scholarly journals Engineering Design Optimization by Dynamic Cluster based Framework using Mixture Surrogates

2019 ◽  
Vol 8 (11S) ◽  
pp. 979-988
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Engineering Application ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimum Number ◽  
Dynamic Cluster ◽  
Engineering Problems ◽  
Costly Function ◽  
Selection Of

The real-world engineering optimization problems utilize complex computational methods like finite element frameworks. These approaches are computationally costly and need high solution time. The work pays attention on finding the optimal solution to these complex engineering problems by using Surrogate Models (SM). SMs are mathematical models, which are utilized to minimize the required number of such costly function evaluations at the time of the optimization cycles. Instead of optimizing the Design Space (DS) as a whole, subregion based strategies are found to be effectual, especially in the cases where prior knowledge of optimal solution is unavailable. In the present work, a surrogate centered optimization scheme is presented for local search, which dynamically sub-divides the DS into an optimum number of sub-regions by choosing the best cluster evaluation techniques as followed by the selection of best mixture SMs for each optimization cycle. For all objective functions and constraint functions in every sub-region, the mixture SMs are created by a combination of two or more single SMs. The MATSuMoTo, the Matlab based SM Toolbox by Juliane Muller and Robert Piché has been adapted for the creation and selection of best mixture SM. In this method, an individual surrogate is combined by utilizing the DempsterShafer theory (DST). Besides the above local search, a global search module is also introduced for ensuring faster convergence. This approach is tested on a constrained optimization benchmark test problem with smaller, disconnected feasible regions. It is perceived that the proposed algorithm accurately located all the local and global optima points with minimum function evaluations. The approach is applied to engineering problems like optimization of Machine Tool Spindle (MTS) design and frontal crash simulation on a full car body. For these engineering application problems also, mixture SMbased sub-region based search strategy is utilized to attain most accurate global optimum solution with a minimal number of costly function evaluations.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Algoritma Elephant Herding Optimization: Permasalahan Multiple Constraints Knapsack 0-1

2018 ◽  
Vol 18 (1) ◽  
pp. 13
Author(s):  
Yulia Dewi Regita ◽  
Kiswara Agung Santoso ◽  
Ahmad Kamsyakawuni
Keyword(s):  
Knapsack Problem ◽  
Simplex Method ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Secondary Data ◽  
Multiple Constraints ◽  
Microsoft Excel ◽  
Storage Media ◽  
Simulation Results ◽  
Selection Of

Optimization problems are often found in everyday life, such as when determining goods to be a limited storage media. This causes the need for the selection of goods in order to obtain profits with the requirements met. This problem in mathematics is usually called a knapsack. Knapsack problem itself has several variations, in this study knapsack type used is multiple constraints knapsack 0-1 which is solved using the Elephant Herding Optimization (EHO) algorithm. The aim of this study is to obtain an optimal solution and study the effectiveness of the algorithm comparing it to the Simplex method in Microsoft Excel. This study uses two data, consisting of primary and secondary data. Based on the results of parameter testing, the proven parameters are nClan, nCi,α,β and MaxGen have a significant effect. The final simulation results have also shown a comparison of the EHO algorithm with the Simplex method having a very small percentage deviation. This shows that the EHO algorithm is effective for completing optimization multiple constraints knapsack 0-1. Keywords: EHO Algorithm, Multiple Constraints Knapsack 0-1 Problem.

Hookes-Jeeves-Based Variant of Memetic Algorithm

2016 ◽  
pp. 450-475
Author(s):  
Dipti Singh ◽  
Kusum Deep
Keyword(s):  
Genetic Algorithms ◽  
Memetic Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Memetic Algorithms ◽  
Global Optimum ◽  
Benchmark Problems ◽  
New Variant ◽  
Optimum Solution ◽  
Global Optimum Solution

Due to their wide applicability and easy implementation, Genetic algorithms (GAs) are preferred to solve many optimization problems over other techniques. When a local search (LS) has been included in Genetic algorithms, it is known as Memetic algorithms. In this chapter, a new variant of single-meme Memetic Algorithm is proposed to improve the efficiency of GA. Though GAs are efficient at finding the global optimum solution of nonlinear optimization problems but usually converge slow and sometimes arrive at premature convergence. On the other hand, LS algorithms are fast but are poor global searchers. To exploit the good qualities of both techniques, they are combined in a way that maximum benefits of both the approaches are reaped. It lets the population of individuals evolve using GA and then applies LS to get the optimal solution. To validate our claims, it is tested on five benchmark problems of dimension 10, 30 and 50 and a comparison between GA and MA has been made.

scholarly journals Spacecraft Multiple-Impulse Trajectory Optimization Using Differential Evolution Algorithm with Combined Mutation Strategies and Boundary-Handling Schemes

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yuehe Zhu ◽  
Hua Wang ◽  
Jin Zhang
Keyword(s):  
Differential Evolution ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Differential Evolution Algorithm ◽  
Optimal Solution ◽  
Global Optimum ◽  
Local Optimum ◽  
Local Optima ◽  
Trial Vector ◽  
Mutation Strategies

Since most spacecraft multiple-impulse trajectory optimization problems are complex multimodal problems with boundary constraint, finding the global optimal solution based on the traditional differential evolution (DE) algorithms becomes so difficult due to the deception of many local optima and the probable existence of a bias towards suboptimal solution. In order to overcome this issue and enhance the global searching ability, an improved DE algorithm with combined mutation strategies and boundary-handling schemes is proposed. In the first stage, multiple mutation strategies are utilized, and each strategy creates a mutant vector. In the second stage, multiple boundary-handling schemes are used to simultaneously address the same infeasible trial vector. Two typical spacecraft multiple-impulse trajectory optimization problems are studied and optimized using the proposed DE method. The experimental results demonstrate that the proposed DE method efficiently overcomes the problem created by the convergence to a local optimum and obtains the global optimum with a higher reliability and convergence rate compared with some other popular evolutionary methods.

scholarly journals Local Search with a SAT Oracle for Combinatorial Optimization

2021 ◽  
pp. 87-104
Author(s):  
Aviad Cohen ◽  
Alexander Nadel ◽  
Vadim Ryvchin
Keyword(s):  
Combinatorial Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Hill Climbing ◽  
Variable Neighbourhood Search ◽  
Np Hard ◽  
Neighbourhood Search ◽  
Sat Solver ◽  
Cell Placement

AbstractNP-hard combinatorial optimization problems are pivotal in science and business. There exists a variety of approaches for solving such problems, but for problems with complex constraints and objective functions, local search algorithms scale the best. Such algorithms usually assume that finding a non-optimal solution with no other requirements is easy. However, what if it is NP-hard? In such case, a SAT solver can be used for finding the initial solution, but how can one continue solving the optimization problem? We offer a generic methodology, called Local Search with SAT Oracle (), to solve such problems. facilitates implementation of advanced local search methods, such as variable neighbourhood search, hill climbing and iterated local search, while using a SAT solver as an oracle. We have successfully applied our approach to solve a critical industrial problem of cell placement and productized our solution at Intel.

Mixture Surrogate Models for Multi- Objective Optimization

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Shailesh S. Kadre ◽  
Vipin K. Tripathi
Keyword(s):  
Finite Element ◽  
Optimization Problems ◽  
Surrogate Models ◽  
Optimization Techniques ◽  
Optimization Process ◽  
Multiple Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Costly Function ◽  
Selection Of

Multi-objective optimization problems (MOOP) involve minimization of more than one objective functions and all of them are to be simultaneously minimized. The solution of these problems involves a large number of iterations. The multi- objective optimization problems related structural optimization of complex engineering structures is usually solved with finite element analysis (FEA). The solution time required to solve these FEA based solutions are very high. So surrogate models or meta- models are used to approximate the finite element solution during the optimization process. These surrogate assisted multi- objective optimization techniques are very commonly used in the current literature. These optimization techniques use evolutionary algorithm and it is very difficult to guarantee the convergence of the final solution, especially in the cases where the budget of costly function evaluations is low. In such cases, it is required to increase the efficiency of surrogate models in terms of accuracy and total efforts required to find the final solutions.In this paper, an advanced surrogate assisted multi- objective optimization algorithm (ASMO) is developed. This algorithm can handle linear, equality and non- linear constraints and can be applied to both benchmark and engineering application problems. This algorithm does not require any prior knowledge for the selection of surrogate models. During the optimization process, best single and mixture surrogate models are automatically selected. The advanced surrogate models are created by MATSuMoTo, the MATLAB based tool box. These mixture models are built by Dempster- Shafer theory (DST). This theory has a capacity to handle multiple model characteristics for the selection of best models. By adopting this strategy, it is ensured that most accurate surrogate models are selected. There can be different kind of surrogate models for objective and constraint functions. Multi-objective optimization of machine tool spindle is studied as the test problem for this algorithm and it is observed that the proposed strategy is able to find the non- dominated solutions with minimum number of costly function evaluations. The developed method can be applied to other benchmark and engineering applications.

Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview

2015 ◽  
Vol 24 (3-4) ◽  
pp. 129-143
Author(s):  
André A. Keller
Keyword(s):  
System Analysis ◽  
Convex Set ◽  
Optimization Problems ◽  
Convex Relaxation ◽  
Engineering Application ◽  
Global Optimum ◽  
Linear Matrix ◽  
Quadratic Term ◽  
Relaxation Techniques ◽  
Convex Envelopes

AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are replaced by new numerous pairwise products of the constraints. In the linearization phase, each distinct quadratic term is replaced by a single new RLT variable. This RLT process produces an LP relaxation. The LP-RLT yieds a lower bound on the global minimum. LMI formulations (linear matrix inequalities) have been proposed to treat efficiently with nonconvex sets. An LMI is equivalent to a system of polynomial inequalities. A semialgebraic convex set describes the system. The feasible sets are spectrahedra with curved faces, contrary to the LP case with polyhedra. Successive LMI relaxations of increasing size yield the global optimum. Nonlinear inequalities are converted to an LMI form using Schur complements. Optimizing a nonconvex polynomial is equivalent to the LP over a convex set. Engineering application interests include system analysis, control theory, combinatorial optimization, statistics, and structural design optimization.

scholarly journals An Enhanced Differential Evolution with Elite Chaotic Local Search

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Zhaolu Guo ◽  
Haixia Huang ◽  
Changshou Deng ◽  
Xuezhi Yue ◽  
Zhijian Wu
Keyword(s):  
Local Search ◽  
Differential Evolution ◽  
Search Strategy ◽  
Optimization Problems ◽  
Test Functions ◽  
Adaptation Mechanism ◽  
Parameter Adaptation ◽  
Chaotic Search ◽  
Engineering Problems ◽  
Complex Optimization

Differential evolution (DE) is a simple yet efficient evolutionary algorithm for real-world engineering problems. However, its search ability should be further enhanced to obtain better solutions when DE is applied to solve complex optimization problems. This paper presents an enhanced differential evolution with elite chaotic local search (DEECL). In DEECL, it utilizes a chaotic search strategy based on the heuristic information from the elite individuals to promote the exploitation power. Moreover, DEECL employs a simple and effective parameter adaptation mechanism to enhance the robustness. Experiments are conducted on a set of classical test functions. The experimental results show that DEECL is very competitive on the majority of the test functions.

scholarly journals A bi-stage surrogate-assisted hybrid algorithm for expensive optimization problems

2021 ◽  
Author(s):  
Zhihai Ren ◽  
Chaoli Sun ◽  
Ying Tan ◽  
Guochen Zhang ◽  
Shufen Qin
Keyword(s):  
Local Search ◽  
Hybrid Algorithm ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Second Stage ◽  
Expensive Problems ◽  
Expensive Optimization Problems ◽  
Expensive Optimization

AbstractSurrogate-assisted meta-heuristic algorithms have shown good performance to solve the computationally expensive problems within a limited computational resource. Compared to the method that only one surrogate model is utilized, the surrogate ensembles have shown more efficiency to get a good optimal solution. In this paper, we propose a bi-stage surrogate-assisted hybrid algorithm to solve the expensive optimization problems. The framework of the proposed method is composed of two stages. In the first stage, a number of global searches will be conducted in sequence to explore different sub-spaces of the decision space, and the solution with the maximum uncertainty in the final generation of each global search will be evaluated using the exact expensive problems to improve the accuracy of the approximation on corresponding sub-space. In the second stage, the local search is added to exploit the sub-space, where the best position found so far locates, to find a better solution for real expensive evaluation. Furthermore, the local and global searches in the second stage take turns to be conducted to balance the trade-off of the exploration and exploitation. Two different meta-heuristic algorithms are, respectively, utilized for the global and local search. To evaluate the performance of our proposed method, we conduct the experiments on seven benchmark problems, the Lennard–Jones potential problem and a constrained test problem, respectively, and compare with five state-of-the-art methods proposed for solving expensive problems. The experimental results show that our proposed method can obtain better results, especially on high-dimensional problems.

scholarly journals Visekriterijumska optimizacija izbora izvodjaca projekta

2003 ◽  
Vol 44 (157) ◽  
pp. 7-40
Author(s):  
Jovo Vuleta
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Real Problem ◽  
Multicriterial Optimization ◽  
Past Experiences ◽  
The Given ◽  
Mathematical Operations ◽  
Theory Of Graphs ◽  
Project Realization ◽  
Selection Of

The selection of the best (multicriterial optimal) contractors for project realization is analised in this paper. This problem is one of the most important problems that occurs during the realization of every project, especially the complex one. First we point the problem importance and past experiences and results in its solving. As a conclusion, we state that the problem of selection project realization contractors has been solved by discovering any possible solution, not necessary the optimal one. We have tried to solve one real problem using the model of integer multicriterial optimization type 0-1. The problem was presented by the appropriate mathematical model whose solving leads to multicriterial optimal solution. The special attention was paid to technique and procedure for solving the given model of integer multicriterial optimization. In order to minimize the efforts, the model has been transformed in corresponding network model whose further solving is based on the theory of graphs. The presented procedure decreases the number of mathematical operations and is more simply than most of the usual methods for solving the integer multicriterial type 0-1 optimization problems. At the end, the recommended procedure has been illustrated by a numerical example.

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