Mathematical Model of Object Classifier based on Bayesian Approach

The subject matter of the article is the processes of synthesis of the information and telecommunication network (ITN) for solving applied problems of safety-critical systems (SCS). The goalis to develop a mathematical model for the optimal distribution of applied tasks of safety-critical systems over the ITN nodes. The tasks to be solved are: to formalize the procedure of distribution of applied tasks and SCS software over the ITN nodes; to develop a mathematical model of optimal distribution in order to minimize the cost of network resources; to select an effective algorithm for solving it. The methods used are: alternative-graph approach, mathematical optimization models, methods for solving nonlinear integer programming problems with Boolean variables. The following results were obtained: the task of selecting the ITN optimal structure was formulated according to the alternative-graph model of information processing; in addition to structural characteristics, the requirements for the parameters necessary for performing applied tasks were taken into account while constructing a mathematical model; when minimizing the cost of a computing resource, constraints related to the capabilities for financing the development and operation of the network are taken into account; the costs for organizing additional connections among the network nodes are considered as well. As a result, a mathematical model of distributing SCS applied problems over the ITN environment was obtained in order to minimize the total costs of computing resource, data transmission, network setting and maintenance. This model is a non-linear integer programming problem with Boolean variables. Taking into account the specific nature of the objective function and model constraints with the use of pseudo-Boolean functions, the original task is reduced to a linear form. The obtained model represents the canonical form of the linear optimizing problem of large-dimensional Boolean programming, for which the method of the recession vector is effective. Conclusions. The scientific novelty of the results obtained is as follows: 1) the optimization model of distributing applied tasks over the nodes of the computer network was improved by defining the objective function in order to minimize the costs of both computational and data transmission and the constraints caused by the requirements for the technical and information struct ure of the network; 2) methods for solving the problems of optimizing the ITN structure on the basis of models of nonlinear Boolean programming by transforming the initial task into a linear form and applying the recession vector method was further developed, which makes obtaining a quasi-optimal solution of the problem in the context of large dimension possible.

The simultaneous heat exchanger network (HEN) synthesis problem is generally formulated as a mixed integer non-linear programming (MINLP) problem by using superstructures, which embed several possible stream matches and various alternative HEN designs. The superstructures proposed by Yee et al. [1] and by Floudas et al. [2] are used for this purpose. In the present work, the graph theoretic principles used by Shivakumar and Narasimhan [3] to develop an efficient nonlinear program (NLP) formulation for Yee superstructure has been extended to the Floudas superstructure. A comparison of the NLP formulations based on the two superstructures, in terms of efficiency, scalability, convergence and quality of solution has been carried out using several test problems available in the literature. It has been shown that the Floudas superstructure is superior in terms of these performance metrics, and appears to be the best suited for optimisation based HEN synthesis.

It has recently been important to obtain optimal solutions to multidimensional nonlinear integer programming problems with multiple constraints. The surrogate constraint method is very effective in obtaining high-quality solutions of the original multidimensional problems. The surrogate constraint method translates a multidimensional problem into a one-dimensional problem by using a surrogate multiplier. But when there exists a surrogate duality gap between the translated one-dimensional problem and the original multidimensional problem, the optimal solution to the surrogate problem is not optimal with respect to the original problem. Nakagawa has recently proposed an improved surrogate constraint (ISC) method that can reduce the surrogate duality gap and provide an exact solution to the original problem. By using this method, we can obtain exact solutions to separable nonlinear integer programming problems with 1000 variables and 5 or 6 constraints. The ISC method requires an optimal surrogate multiplier. However, there are problems of calculation time and memory requirements in the algorithm for obtaining the optimal surrogate multiplier when the number of constraints is large. In this paper, the Dyer algorithm and Nakagawa's Cutting-Off Polyhedron (COP) algorithm for an algorithm that obtains the optimal surrogate multiplier in the ISC method are compared in computational experiments, and the advantages and disadvantages of these algorithms are investigated. In addition, an improved Dyer algorithm is proposed and computational experiments show that the improved algorithm is more effective than the original algorithm. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(8): 38–48, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20114

A nonlinear programming approach to kinematic shakedown analysis of frictional materials

The loading pattern of fuel bundles in a reactor core determines the characteristics of the reloading cycle. The problem of maximizing fuel utilization during a cycle may be formu-lated as a nonlinear mixed integer programming (NLMIP) problem, but has until now mostly been treated by heuristic optimization methods like simulated annealing. This paper evaluates the performance of state-of-the-art nonlinear programming routines on a simplified model of this problem, and compares results with available heuristic solutions.

There is a growing trend for service providers to migrate their services from local clusters to the cloud data center. When there is no single service can satisfy the functionality requirement of the end user, existing services are combined together to fulfill the requirements. The data communication between component service hosting servers imposes a heavy burden on the data center network. In this article, we seek to reduce the data center network resource consumption by designing a novel service composition aware virtual machine migration approach. First, we formulate the problem as a multi-object integer non-linear(INLP) programming problem. The problem, which can be reduced into a well-known multi-object quadratic assignment problem, is proved to be NP-hard. Second, we simplify the multiple-objects INLP formulation into an equivalent, but much simplified single object ILP formulation. Then, we prove that the simplified formulation can also lead to the optimal solutions. Finally, optimization problem solvers, such as LPSolver, are employed to solve the problem. Experimental results in a large scale cloud data center demonstrate that our method significantly reduce the network resource consumption than other approaches.

Efficient ant colony optimization (EACO) for solvent selection using computer aided molecular design

With the advance of electricity market, all distributed power generators will participate in electric power bidding, start-up and shutdown of the unit must be considered in objective function of purchasing electricity. Therefore, this paper establishes the mathematical model of purchasing electricity optimization from distributed generators, which takes total costs from many distributed generators as an objective function, and synthetically considers supply and demand, transmission ability constraints. The mathematical model is a constrained nonlinear mixed integer programming problem. This paper presents an improved hybrid PSO algorithm to solve the problem, which is hybridization of the binary PSO and chaotic optimization. The hybrid PSO algorithm enhances the global search ability of the algorithm, and has been successfully applied to solving the problem. The simulation results show that the hybrid methodology was successfully validated for eight distributed generators, which can reach the expected requirements.

Converting general nonlinear programming problems into separable programming problems with feedforward neural networks

An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

This paper proposes on-line energy plant optimal operation planning (EPOOP) using dependable parallel multi-population improved brain storm optimization with differential evolution (DPMP-IBSODE). Parallel distributed processing (PDP) enables on-line optimal operation planning for a large number of energy plants with a few cluster computers, and therefore reduces the operational cost. While speedy EPOOP has been studied using PDP, there are still challenges for countermeasures for malfunction of computer processes such as breakdown or response delay of cluster computers and communication delay of local area networks (LANs). In order to execute on-line calculation of EPOOP with appropriate solution quality, dependable parallel EPOOP is required, where operational set points for various energy facilities are continuously sent to distributed control systems (DCSs). By formulating On-line EPOOP as a mixed integer nonlinear optimization programming (MINLP) problem, in this paper, the proposed method has been verified to be able to keep higher quality solutions at high speed than conventional method.

In this dissertation we develop numerical algorithms and software tools to facilitate parallel solutions of nonlinear programming (NLP) problems. In particular, we address large-scale, block-structured problems with an intrinsic decomposable configuration. These problems arise in a great number of engineering applications, including parameter estimation, optimal control, network optimization, and stochastic programming. The structure of these problems can be leveraged by optimization solvers to accelerate solutions and overcome memory limitations, and we propose variants to two classes of optimization algorithms: augmented Lagrangian (AL) schemes and Schur-complement interior-point methods. The convergence properties of augmented Lagrangian decomposition schemes like the alternating direction method of multipliers (ADMM) and progressive hedging (PH) are well established for convex optimization but convergence guarantees in non-convex settings are still poorly understood. In practice, however, ADMM and PH often perform satisfactorily in complex non-convex NLPs. In this work, we study connections between the method of multipliers (MM), ADMM, and PH to derive benchmarking metrics that explain why PH and ADMM work in practice. We illustrate the concepts using challenging dynamic optimization problems. Our exposition seeks to establish more formalism in benchmarking ADMM, PH, and AL schemes and to motivate algorithmic improvements. The effectiveness of nonlinear interior-point solvers for solving large-scale problems relies quite heavily on the solution of the underlying linear algebra systems. The schur-complement decomposition is very effective for parallelizing the solution of linear systems with modest coupling. However, for systems with large number of coupling variables the schur-complement method does not scale favorably. We implement an approach that uses a Krylov solver (GMRES) preconditioned with ADMM to solve block-structured linear systems that arise in the interior-point method. We show that this ADMM-GMRES approach overcomes the well-known scalability issues of Schur decomposition. One important drawback of using decomposition approaches like ADMM and PH is their convergence rate. Unlike Schur-complement interior-point algorithms that have super-linear convergence, augmented Lagrangian approaches typically exhibit linear and sublinear rates. We exploit connections between ADMM and the Schur-complement decomposition to derive an accelerated version of ADMM. Specifically, we study the effectiveness of performing a Newton-Raphson algorithm to compute multiplier estimates for augmented Lagrangian methods. We demonstrate using two-stage stochastic programming problems that our multiplier update achieves convergence in fewer iterations for MM on general nonlinear problems. In the case of ADMM, the newton update significantly reduces the number of subproblem solves for convex quadratic programs (QPs). Moreover, we show that using newton multiplier updates makes the method robust to the selection of the penalty parameter. Traditionally, state-of-the-art optimization solvers are implemented in low-level programming languages. In our experience, the development of decomposition algorithms in these frameworks is challenging. They present a steep learning curve and can slow the development and testing of new numerical algorithms. To mitigate these challenges, we developed PyNumero, a new open source framework implemented in Python and C++. The package seeks to facilitate development of optimization algorithms for large-scale optimization within a high-level programming environment while at the same time minimizing the computational burden of using Python. The efficiency of PyNumero is illustrated by implementing algorithms for problems arising in stochastic programming and optimal control. Timing results are presented for both serial and parallel implementations. Our computational studies demonstrate that with the appropriate balance between compiled code and Python, efficient implementations of optimization algorithms are achievable in these high-level languages.

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

Multi-subsystem co-design refers to the simultaneous optimization of physical plant and controller of a system decomposed into multiple interconnected co-design subsystems. In this paper, a new decentralized approach based on the direct collocation and decomposition-based optimization methods is formulated to solve multi-subsystem co-design problems. First, the problem is decomposed into physical plant and control parts. In the control part, the entire time horizon is discretized into subintervals and grid points. In this way, a continuous optimal control problem is converted into a finite dimensional nonlinear programming (NLP) problem. The optimality condition decomposition (OCD) method is employed to decompose and solve the converted NLP problem in a decentralized manner. Next, the dual decomposition method is used to optimize the plant part. Finally, the plant and control parts are connected by the gradients of Hamiltonian with respect to the plant variables. The proposed approach is applied to two examples. First, a numerical example is presented to illustrate the approach step-by-step. Then in the second example, a spring-mass-damper system is solved. For both examples, the solutions obtained by the proposed decentralized approach are compared against a centralized (all-in-one) approach.

This research aims to optimize the yield for hard disk drive component problem using heuristic methods. This problem is constrained by the limited budget and the requirement on the suppliers rating of the components. Because of complexity of the problem, it is considered as a NP-Hard problem which can be formulated as a nonlinear integer programming problem. Three heuristics, Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Bee Algorithm (BA), are proposed to solve this problem and compare heuristic performance from getting optimum percentage and computation time. Using the actual data from undisclosed HDD manufacturer, computational experiments are conducted under many budget constraints. The results from the experiments show that they can solve the problem with the same condition under reasonable time. Using accuracy, robustness and computation effort, it reveals that BA can solve the case study more efficient than ACO and GA.KeywordsHard Disk DriveCrossover RateHeuristic InformationBudget SettingState Transition RuleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.