A Network Model to Maximize Navy Personnel Readiness and Its Solution

Recently, in structural engineering, many main elements in structural systems such as columns or girders are designed with variable cross-section for certain purposes. In addition, in order to determine the appropriate sizes or suitable shapes of structural elements for optimal volume of material under the effect of certain loading or with the given sizes of elements the structures can be subjected maximum loading, it is required to studied the optimization problem. This paper presents the non-linear weight optimization problem of frames with variable section stiffness of columns according to the strength, stiffness and stability criteria with the help of finite element method. The non-linear optimization problem is solved by the Genetic Algorithm. The calculation procedure of non-linear optimization of plane frames with variable section stiffness of columns is established and implemented using Matlab calculation programming software. From the results of numerical examples, the conclusions and recommendations will be proposed.

This book is on modern continuous nonlinear optimization. Continuous nonlinear optimization problems have a simple mathematical model and always refer to a real physical system, the running of which we want to optimize. Firstly, a nonlinear optimization problem contains an objective function which measures the performances or requirements of the system. Often, this function represents a profit, a time interval, a level, a sort of energy or combination of different quantities which have a physical significance for the modeler. The objective function depends on some characteristics of the system, called variables or unknowns. The purpose of any optimization problem is to find the values of these variables that minimize (or maximize) the objective function subject to some constraints which the variables must satisfy. Constraints of an optimization problem may have different algebraic expressions. There are static and dynamic constraints called functional constraints. The difference between these types of constraints comes from the structure of their Jacobian. The dynamic constraints always involve a Jacobian with a block-diagonal structure. Besides, these functional constraints are nonlinear functions which may be equalities or inequalities, or even range constraints. Another very important type of constraints is the simple bounds on variables. The real applications of optimization include simple bounds on variables which express the constructive engineering conditions and limits of the system to be optimized. The constraints of an optimization problem define the so-called feasible domain of the problem. Both the objective function and the constraints may depend on some parameters with known values which characterize the system under optimization. The process of identifying the variables, parameters, simple bounds on variables, the objective functions, and constraints is known as modeling, one of the finest intellectual activities. In this book we assume that the variables can take real values and the objective function and the constraints are smooth enough (at least twice continuously differentiable) with known first-order derivatives. When the number of variables and the number of constraints is large, then the optimization problem is quite challenging.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Reduced costs obtained from the optimal simplex tableau are not necessarily correct under degeneracy in network flow problems with side constraints. In one application, simplex reduced costs were shown not to be good when applied to actual operations, while reoptimization to find all true reduced costs was too time-consuming. An efficient algorithm to obtain approximate reduced costs was developed in the research to offset these disadvantages. The algorithm combines the uses of Lagrangian relaxation, a minimum-cost network flow algorithm, and a shortest path algorithm. In theory, the approximate reduced costs prove to be a better lower bound than are simplex reduced costs. Numerical experiments have been performed to show its potential usefulness in practice. © 1996 John Wiley & Sons, Inc.

The paper deals with multiobjective nonlinear optimization problems with equality and inequality con- straints. In a corresponding dialogue procedure the decision maker has to determine in each step the aspira- tion and reservation level expressing his goals. This leads to a nonlinear optimization problem which can be solved by using a combination of pathfollowing methods and feasible descent direction methods (so- called jumps). The authors propose the application of a recently published pathfollowing method with jumps to multiobjective optimization problems, discuss its topological properties and present several computational results.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints

The generation expansion planning (GEP) and reactive power planning problems are nonlinear dynamic optimization problems that can only be fully solved by complete enumeration, a process that is computationally impossible for realistic planning problems. Therefore, modern heuristic approaches, such as genetic algorithm (GA), are well suited for these complex planning problems. The GEP is one of the most important decision‐making activities in electric utilities. The chapter introduces an improved genetic algorithm, which can overcome the problems of conventional GA to some extent. Solving a least‐cost GEP problem is equivalent to finding a set of optimal decision vectors over a planning horizon that minimizes an objective function under several constraints. The reactive power planning problem is a nonlinear optimization problem. The planning problem is divided into operational and investment planning subproblems. The reactive power planning problem is to determine the optimal investment of VAR sources over a planning horizon.

Simultaneous measurement of flame temperature and species concentration distribution from nonlinear tomographic absorption spectroscopy

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.

Nonlinear optimization algorithms are rarely discussed from a complexity point of view. Even the concept of solving nonlinear problems on digital computers is not well defined. The focus here is on a complexity approach for designing and analyzing algorithms for nonlinear optimization problems providing optimal solutions with prespecified accuracy in the solution space. We delineate the complexity status of convex problems over network constraints, dual of flow constraints, dual of multi-commodity, constraints defined by a submodular rank function (a generalized allocation problem), tree networks, diagonal dominant matrices, and nonlinear Knapsack problem's constraint. All these problems, except for the latter in integers, have polynomial time algorithms which may be viewed within a unifying framework of a proximity-scaling technique or a threshold technique. The complexity of many of these algorithms is furthermore best possible in that it matches lower bounds on the complexity of the respective problems. In general nonseparable optimization problems are shown to be considerably more difficult than separable problems. We compare the complexity of continuous versus discrete nonlinear problems and list some major open problems in the area of nonlinear optimization.

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 214+3x192 boundary scenarios are considered. A validation with randomly drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used.

A nonlinear programming optimization problem is considered for the case in which the decision vector is the vector of zonal irradiation while the objective function is the equilibrium fuel feed rate with a CANDU-600 reactor subject to certain restrictions regarding the reactivity excess and the maximum powers per channel and bundle. The objective and restriction functions of the system are estimated within a time average approximation of a three-dimensional two-group diffusion type, with the control systems uniformly immersed within the reactor, and also considering the newest increments of the parasitic absorbents using FMDP program. The optimization problem is solved by means of the SUMT method, modified so as to become a technique of sequential solving for certain subproblems of linear optimization through the application of LPROG program. The results are presented as optimal vectors of zonal irradiation and as optimal values of fuel feed rate, with some two-zone cases, which establish the best zonal configuration. This configuration is then extended to a four-zone case which is analysed in a similar manner, evidencing a saving potential which gives the possibiliy of increasing the reactor performance.

The paper reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including Firefly algorithm, PSO algorithms and ABC algorithm. By implementing these algorithms in Matlab, we will use worked examples to show how each algorithm works. Firefly algorithm is one of the evolutionary optimization algorithms, and is inspired by the flashing behaviour of fireflies in nature. There are many noisy non-linear mathematical optimization problems that can be effectively solved by Metaheuristic Algorithms. Mathematical optimization or programming is the study of such planning and design problems using mathematical tools. Nowadays, computer simulations become an indispensable tool for solving such optimization problems with various efficient search algorithms. Nature-inspired algorithms are among the most powerful algorithms for optimization. Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behaviour of fireflies. A Firefly Algorithm (FA) is a recent nature inspired optimization algorithm, which simulates the flash pattern and characteristics of fireflies. It is a powerful swarm intelligence algorithm inspired by the flash phenomenon of the fireflies. In this context, three types of meta-heuristics called Artificial bee Colony algorithm, Particle Swarm Optimization (PSO) and Firefly algorithms were devised to find optimal solutions of noisy non-linear continuous mathematical models. A series of computational experiments using each algorithm were conducted. The stimulation result of this experiment were analyzed and compared to the best solutions found so The Firefly algorithm in each noisy non linear optimization function seems to perform better and efficient.

Restricted Simplicial Decomposition with Side Constraints is a price decomposition method designed for large‐scale nonlinear problems with a set of linear constraints with special structure and an additional set of linear side constraints. The resultant algorithm iterates by solving a linear subproblem subject to the set of structured constraints and a small nonlinear master problem whose feasible region is defined by the intersection of a simplex and the set of side constraints. The number of variables of the master problem is controlled by a parameter named r. The conditions required for the parameter r and the rules for dropping extreme points of the simplex are established for global convergence of the algorithm. Computational results are presented for nonlinear network problems with side constraints.