Bilevel Toll Optimization Problems: A Heuristic Algorithm Based Upon Sensitivity Analysis

2012 ◽  
pp. 135-143
Author(s):  
Nataliya I. Kalashnykova ◽  
Vyacheslav V. Kalashnikov ◽  
Roberto C. Herrera Maldonado
Keyword(s):  
Sensitivity Analysis ◽  
Heuristic Algorithm ◽  
Optimization Problems

Parameter Sensitivity Analysis of a Large-Scale System With Several Components Interacting in Series

1989 ◽  
Author(s):  
H. Torab
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Optimization Problems ◽  
Parameter Sensitivity ◽  
Engineering Optimization ◽  
Parameter Sensitivity Analysis ◽  
Large Scale Systems ◽  
In Series ◽  
Special Case ◽  
Engineering Optimization Problems

Abstract Parameter sensitivity for large-scale systems that include several components which interface in series is presented. Large-scale systems can be divided into components or sub-systems to avoid excessive calculations in determining their optimum design. Model Coordination Method of Decomposition (MCMD) is one of the most commonly used methods to solve large-scale engineering optimization problems. In the Model Coordination Method of Decomposition, the vector of coordinating variables can be partitioned into two sub-vectors for systems with several components interacting in series. The first sub-vector consists of those variables that are common among all or most of the elements. The other sub-vector consists of those variables that are common between only two components that are in series. This study focuses on a parameter sensitivity analysis for this special case using MCMD.

scholarly journals Multi-Objective Robust Optimization Using a Postoptimality Sensitivity Analysis Technique: Application to a Wind Turbine Design

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis ◽  
Ricardo Soto ◽  
Broderick Crawford
Keyword(s):  
Sensitivity Analysis ◽  
Robust Optimization ◽  
Wind Turbine ◽  
Optimization Design ◽  
Optimization Problems ◽  
Design Environment ◽  
Multi Objective ◽  
Pareto Ranking ◽  
Analysis Technique ◽  
Robust Optimization Design

Toward a multi-objective optimization robust problem, the variations in design variables (DVs) and design environment parameters (DEPs) include the small variations and the large variations. The former have small effect on the performance functions and/or the constraints, and the latter refer to the ones that have large effect on the performance functions and/or the constraints. The robustness of performance functions is discussed in this paper. A postoptimality sensitivity analysis technique for multi-objective robust optimization problems (MOROPs) is discussed, and two robustness indices (RIs) are introduced. The first one considers the robustness of the performance functions to small variations in the DVs and the DEPs. The second RI characterizes the robustness of the performance functions to large variations in the DEPs. It is based on the ability of a solution to maintain a good Pareto ranking for different DEPs due to large variations. The robustness of the solutions is treated as vectors in the robustness function space (RF-Space), which is defined by the two proposed RIs. As a result, the designer can compare the robustness of all Pareto optimal solutions and make a decision. Finally, two illustrative examples are given to highlight the contributions of this paper. The first example is about a numerical problem, whereas the second problem deals with the multi-objective robust optimization design of a floating wind turbine.

Economic Load Dispatch With Multiple Fuel Options and Valve Point Effect Using Cuckoo Search Algorithm With Different Distributions

2020 ◽  
Vol 9 (3) ◽  
pp. 24-38
Author(s):  
Cuong Dinh Tran ◽  
Tam Thanh Dao ◽  
Ve Song Vo
Keyword(s):  
Random Walk ◽  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cauchy Distribution ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Natural Phenomenon ◽  
Economic Load Dispatch ◽  
Valve Point Effect

The cuckoo search algorithm (CSA), a new meta-heuristic algorithm based on natural phenomenon of the cuckoo species and Lévy flights random walk has been widely and successfully applied to several optimization problems so far. In the article, two modified versions of CSA, where new solutions are generated using two distributions including Gaussian and Cauchy distributions in addition to imposing bound by best solutions mechanisms are proposed for solving economic load dispatch (ELD) problems with multiple fuel options. The advantages of CSA with Gaussian distribution (CSA-Gauss) and CSA with Cauchy distribution (CSA-Cauchy) over CSA with Lévy distribution and other meta-heuristic are fewer parameters. The proposed CSA methods are tested on two systems with several load cases and obtained results are compared to other methods. The result comparisons have shown that the proposed methods are highly effective for solving ELD problem with multiple fuel options and/nor valve point effect.

Origami Folding and Bar Frameworks

2014 ◽  
Author(s):  
Alejandro R. Diaz
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Optimization Problems ◽  
Undirected Graph ◽  
Geometric Optimization ◽  
Order Effects ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Higher Order Effects

One of the more computationally demanding tasks in a process of synthesizing “from scratch” origami crease patterns designed for a given purpose involve a simulation capability to track the progression of the folding process as the pattern folds. This work presents an approach to simulate origami folding based on bar frameworks. The work is related to joint frameworks and projected polyhedral, as they apply to folding. The analysis starts from a representation of a crease pattern as an undirected graph G(E,V) formed by edges E and vertices V. A framework G(p) is an instance of G where the vertex locations are assigned positions according to a vector valued function p(t), where t marks the folding progression and t=0 represents the initial, flat configuration. The strategy presented is based on finding a sequence of instances {p(1), p(2), …} corresponding to an analytic flex p, i.e., functions such that edges in all G(p(t)) have the same length. The method is based on using a finite element description of a bar framework corresponding to a truss-like structure congruent with G(p). Solutions to an eigenvalue problem associated with this structure provide the means to update from p(t) to p(t+1). Two simple (purely geometric) optimization problems adjust the update to compensate for higher order effects, guaranteeing that the length of the edges remain constant. The methodology can be used to achieve configurations close to “flat folding”, provided that no interference of the faces occurs along the way. We expected that physically-motivated constraints (stresses, deformations, etc.) and sensitivity analysis computations will be more easily represented in this framework and therefore this formulation will have an advantage over more standard “origami mathematics” approaches. The approach is illustrated with an example of folding a simple 10-crease pattern.

Using Chemotherapy Science Algorithm (CSA) to Solve the Knapsack Problem

2018 ◽  
Vol 7 (1) ◽  
pp. 86-103
Author(s):  
Mohammad Hassan Salmani ◽  
Kourosh Eshghi
Keyword(s):  
Cell Size ◽  
Knapsack Problem ◽  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Cell Area ◽  
Collateral Damage ◽  
Cell Position ◽  
Feasible Solutions

Optimization, which, by definition, can help one find the best solution from all feasible solutions, has sometimes been an interesting and important area for research in science. Solving real and hard optimization problems calls for developing approximate, heuristic, and meta-heuristic algorithms. In this article, a new meta-heuristic algorithm is proposed on the basis of the chemotherapy method to cure cancers – this algorithm mainly searches the infeasible region. As in chemotherapy, this algorithm tries to kill unsatisfactory (especially infeasible) solutions (cancers cells); however, collateral damage is sometimes inevitable – some healthy, innocuous, and good cells might be targeted as well. Also, different conceptual terms including Cell Size, Cell Position, Cell Area, and Random Cells are presented and defined in this article. Furthermore, Chemotherapy Science Algorithm (CSA) and its structure are tested based on benchmark Knapsack Problem. Reported results show the efficiency of the proposed algorithm.

scholarly journals Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by Arcs

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Igor Stojanović ◽  
Ivona Brajević ◽  
Predrag S. Stanimirović ◽  
Lev A. Kazakovtsev ◽  
Zoran Zdravev
Keyword(s):  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Facility Location Problem ◽  
Metaheuristic Algorithms ◽  
Feasible Region ◽  
Weber Problem ◽  
Bee Colony ◽  
Feasible Solutions ◽  
Weiszfeld Procedure

The continuous planar facility location problem with the connected region of feasible solutions bounded by arcs is a particular case of the constrained Weber problem. This problem is a continuous optimization problem which has a nonconvex feasible set of constraints. This paper suggests appropriate modifications of four metaheuristic algorithms which are defined with the aim of solving this type of nonconvex optimization problems. Also, a comparison of these algorithms to each other as well as to the heuristic algorithm is presented. The artificial bee colony algorithm, firefly algorithm, and their recently proposed improved versions for constrained optimization are appropriately modified and applied to the case study. The heuristic algorithm based on modified Weiszfeld procedure is also implemented for the purpose of comparison with the metaheuristic approaches. Obtained numerical results show that metaheuristic algorithms can be successfully applied to solve the instances of this problem of up to 500 constraints. Among these four algorithms, the improved version of artificial bee algorithm is the most efficient with respect to the quality of the solution, robustness, and the computational efficiency.

A Hybrid Meta-Heuristic Algorithm for Vehicle Routing Problem with Time Windows

2015 ◽  
Vol 24 (06) ◽  
pp. 1550021 ◽  
Author(s):  
Esam Taha Yassen ◽  
Masri Ayob ◽  
Mohd Zakree Ahmad Nazri ◽  
Nasser R. Sabar
Keyword(s):  
Simulated Annealing ◽  
Vehicle Routing ◽  
Heuristic Algorithm ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Time Windows ◽  
Harmony Search ◽  
Harmony Search Algorithm ◽  
Routing Problem

Harmony search algorithm, which simulates the musical improvisation process in seeking agreeable harmony, is a population based meta-heuristics algorithm for solving optimization problems. Although it has been successfully applied on various optimization problems; it suffers the slow convergence problem, which greatly hinders its applicability for getting good quality solution. Therefore, in this work, we propose a hybrid meta-heuristic algorithm that hybridizes a harmony search with simulated annealing for the purpose of improving the performance of harmony search algorithm. Harmony search algorithm is used to explore the search spaces. Whilst, simulated annealing algorithm is used inside the harmony search algorithm to exploit the search space and further improve the solutions that are generated by harmony search algorithm. The performance of the proposed algorithm is tested using the Solomon's Vehicle Routing Problem with Time Windows (VRPTW) benchmark. Numerical results demonstrate that the hybrid approach is better than the harmony search without simulated annealing and the hybrid also proves itself to be more competent (if not better on some instances) when compared to other approaches in the literature.

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