A New Approach for Large Non-Linear Integer Optimization Suitable for Implementation on a Distributed Collection of Computers

2000 ◽  
Author(s):  
Ronald H. Nickel ◽  
Igor Mikolic-Torreira ◽  
Jon W. Tolle
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Minimum Cost ◽  
Spare Parts ◽  
Integer Optimization ◽  
Aircraft Carrier ◽  
Windows Nt ◽  
Non Linear ◽  
Super Computer

Abstract We present a new methodology called Multi-Indenture, Multi-Echelon Readiness-Based Sparing (MIMERBS) for solving large, non-linear integer optimization problems that arise in determining the retail and wholesale sparing policies that support the aircraft operating from a deployed aircraft carrier. MIMERBS determines the minimum cost mix of spare parts that meets required levels of expected aircraft availability. The size (thousands of variables), the nonlinear relationship between spare parts and aircraft availability, and the requirement that the variables be integers make this problem hard. We provide a concise description of the MIMERBS model and present data to show how it improves on earlier sparing models. This improvement comes at the price of significant computationally complexity, which in turn makes the optimization problem hard to solve. We describe how we integrated an interior point method with a direct search algorithm to solve this optimization problem. This hybrid algorithm is well suited for implementation on a home-made virtual super-computer made up of several dozen Windows NT computers connected by an office LAN. A description of the virtual super-computer is given in a separate paper. We report on three specific cases we solved using the MIMERBS model, having from 1,000 to 8,000 optimization variables.

An Innovative Multi-Stage Multi-Dimensional Multiple-Inhomogeneous Melody Search Algorithm

2017 ◽  
pp. 1-40 ◽  
Author(s):  
Mohammad Kiani-Moghaddam ◽  
Mojtaba Shivaie
Keyword(s):  
Convex Optimization ◽  
Large Scale ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Symphony Orchestra ◽  
Solution Space ◽  
Innovative Strategy ◽  
Multi Stage ◽  
Non Linear

In this book chapter, the authors present an innovative strategy to enhance performance of the music-inspired algorithms. In this strategy, by using multiple-inhomogeneous music players and three different well-organized stages for improvisation, an innovative symphony orchestra search algorithm (SOSA) is proposed to solve large-scale non-linear non-convex optimization problems. Using multiple-inhomogeneous music players with different tastes, ideas, experiences can conduct players to choose better pitches, and increase the probability of playing a better melody. The strength of the newly proposed algorithm can enhance its superiority in comparison with other music-inspired algorithms, when feasible area of the solution space, and or dimensions of the optimization problem increases. Network expansion planning (NEP) problem has been employed to evaluate the performance of the newly proposed SOSA, compared with other existing optimization algorithms. The NEP problem is a large-scale non-convex optimization problem having a non-linear, mixed-integer nature.

Implementing a Large Non-Linear Integer Optimization on a Distributed Collection of Office Computers

2000 ◽  
Author(s):  
Ronald H. Nickel ◽  
Igor Mikolic-Torreira ◽  
Jon W. Tolle
Keyword(s):  
Fault Tolerant ◽  
Integer Optimization ◽  
Windows Nt ◽  
Non Linear ◽  
Super Computer ◽  
Virtual Computer ◽  
Optimization Methodology ◽  
Performance Results ◽  
Dynamically Configurable ◽  
Computer Resources

Abstract We describe how we implemented the MIMERBS non-linear integer optimization methodology to run across a virtual super-computer of existing Windows NT computers networked together by an ordinary office LAN. We describe how we configured this virtual computer and how we parallelized MIMERBS to work efficiently in view of the high communications costs of our virtual computer. We also describe how we made MIMERBS highly fault-tolerant and dynamically configurable; in particular we describe techniques for handling the loss of individual computers, for automatic on-the-fly addition of new computers, and for dynamic load-balancing. We also describe the techniques we used to share computer resources gracefully with officer workers using the same computers concurrently for ordinary word and data processing. We present performance results from specific MIMERBS applications. These examples show that performance of several gigaFLOPS is possible with just a few dozen ordinary computers on an office LAN.

Optimization Problem

2020 ◽  
pp. 276-291
Author(s):  
Albert N. Voronin
Keyword(s):  
Wide Class ◽  
Multicriteria Optimization ◽  
System Approach ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Systemic Approach ◽  
Multicriteria Decision ◽  
Multicriteria Problems ◽  
Linear Scheme ◽  
Non Linear

A systemic approach to solving multicriteria optimization problems is proposed. The system approach allowed uniting the models of individual schemes of compromises into a single integrated structure that adapts to the situation of adopting a multi-criteria solution. The advantage of the concept of non-linear scheme of compromises is the possibility of making a multicriteria decision formally, without the direct participation of a person. The apparatus of the non-linear scheme of compromises, developed as a formalized tool for the study of control systems with conflicting criteria, makes it possible to solve practically multicriteria problems of a wide class.

Two Meta-Heuristics for Solving Unconstrained Optimization Problems and Machinery Problems

2014 ◽  
Vol 1044-1045 ◽  
pp. 1418-1423
Author(s):  
Pasura Aungkulanon
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Harmony Search ◽  
Particle Swarm ◽  
Finite Sequence ◽  
Swarm Optimization ◽  
Machining Optimization

Machining optimization problem aims to optimize machinery conditions which are important for economic settings. The effective methods for solving these problems using a finite sequence of instructions can be categorized into two groups; exact optimization algorithm and meta-heuristic algorithms. A well-known meta-heuristic approach called Harmony Search Algorithm was used to compare with Particle Swarm Optimization. We implemented and analysed algorithms using unconstrained problems under different conditions included single, multi-peak, curved ridge optimization, and machinery optimization problem. The computational outputs demonstrated the proposed Particle Swarm Optimization resulted in the better outcomes in term of mean and variance of process yields.

Study on Free Search for Combinatorial Optimization Problem

2013 ◽  
Vol 411-414 ◽  
pp. 1904-1910
Author(s):  
Kai Zhong Jiang ◽  
Tian Bo Wang ◽  
Zhong Tuan Zheng ◽  
Yu Zhou
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Process ◽  
Standard Data ◽  
Combinatorial Optimization Problems ◽  
Free Search

An algorithm based on free search is proposed for the combinatorial optimization problems. In this algorithm, a feasible solution is converted into a full permutation of all the elements and a transformation of one solution into another solution can be interpreted the transformation of one permutation into another permutation. Then, the algorithm is combined with intersection elimination. The discrete free search algorithm greatly improves the convergence rate of the search process and enhances the quality of the results. The experiment results on TSP standard data show that the performance of the proposed algorithm is increased by about 2.7% than that of the genetic algorithm.

A Mixed-Integer Memetic Algorithm Applied to Batch Process Optimization

2013 ◽  
Vol 300-301 ◽  
pp. 645-648 ◽  
Author(s):  
Yung Chien Lin
Keyword(s):  
Memetic Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Memetic Algorithms ◽  
Batch Processes ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Genetic Operators ◽  
Search Methods

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a mixed-integer memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and applied to the optimal design of batch processes. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

Thermal morphing anisogrid smart space structures part 2: Ranking of geometric parameter importance, trust region optimization, and performance evaluation

2017 ◽  
Vol 24 (13) ◽  
pp. 2873-2893 ◽  
Author(s):  
Austin A Phoenix ◽  
Jeff Borggaard ◽  
Pablo A Tarazaga
Keyword(s):  
Parameter Optimization ◽  
Optimization Problem ◽  
Optimal Allocation ◽  
Search Algorithm ◽  
Thermal Strain ◽  
Computational Cost ◽  
Trust Region ◽  
Minimum Cost ◽  
Space Mission ◽  
Model Parameters

As future space mission structures are required to achieve more with scarcer resources, new structural configurations and modeling capabilities will be needed to meet the next generation space structural challenges. A paradigm shift is required away from the current structures that are static, heavy, and stiff, to innovative lightweight structures that meet requirements by intelligently adapting to the environment. As the complexity of these intelligent structures increases, the computational cost of the modeling and optimization efforts become increasingly demanding. Novel methods that identify and reduce the number of parameters to only those most critical considerably reduce these complex problems, allowing highly iterative evaluations and in-depth optimization efforts to be computationally feasible. This parameter ranking methodology will be demonstrated on the optimization of the thermal morphing anisogrid boom. The proposed novel morphing structure provides high precision morphing through the use of thermal strain as the sole actuation mechanism. The morphing concept uses the helical members in the anisogrid structure to provide complex constrained actuations that can achieve the six degree of freedom morphing capability. This structure provides a unique potential to develop an integrated structural morphing system, where the adaptive morphing capability is integrated directly into the primary structure. To identify parameters of interest, the Q-DEIM model reduction algorithm is implemented to rank the model parameters based on their impact on the morphing performance. This parameter ranking method provides insight into the system and enables the optimal allocation of computational and engineering resources to the most critical areas of the system for optimization. The methodology, in conjunction with a singular value decomposition (SVD), provides a ranking and identifies parameters of relative importance. The SVD is used to truncate the nine parameters problem at two locations, generating a five parameter optimization problem and a three parameter optimization problem. To evaluate the ranking, a parameter sweep in conjunction with a simple minimum cost function search algorithm will compare all 120 five parameter ranking orders to the Q-DEIM ranking. This reduced parameter set significantly reduces the parameter complexity and the computational cost of the model optimization. This paper will present the methodology to define the resulting performance of the optimal thermal morphing anisogrid structure, minimum morphing control, and the systems frequency response capability as a function of available power.

Gradient-based optimization method for interference suppression of linear arrays by the amplitude-only and phase-only control

2021 ◽  
pp. 1-7
Author(s):  
Renjing Gao ◽  
Yi Tang ◽  
Qi Wang ◽  
Shutian Liu
Keyword(s):  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Interference Suppression ◽  
Computation Time ◽  
Optimization Method ◽  
Main Beam ◽  
Linear Arrays ◽  
Gradient Based

Abstract This paper presents a gradient-based optimization method for interference suppression of linear arrays by controlling the electrical parameters of each array element, including the amplitude-only and phase-only. Gradient-based optimization algorithm (GOA), as an efficient optimization algorithm, is applied to the optimization problem of the anti-interference arrays that is generally solved by the evolutionary algorithms. The goal of this method is to maximize the main beam gain while minimizing the peak sidelobe level (PSLL) together with the null constraint. To control the nulls precisely and synthesize the radiation pattern accurately, the full-wave method of moments is used to consider the mutual coupling among the array elements rigorously. The searching efficiency is improved greatly because the gradient (sensitivity) information is used in the algorithm for solving the optimization problem. The sensitivities of the design objective and the constraint function with respect to the design variables are analytically derived and the optimization problems are solved by using GOA. The results of the GOA can produce the desired null at the specific positions, minimize the PSLL, and greatly shorten the computation time compared with the often-used non-gradient method such as genetic algorithm and cuckoo search algorithm.

Structural Optimization With Nonlinear Goal Programming Using Powell’s Method

1991 ◽  
Author(s):  
Mohamed E. M. El-Sayed ◽  
T. S. Jang
Keyword(s):  
Structural Optimization ◽  
Goal Programming ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Numerical Test ◽  
Design Tool ◽  
Test Cases ◽  
Programming Techniques ◽  
Ordered Design

Abstract This paper presents a method for solving structural optimization problems using nonlinear goal programming techniques. The developed method removes the difficulty of having to define an objective function and constraints. It also has the capacity of handling rank ordered design objectives or goals. The formulation of the structural optimization problem into a goal programming form is discussed. The resulting optimization problem is solved using Powell’s conjugate direction search algorithm. To demonstrate the effectiveness of the method, as a design tool, the solutions of some numerical test cases are included.

Sign in / Sign up

Export Citation Format

Share Document