten columns of control matrix to form a column matrix. The singular value of column control matrix is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with GA. Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions using Linear Quadratic regulator) scheme. It is observed that MCSVD approach has given the position of patches adjacent to each-other, symmetric to the centre axis and given greater vibration suppression than other previously published results on SVD. 

Keywords: Closed loop Average dB gain, Genetic Algorithm (GA), LQR Controller, MCSVD, Optimal positions, Singular Value Decomposition (SVD) Approaches.

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Authors: Shiping Zhou, Minggen Cui

Abstract:

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

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Authors: Omid S. Fard, Akbar H. Borzabadi

Abstract:

In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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