A new approach for solving fully intuitionistic fuzzy transportation problems

In this paper, a well-known network-structured problem called the transportation problem (TP) is considered in an uncertain environment. The transportation costs, supply and demand are represented by trapezoidal intuitionistic fuzzy numbers (TrIFNs) which are the more generalized form of trapezoidal fuzzy numbers involving a degree of acceptance and a degree of rejection. We formulate the intuitionistic fuzzy TP (IFTP) and propose a solution approach to solve the problem. The IFTP is converted into a deterministic linear programming (LP) problem, which is solved using standard LP algorithms. The main contributions of this paper are fivefold: (1) we convert the formulated IFTP into a deterministic classical LP problem based on ordering of TrIFNs using accuracy function; (2) in contrast to most existing approaches, which provide a crisp solution, we propose a new approach that provides an intuitionistic fuzzy optimal solution; (3) in contrast to existing methods that include negative parts in the obtained intuitionistic fuzzy optimal solution and intuitionistic fuzzy optimal cost, we propose a new method that provides non-negative intuitionistic fuzzy optimal solution and optimal cost; (4) we discuss about the advantages of the proposed method over the existing methods for solving IFTPs; (5) we demonstrate the feasibility and richness of the obtained solutions in the context of two application examples.     

A global approach to fully nonlinear parabolic problems

We consider the general initial-boundary value problem

(1)        
(2)        
(3)        
where is a bounded open set in with sufficiently smooth boundary.  The problem (1)-(3) is first reduced to the analogous problem in the space with zero initial condition and

The resulting problem is then reduced to the problem where the operator satisfies Condition  This reduction is based on a priori estimates which are developed herein for linear parabolic operators with coefficients in Sobolev spaces.  The local and global solvability of the operator equation are achieved via topological methods developed by I. V. Skrypnik. Further applications are also given involving relevant coercive problems, as well as Galerkin approximations.

     

New approach for the identification of power system economic dispatch parameters

It is well known that the coefficients of the input-output characteristics of the thermal steam-turbine model as well as the network model parameters have a great effect on the optimal economic operation of all thermal-electric power systems. Until today, these coefficients, the loss formula coefficients, theB-coefficients, and the active-reactive power loss models have been estimated using the well-known least-square estimation algorithm.In this paper, we present a new algorithm to estimate the power system parameters for economic dispatch calculation (EDC); this algorithm is based on the least absolute-value approximation (LAV)l ₁-norm. We compare the results obtained using the proposed algorithms with those obtained using the least-square error algorithm (LS). Optimal costs as well as overall network performance resulting from the implementation of each technique provide the basis of our conclusion.This work was supported by the Natural Science and Engineering Research Council of Canada, Grant No. A4146.     

A simple recourse model for power dispatch under uncertain demand

Optimal power dispatch under uncertainty of power demand is tackled via a stochastic programming model with simple recourse. The decision variables correspond to generation policies of a system comprising thermal units, pumped storage plants and energy contracts. The paper is a case study to test the kernel estimation method in the context of stochastic programming. Kernel estimates are used to approximate the unknown probability distribution of power demand. General stability results from stochastic programming yield the asymptotic stability of optimal solutions. Kernel estimates lead to favourable numerical properties of the recourse model (no numerical integration, the optimization problem is smooth convex and of moderate dimension). Test runs based on real-life data are reported. We compute the value of the stochastic solution for different problem instances and compare the stochastic programming solution with deterministic solutions involving adjusted demand portions.This research is supported by the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung of the Deutsche Forschungsgemeinschaft.     

A distributed global optimization method for packing problems

Packing optimization problems aim to seek the best way of placing a given set of rectangular cartons within a minimum volume rectangular container. Currently, packing optimization methods either have difficulty in finding a globally optimal solution or are computationally inefficient, because models involve too many 0–1 variables and because use of just a single computer. This study proposes a distributed computation method for solving a packing problem by a set of personal computers via the Internet. First, the traditional packing optimization model is converted into an equivalent model containing many fewer 0–1 variables. Then the model is decomposed into several sub-problems by dividing the objective value into many intervals. Each of these sub-problems is a linearized logarithmic program expressed as a linear mixed 0–1 problem. The whole problem is solvable and reaches a globally optimal solution. The numerical examples demonstrate that the proposed method can obtain the global optimum of a packing problem effectively.     

A new multiobjective procedure for solving nonconvex environmental/economic power dispatch

In this article, an improved multiobjective chaotic interactive honey bee mating optimization (CIHBMO) is proposed to find the feasible optimal solution of the environmental/economic power dispatch problem with considering operational constraints of the generators. The three conflicting and noncommensurable: fuel cost, pollutant emissions, and system loss, should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multiobjective optimization problem, Pareto dominance concept is used to generate and sort the dominated and nondominated solutions. Also, fuzzy set theory is used to extract the best compromise solution. The propose method has been individually examined and applied to the standard Institute of Electrical and Electronics Engineers (IEEE) 30‐bus six generator, IEEE 180‐bus 14 generator and 40 generating unit (with valve point effect) test systems. The computational results reveal that the multiobjective CIHBMO algorithm has excellent convergence characteristics and is superior to other multiobjective optimization algorithms. Also, the result shows its great potential in handling the multiobjective problems in power systems. © 2014 Wiley Periodicals, Inc. Complexity 20: 47–62, 2014     

A new method for solving fully fuzzy linear programming problems

Lotfi et al. [Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33 (2009) 3151–3156] pointed out that there is no method in literature for finding the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints. In this paper, a new method is proposed to find the fuzzy optimal solution of same type of fuzzy linear programming problems. It is easy to apply the proposed method compare to the existing method for solving the FFLP problems with equality constraints occurring in real life situations. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.     

A stochastic approximation for fully nonlinear free boundary parabolic problems

We present a stochastic numerical method for solving fully nonlinear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the nonlinearity. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 902–929, 2014     

A network-related nuclear power plant model with an intelligent branch-and-bound solution approach

This paper presents a network model with discrete requirements for a nuclear power plant. The model determines the batch size and timing for nuclear unit refueling and how much energy should be produced by nuclear and non-nuclear units for each time period to satisfy forecasted demand with minimum total operating costs over the planning horizon. Efficient modeling and solution strategies are developed which constitute a merger of operations research and artificial intelligence. A branch-and-bound solution approach is combined with a pattern recognition component, involving non-parametric discrimination analyses, to select branching variables and directions. By coupling this approach with network optimization techniques to exploit the underlying network structure of the problem, substantial improvements are obtained both in solution quality and solution efficiency.This research was supported in part by the Center for Business Decision Analysis, the Hugh Roy Cullen Centennial Chair in Business Administration, and the Office of Naval Research under contract N00014-87-K-0190. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. CENTER FOR BUSINESS DECISION ANALYSIS Darwin Klingman, Director The University of Texas at Austin Austin, TX 78712, U.S.A.     

A distributed Douglas-Rachford splitting method for multi-block convex minimization problems

A customized Douglas-Rachford splitting method (DRSM) was recently proposed to solve two-block separable convex optimization problems with linear constraints and simple abstract constraints. The algorithm has advantage over the well-known alternating direction method of multipliers (ADMM), the dual application of DRSM to the two-block convex minimization problem, in the sense that the subproblems can have larger opportunity of possessing closed-form solutions since they are unconstrained. In this paper, we further study along this way by considering the primal application of DRSM for the general case m≥3, i.e., we consider the multi-block separable convex minimization problem with linear constraints where the objective function is separable into m individual convex functions without coupled variables. The resulting method fully exploits the separable structure and enjoys decoupled subproblems which can be solved simultaneously. Both the exact and inexact versions of the new method are presented in a unified framework. Under mild conditions, we manage to prove the global convergence of the algorithm. Preliminary numerical experiments for extracting the background from corrupted surveillance video verify the encouraging efficiency of the new algorithm.     

A virtual control concept for state constrained optimal control problems

A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain. In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper. The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the paper. The theory is illustrated by numerical tests.     

A multi-objective multi-population ant colony optimization for economic emission dispatch considering power system security

With increasing concern about global warming and haze, environmental issue has drawn more attention in daily optimization operation of electric power systems. Economic emission dispatch (EED), which aims at reducing the pollution by power generation, has been proposed as a multi-objective, non-convex and non-linear optimization problem. In a practical power system, the problem of EED becomes more complex due to conflict between the objectives of economy and emission, valve-point effect, prohibited operation zones of generating units, and security constraints of transmission networks. To solve this complex problem, an algorithm of a multi-objective multi-population ant colony optimization for continuous domain (MMACO_R) is proposed. MMACO_R reconstructs the pheromone structure of ant colony to extend the original single objective method to multi-objective area. Furthermore, to enhance the searching ability and overcome premature convergence, multi-population ant colony is also proposed, which contains ant populations with different searching scope and speed. In addition, a Gaussian function based niche search method is proposed to enhance distribution and accuracy of solutions on the Pareto optimal front. To verify the performance of MMACO_R in different multi-objective problems, benchmark tests have been conducted. Finally, the proposed algorithm is applied to solve EED based on a six-unit system, a ten-unit system and a standard IEEE 30-bus system. Simulation results demonstrate that MMACO_R is effective in solving economic emission dispatch in practical power systems.     

A search tree algorithm for plant location problems

This paper deals with the classical plant location problem, by introducing a new algorithm based on a ranking procedure of all the possible combinations of plant locations. The ranking is obtained by introducing a properly defined search tree and by exploiting its structural properties, so that the algorithm suitably combines a search procedure on the tree with a ranking method. The number of subproblems to be examined is greatly reduced by the use of a stopping rule and a lower bound. The lower bound is given by the value of the objective function of a dual feasible solution for the transportation problem associated to each combination. Computational results for a set of real size problems with different data structures are finally discussed.     

A model-hybrid approach for unconstrained optimization problems

In this paper, we propose a model-hybrid approach for nonlinear optimization that employs both trust region method and quasi-Newton method, which can avoid possibly resolve the trust region subproblem if the trial step is not acceptable. In particular, unlike the traditional trust region methods, the new approach does not use a single approximate model from beginning to the end, but instead employs quadratic model or conic model at every iteration adaptively. We show that the new algorithm preserves the strong convergence properties of trust region methods. Numerical results are also presented.     

A power penalty method for linear complementarity problems

We propose a power penalty approach to a linear complementarity problem (LCP) in Rⁿ based on approximating the LCP by a nonlinear equation. We prove that the solution to this equation converges to that of the LCP at an exponential rate when the penalty parameter tends to infinity.