scholarly journals A transformation-based discretization method for solving general semi-infinite optimization problems

2020 ◽  
Author(s):  
Jan Schwientek ◽  
Tobias Seidel ◽  
Karl-Heinz Küfer
Keyword(s):  
Test Problem ◽  
Optimization Problems ◽  
The Other ◽  
Discretization Method ◽  
Infinite Index ◽  
Index Set ◽  
Solution Approach ◽  
Discretization Methods ◽  
Convergence Results ◽  
Multiple Variable

Abstract Discretization methods are commonly used for solving standard semi-infinite optimization (SIP) problems. The transfer of these methods to the case of general semi-infinite optimization (GSIP) problems is difficult due to the $$\mathbf {x}$$ x -dependence of the infinite index set. On the other hand, under suitable conditions, a GSIP problem can be transformed into a SIP problem. In this paper we assume that such a transformation exists globally. However, this approach may destroy convexity in the lower level, which is very important for numerical methods. We present in this paper a solution approach for GSIP problems, which cleverly combines the above mentioned two techniques. It is shown that the convergence results for discretization methods in the case of SIP problems can be transferred to our transformation-based discretization method under suitable assumptions on the transformation. Finally, we illustrate the operation of our approach as well as its performance on several examples, including a problem of volume-maximal inscription of multiple variable bodies into a larger fixed body, which has never before been considered as a GSIP test problem.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Discrete Social Spider Algorithm for Solving Traveling Salesman Problem

2021 ◽  
pp. 2150020
Author(s):  
Asieh Khosravanian ◽  
Mohammad Rahmanimanesh ◽  
Parviz Keshavarzi
Keyword(s):  
Genetic Algorithm ◽  
Discrete Optimization ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Fitness Function ◽  
Traveling Salesman ◽  
The Other ◽  
Discrete Optimization Problem ◽  
Social Spider ◽  
Social Spider Algorithm

The Social Spider Algorithm (SSA) was introduced based on the information-sharing foraging strategy of spiders to solve the continuous optimization problems. SSA was shown to have better performance than the other state-of-the-art meta-heuristic algorithms in terms of best-achieved fitness values, scalability, reliability, and convergence speed. By preserving all strengths and outstanding performance of SSA, we propose a novel algorithm named Discrete Social Spider Algorithm (DSSA), for solving discrete optimization problems by making some modifications to the calculation of distance function, construction of follow position, the movement method, and the fitness function of the original SSA. DSSA is employed to solve the symmetric and asymmetric traveling salesman problems. To prove the effectiveness of DSSA, TSPLIB benchmarks are used, and the results have been compared to the results obtained by six different optimization methods: discrete bat algorithm (IBA), genetic algorithm (GA), an island-based distributed genetic algorithm (IDGA), evolutionary simulated annealing (ESA), discrete imperialist competitive algorithm (DICA) and a discrete firefly algorithm (DFA). The simulation results demonstrate that DSSA outperforms the other techniques. The experimental results show that our method is better than other evolutionary algorithms for solving the TSP problems. DSSA can also be used for any other discrete optimization problem, such as routing problems.

scholarly journals The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

2021 ◽  
Author(s):  
Zhenkun Wang ◽  
Qingyan Li ◽  
Qite Yang ◽  
Hisao Ishibuchi
Keyword(s):  
Evolutionary Algorithms ◽  
Coping Strategies ◽  
Test Problem ◽  
Pareto Front ◽  
Optimization Problems ◽  
Feasible Region ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Pareto Fronts ◽  
Boundary Solutions

AbstractIt has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

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 Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

2021 ◽  
Author(s):  
Shufen Qin ◽  
Chan Li ◽  
Chaoli Sun ◽  
Guochen Zhang ◽  
Xiaobo Li
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Search ◽  
Model Management ◽  
The Other ◽  
Local Searches ◽  
Fitness Value ◽  
Expensive Problems ◽  
Computationally Expensive

AbstractSurrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

scholarly journals Comparison of synchronous and asynchronous parallelization of extreme surrogate-assisted multi-objective evolutionary algorithm

2020 ◽  
Author(s):  
Tomohiro Harada ◽  
Misaki Kaidan ◽  
Ruck Thawonmas
Keyword(s):  
Machine Learning ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computing Time ◽  
The Other ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Evaluation Time ◽  
Surrogate Function

Abstract This paper investigates the integration of a surrogate-assisted multi-objective evolutionary algorithm (MOEA) and a parallel computation scheme to reduce the computing time until obtaining the optimal solutions in evolutionary algorithms (EAs). A surrogate-assisted MOEA solves multi-objective optimization problems while estimating the evaluation of solutions with a surrogate function. A surrogate function is produced by a machine learning model. This paper uses an extreme learning surrogate-assisted MOEA/D (ELMOEA/D), which utilizes one of the well-known MOEA algorithms, MOEA/D, and a machine learning technique, extreme learning machine (ELM). A parallelization of MOEA, on the other hand, evaluates solutions in parallel on multiple computing nodes to accelerate the optimization process. We consider a synchronous and an asynchronous parallel MOEA as a master-slave parallelization scheme for ELMOEA/D. We carry out an experiment with multi-objective optimization problems to compare the synchronous parallel ELMOEA/D with the asynchronous parallel ELMOEA/D. In the experiment, we simulate two settings of the evaluation time of solutions. One determines the evaluation time of solutions by the normal distribution with different variances. On the other hand, another evaluation time correlates to the objective function value. We compare the quality of solutions obtained by the parallel ELMOEA/D variants within a particular computing time. The experimental results show that the parallelization of ELMOEA/D significantly reduces the computational time. In addition, the integration of ELMOEA/D with the asynchronous parallelization scheme obtains higher quality of solutions quicker than the synchronous parallel ELMOEA/D.

scholarly journals An Adaptive Multi-Swarm Competition Particle Swarm Optimizer for Large-Scale Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 521 ◽  
Author(s):  
Fanrong Kong ◽  
Jianhui Jiang ◽  
Yan Huang
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Particle Swarm ◽  
The Other ◽  
Large Scale Optimization ◽  
Particle Swarm Optimizer ◽  
Competition Mechanism ◽  
Benchmark Suite ◽  
Scale Optimization ◽  
The One

As a powerful tool in optimization, particle swarm optimizers have been widely applied to many different optimization areas and drawn much attention. However, for large-scale optimization problems, the algorithms exhibit poor ability to pursue satisfactory results due to the lack of ability in diversity maintenance. In this paper, an adaptive multi-swarm particle swarm optimizer is proposed, which adaptively divides a swarm into several sub-swarms and a competition mechanism is employed to select exemplars. In this way, on the one hand, the diversity of exemplars increases, which helps the swarm preserve the exploitation ability. On the other hand, the number of sub-swarms adaptively changes from a large value to a small value, which helps the algorithm make a suitable balance between exploitation and exploration. By employing several peer algorithms, we conducted comparisons to validate the proposed algorithm on a large-scale optimization benchmark suite of CEC 2013. The experiments results demonstrate the proposed algorithm is effective and competitive to address large-scale optimization problems.

scholarly journals A Competitive Memory Paradigm for Multimodal Optimization Driven by Clustering and Chaos

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 934
Author(s):  
Jorge Gálvez ◽  
Erik Cuevas ◽  
Krishna Gopal Dhal
Keyword(s):  
Optimization Problems ◽  
Optimization Methods ◽  
Global Optimum ◽  
Point Of View ◽  
The Other ◽  
Memory Mechanism ◽  
Dominant Individual ◽  
Complex Optimization ◽  
Optimal Values ◽  
Evolutionary Operators

Evolutionary Computation Methods (ECMs) are proposed as stochastic search methods to solve complex optimization problems where classical optimization methods are not suitable. Most of the proposed ECMs aim to find the global optimum for a given function. However, from a practical point of view, in engineering, finding the global optimum may not always be useful, since it may represent solutions that are not physically, mechanically or even structurally realizable. Commonly, the evolutionary operators of ECMs are not designed to efficiently register multiple optima by executing them a single run. Under such circumstances, there is a need to incorporate certain mechanisms to allow ECMs to maintain and register multiple optima at each generation executed in a single run. On the other hand, the concept of dominance found in animal behavior indicates the level of social interaction among two animals in terms of aggressiveness. Such aggressiveness keeps two or more individuals as distant as possible from one another, where the most dominant individual prevails as the other withdraws. In this paper, the concept of dominance is computationally abstracted in terms of a data structure called “competitive memory” to incorporate multimodal capabilities into the evolutionary operators of the recently proposed Cluster-Chaotic-Optimization (CCO). Under CCO, the competitive memory is implemented as a memory mechanism to efficiently register and maintain all possible optimal values within a single execution of the algorithm. The performance of the proposed method is numerically compared against several multimodal schemes over a set of benchmark functions. The experimental study suggests that the proposed approach outperforms its competitors in terms of robustness, quality, and precision.

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