Many optimization applications have two or more decision variables. The previous chapters focused on univariate, one-DV, one-dimensional (1-D) applications. Although N -DV applications are more frequently encountered, univariate searches are important, and they reveal key issues in relatively uncomplicated situations. There are new issues and techniques associated with 2-D and higher-dimension applications, and this chapter begins a section related to 2-D, two-decision variable, and N -D applications. Each section of this book on optimization algorithms introduces techniques with 2-D examples and then extends the optimization techniques to N -D applications. In 2-D, we still have the generic optimization concept for maximization.

The objective is to improve the optimizers, to optimize the optimization algorithms. Specific metrics would be to maximize the probability of finding the global optimum and robustness to aberrations (constraints, nonlinearities, stochastic response, discontinuities, flat spots, etc.) while minimizing computational work (of both the algorithm and number of function evaluations) and minimizing complexity (for either programmer or user). In any one optimizer, there seem to be dozens of enhancements the lead to improvements.

The term surface aberrations refers to features of the OF response to DVs, features of the topology, that make it difficult for optimization algorithms. Finding the optimum of an unconstrained quadratic surface is a trivial exercise. However, for many applications several types of OF features cause difficulty for the algorithm. These are easily visualized in the three dimension of a 2-D application (OF response to DV1 and DV2) but translate to 1-D and N -D applications. The following illustrations show the 3-D net and/or 2-D contour map patterns.

For the most part, you will use pre-written optimizers to solve for the model coefficient values. In optimization terminology these are the optimal DV (decision variable) values, noted by the symbol DV*. However, you will need to make many choices related to the algorithm and its parameter choices, to the convergence criterion and its thresholds, to the number of starts, to the start locations, and so on. Accordingly, you should understand optimization.

Light ray optimization is an intelligent algorithm simulating the propagation process of light rays in inhomogeneous media. The searching area is divided by grids in this algorithm, and then the optimal searching path is assumed to be the propagation path of light rays. Gradient information is not necessary and only a few parameters are needed to be adjusted in light ray optimization, so it is simple and easy to be used. Light ray optimization algorithm was used to solve one dimensional optimization problems, and convergence for single extreme value problems was proved in this paper. Numerical experimental results showed that the algorithm is feasible and effective.

XML is rapidly emerging as a standard on the Wiki. How to rapidly search and query XML documents efficiently has received many attentions. To improve the efficiency of index bulk deletion on XML data, an optimization algorithm framework is brought forward to combine the ant optimization algorithm and index bulk deletion algorithm. In this framework, information collection model collects the information when the system is running, cost estimation model collects the cost information of all index bulk deletion algorithms, the optimization algorithm framework simulates the information collected by information collection model and cost estimation, and chooses the optimization bulk deletion algorithm, and the index model finish the index bulk deletion. To improve deletion efficiency, a vertical bulk deletion algorithm is brought forward in this paper. Experimental results from our prototype system implementation highlight the correctness and efficiency of our solution, and the framework can choose the optimization bulk deletion algorithm in all case.

Grid computing has emerged as an important new field, distinguished from conventional distributed computing by its focus on large-scale resource sharing, innovative applications, and, in some cases, high-performance orientation. QoS-aware service composition is a key requirement in Grid environments since it enables users to fulfill his/her required complex tasks while meeting different global Quality of Service (QoS) constraints. The problem of QoS-aware grid service composition is known to be a NP-hard problem. In this paper a novel Ant Colony Optimization (ACO) algorithm is proposed for QoSaware grid service composition to find near optimal composite service. This paper also presents a set of experiments conducted to evaluate the efficiency of proposed algorithm.

Ship stowage scheduling of container terminal needs to consider the safety of the ship and transport economics. The strategic decisions of this paper are that which bay each stacking unit is assigned and the stacking location of each stacking unit in bay. The goals are minimizing container reshuffle rate on board, minimizing the center of gravity of the ship, holding appropriate trim and ensuring that the heavy containers stacking in the middle of the ship. The classification strategy and stacking strategy in bay are proposed. Based on this, a scheduling model of ship stowage is established. A genetic algorithm which bases on group coding method and the stacking strategy in bay which bases on the greedy algorithm are proposed as the resolution of the model. It can be concluded that combinatorial optimization algorithm and strategy are efficient and effective as the approach to ship stowage scheduling of container terminal from the analysis of the experiment's result.

On-Line Analytical Processing (OLAP) tools are frequently used in business, science and health to extract useful knowledge from massive databases. An important and hard optimization problem in OLAP data warehouses is the view selection problem, consisting of selecting a set of aggregate views of the data for speeding up future query processing. We apply the Bayesian optimization algorithm (BOA)to view selection under a size constraint. Our emphasis is to determine the suitability of the combination of BOA with constraint handling to the view selection problem, compared to a widely used UMDA. The BOA are competitive with the UMDA on a variety of problem instances, often finding approximate optimal solutions in a reasonable amount of time.

Genetic Algorithm (GA) is restricted by actual system computing ability. Because of the limited number of population and iteration, the choice of initiation Population is a vital of fact, which directly influents the result of algorithm and the efficiency. GA's Initiation Population is created by the path of well-proportioned choosing seed or stochastic choosing seed generally, but both of them have a vice of inefficient search. The paper, combining with interrelated theories in graph theory, brings forward two kinds of Optimization Algorithms of Initiation Population based on Minimize Spanning Tree Local-Effective-Information Theory towards the limitations of them, and we successes it to TSP by example analysis.

The science of quantum information is a class of calculation that's the result of a tie between Quantum Physics and Computer Science. Observing and studying the single quantum objects, is the basis of quantum calculations because these quantum items can be used as physical locations of quantum bits. In the quantum calculations, the basis that we introduce is the q-bit. The concept of quantum parallelism leads to development of quantum algorithm like the Shore Algorithm. These algorithms, using the new mechanisms and using the abilities of quantum mechanics can solve a great deal of problems more widely with more efficiency in comparison to classical algorithms. Such algorithms are very successful in doing repetitive calculations to decode the codes. Usually in order to optimize the development of test data is evolutionary algorithms are used. In this research, we are going to develop the efficiency of this mutation test optimization algorithms that's used in the optimizer segment. Then, we want to make a comparison with common optimizer algorithms such as usual genetics and bacteriological. In the end, we want to reduce some of the problems including getting stuck in the local minimums.

Gray Code Optimization (GCO) algorithm is a deterministic algorithm based on the Gray code representation. It sometimes suffers from slow convergence and sub-optimal solutions. Expectation Maximization (EM) algorithm is used to analyze how the GCO explores the search space. The results indicate that it is similar to generating samples with a mixture Gaussian distribution. Based on these findings, a novel stochastic optimization algorithm based on the mixture Gaussian model is proposed. The new algorithm is applied to molecule conformation search. Obtaining global minimum energy conformations of molecule is a very hard optimization problem. The difficulty arises from the following two factors: the conformational space of a reasonable size molecular is very large, and there are many local minima that are hard to sample efficiently. The energy landscape in the conformational space is very rugged, and there are many large barriers between local minima.