scholarly journals Decentralized Multisubsystem Co-Design Optimization Using Direct Collocation and Decomposition-Based Methods

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Tianchen Liu ◽  
Shapour Azarm ◽  
Nikhil Chopra
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Bilevel Optimization ◽  
Simultaneous Optimization ◽  
Computational Time ◽  
Nonlinear Program ◽  
Design Problems ◽  
Direct Collocation ◽  
Physical Plant

Abstract Multisubsystem co-design refers to the simultaneous optimization of physical plant and controller of a system decomposed into multiple interconnected subsystems. In this paper, two decentralized (multilevel and bilevel) approaches are formulated to solve multisubsystem co-design problems, which are based on the direct collocation and decomposition-based optimization methods. In the multilevel approach, the problem is decomposed into two bilevel optimization problems, one for the physical plant and the other for the control part. In the bilevel approach, the problem is decomposed into subsystem optimization subproblems, with each subproblem having the optimization model for physical plant and control parts together. In both cases, the entire time horizon is discretized to convert the continuous optimal control problem into a finite-dimensional nonlinear program. The optimality condition decomposition method is employed to solve the converted problem in a decentralized manner. Using the proposed approaches, it is possible to obtain an optimal solution for more generalized multisubsystem co-design problems than was previously possible, including those with nonlinear dynamic constraints. The proposed approaches are applied to a numerical and engineering example. For both examples, the solutions obtained by the decentralized approaches are compared with a centralized (all-at-once) approach. Finally, a scalable version of the engineering example is solved to demonstrate that using a simulated parallelization with and without communication delays, the computational time of the proposed decentralized approaches can outperform a centralized approach as the size of the problem increases.

A Decentralized Approach for Multi-Subsystem Co-Design Optimization Using Direct Collocation Method

2017 ◽  
Author(s):  
Tianchen Liu ◽  
Shapour Azarm ◽  
Nikhil Chopra
Keyword(s):  
Optimization Methods ◽  
Simultaneous Optimization ◽  
Dual Decomposition ◽  
Design Problems ◽  
Direct Collocation ◽  
Physical Plant ◽  
Finite Dimensional ◽  
Direct Collocation Method ◽  
Grid Points ◽  
And Control

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.

Genetic Algorithms for Optimization of Building Envelopes and the Design and Control of HVAC Systems

2003 ◽  
Vol 125 (3) ◽  
pp. 343-351 ◽  
Author(s):  
L. G. Caldas ◽  
L. K. Norford
Keyword(s):  
Genetic Algorithms ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimization Method ◽  
Hvac Systems ◽  
Design Problems ◽  
Building Walls ◽  
Building Form ◽  
And Control ◽  
Future Work

Many design problems related to buildings involve minimizing capital and operating costs while providing acceptable service. Genetic algorithms (GAs) are an optimization method that has been applied to these problems. GAs are easily configured, an advantage that often compensates for a sacrifice in performance relative to optimization methods selected specifically for a given problem, and have been shown to give solutions where other methods cannot. This paper reviews the basics of GAs, emphasizing multi-objective optimization problems. It then presents several applications, including determining the size and placement of windows and the composition of building walls, the generation of building form, and the design and operation of HVAC systems. Future work is identified, notably interfaces between a GA and both simulation and CAD programs.

Non-convex Optimization via Strongly Convex Majorization-minimization

2019 ◽  
Vol 63 (4) ◽  
pp. 726-737
Author(s):  
Azita Mayeli
Keyword(s):  
Convex Optimization ◽  
Cost Function ◽  
Local Minimum ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Small Radius ◽  
Mm Algorithm ◽  
Strongly Convex ◽  
Nonsmooth Nonconvex Optimization

AbstractIn this paper, we introduce a class of nonsmooth nonconvex optimization problems, and we propose to use a local iterative minimization-majorization (MM) algorithm to find an optimal solution for the optimization problem. The cost functions in our optimization problems are an extension of convex functions with MC separable penalty, which were previously introduced by Ivan Selesnick. These functions are not convex; therefore, convex optimization methods cannot be applied here to prove the existence of optimal minimum point for these functions. For our purpose, we use convex analysis tools to first construct a class of convex majorizers, which approximate the value of non-convex cost function locally, then use the MM algorithm to prove the existence of local minimum. The convergence of the algorithm is guaranteed when the iterative points $x^{(k)}$ are obtained in a ball centred at $x^{(k-1)}$ with small radius. We prove that the algorithm converges to a stationary point (local minimum) of cost function when the surregators are strongly convex.

scholarly journals A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 377
Author(s):  
Nimit Nimana
Keyword(s):  
Fixed Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Splitting Method ◽  
Optimal Solution ◽  
Bilevel Optimization ◽  
Convergence Properties ◽  
Nonlinear Operators ◽  
Convex Optimization Problems ◽  
Feasible Points

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.

Hybrid Weights-Utility and Taguchi Method for Multi-Objective Optimization Problems

2015 ◽  
Vol 764-765 ◽  
pp. 305-308
Author(s):  
Kuang Hung Hsien ◽  
Shyh Chour Huang
Keyword(s):  
Taguchi Method ◽  
Engineering Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Utility Concept ◽  
Engineering Design Problems

In this paper, hybrid weights-utility and Taguchi method is proposed to solve multi-objective optimization problems. The new method combines the Taguchi method and the weights-utility concept. The weights of the objective function and overall utility values are very important for the weights-utility, and must be set correctly in order to obtain an optimal solution. Application of this method to engineering design problems is illustrated with the aid of one case study, and the result shows that the weights-utlity method is able to handle multi-objective optimization problems, with an optimal solution which better meets the demand of multi-objective optimization problems than the utility concept does.

scholarly journals Optimization of Traveling Salesman Problem Using Affinity Propagation Clustering and Genetic Algorithm

2015 ◽  
Vol 5 (4) ◽  
pp. 239-245 ◽  
Author(s):  
Ahmad Fouad El-Samak ◽  
Wesam Ashour
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solution Space ◽  
Affinity Propagation ◽  
Computational Time ◽  
Combinatorial Optimization Problems ◽  
Affinity Propagation Clustering ◽  
Core Idea ◽  
Computation Algorithms

Abstract Combinatorial optimization problems, such as travel salesman problem, are usually NP-hard and the solution space of this problem is very large. Therefore the set of feasible solutions cannot be evaluated one by one. The simple genetic algorithm is one of the most used evolutionary computation algorithms, that give a good solution for TSP, however, it takes much computational time. In this paper, Affinity Propagation Clustering Technique (AP) is used to optimize the performance of the Genetic Algorithm (GA) for solving TSP. The core idea, which is clustering cities into smaller clusters and solving each cluster using GA separately, thus the access to the optimal solution will be in less computational time. Numerical experiments show that the proposed algorithm can give a good results for TSP problem more than the simple GA.

Grillage Optimization with Multiple Objectives

2006 ◽  
Vol 306-308 ◽  
pp. 517-522
Author(s):  
Ki Sung Kim ◽  
Kyung Su Kim ◽  
Ki Sup Hong
Keyword(s):  
Structural Optimization ◽  
Structural Design ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Pareto Optimal Solution ◽  
Multiple Objectives ◽  
Pareto Optimal ◽  
Design Environment ◽  
Design Problems ◽  
Solution Methods

The structural design problems are acknowledged to be commonly multicriteria in nature. The various multicriteria optimization methods are reviewed and the most efficient and easy-to-use Pareto optimal solution methods are applied to structural optimization of grillages under lateral uniform load. The result of the study shows that Pareto optimal solution methods can easily be applied to structural optimization with multiple objectives, and the designer can have a choice from those Pareto optimal solutions to meet an appropriate design environment.

scholarly journals Surrogate Modeling Approaches for Multiobjective Optimization: Methods, Taxonomy, and Results

2020 ◽  
Vol 26 (1) ◽  
pp. 5
Author(s):  
Kalyanmoy Deb ◽  
Proteek Chandan Roy ◽  
Rayan Hussein
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Adaptive Strategy ◽  
Optimization Methods ◽  
Superior Performance ◽  
Pareto Optimal ◽  
Optimization Strategy ◽  
Conflicting Objectives ◽  
The Individual

Most practical optimization problems are comprised of multiple conflicting objectives and constraints which involve time-consuming simulations. Construction of metamodels of objectives and constraints from a few high-fidelity solutions and a subsequent optimization of metamodels to find in-fill solutions in an iterative manner remain a common metamodeling based optimization strategy. The authors have previously proposed a taxonomy of 10 different metamodeling frameworks for multiobjective optimization problems, each of which constructs metamodels of objectives and constraints independently or in an aggregated manner. Of the 10 frameworks, five follow a generative approach in which a single Pareto-optimal solution is found at a time and other five frameworks were proposed to find multiple Pareto-optimal solutions simultaneously. Of the 10 frameworks, two frameworks (M3-2 and M4-2) are detailed here for the first time involving multimodal optimization methods. In this paper, we also propose an adaptive switching based metamodeling (ASM) approach by switching among all 10 frameworks in successive epochs using a statistical comparison of metamodeling accuracy of all 10 frameworks. On 18 problems from three to five objectives, the ASM approach performs better than the individual frameworks alone. Finally, the ASM approach is compared with three other recently proposed multiobjective metamodeling methods and superior performance of the ASM approach is observed. With growing interest in metamodeling approaches for multiobjective optimization, this paper evaluates existing strategies and proposes a viable adaptive strategy by portraying importance of using an ensemble of metamodeling frameworks for a more reliable multiobjective optimization for a limited budget of solution evaluations.

scholarly journals Discrete self-organizing migration algorithm and p-location problems

2020 ◽  
Vol 11 (2) ◽  
pp. 241-248
Author(s):  
Jaroslav Janacek ◽  
Marek Kvet
Keyword(s):  
Optimization Problems ◽  
Computational Study ◽  
Human Life ◽  
Optimal Solution ◽  
Location Problems ◽  
Computational Time ◽  
Exact Methods ◽  
Practical Applications ◽  
Special Adaptation ◽  
Self Organizing

Mathematical modelling, and integer programming generally, has many practical applications in different areas of human life. Effective and fast solving approaches for various optimization problems play an important role in the decision-making process and therefore, big attention is paid to the development of many exact and approximate algorithms. This paper deals only with a special class of location problems in which given number of facilities are to be chosen to minimize the objective function value. Since the exact methods are not suitable for their unpredictable computational time or memory demands, we focus here on possible usage of a special type of a particle swarm optimization algorithm transformed by discretization and meme usage into so-called discrete self-organizing migrating algorithm. In the paper, there is confirmed that it is possible to suggest a sophisticated heuristic for zero-one programming problem, which can produce near-to-optimal solution in much smaller time than the time demanded by exact methods. We introduce a special adaptation of the discrete self-organizing migration algorithm to the $p$-location problem making use of the path-relinking method. In the theoretical part of this paper, we introduce several strategies of the migration process. To verify their features and effectiveness, a computational study with real-sized benchmarks was performed. The main goal of the experiments was to find the most efficient version of the suggested solving tool.

A Constraint Satisfaction Approach for Multi-Attribute Design Optimization Problems

1997 ◽  
Author(s):  
Joseph D’Ambrosio ◽  
Timothy Darr ◽  
William Birmingham
Keyword(s):  
Constraint Satisfaction ◽  
Value Function ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Compact Representation ◽  
Constrained Optimization Problems ◽  
Design Problems ◽  
Trade Off ◽  
The Value Function

Abstract In this paper, we describe a multi-attribute domain CSP approach for solving a class of discrete, constrained, optimization problems. The multi-attribute domain CSP formulation provides a compact representation for design problems characterized by multiple, conflicting attributes. Design trade-off information is represented by a multi-attribute value function. Necessary conditions for an optimal solution, defined in terms of the value function, are represented as constraints. This provides a uniform problem-solving approach (constraint satisfaction) for identifying solutions that are both feasible and of high value. We present and characterize a consistency algorithm for this type of CSP.

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