An Evolutionary Algorithm for Black-Box Chance-Constrained Function Optimization

2013 ◽  
Vol 17 (2) ◽  
pp. 272-282
Author(s):  
Kazuyuki Masutomi ◽  
◽  
Yuichi Nagata ◽  
Isao Ono ◽  
◽  
...  
Keyword(s):  
Objective Function ◽  
Evolutionary Algorithm ◽  
Black Box ◽  
Function Optimization ◽  
Benchmark Problems ◽  
Objective Functions ◽  
Neural Network Controller ◽  
Objective Function Values ◽  
The Individual ◽  
Constrained Function

This paper presents an evolutionary algorithm for Black-Box Chance-Constrained Function Optimization (BBCCFO). BBCCFO is to minimize the expectation of the objective function under the constraints that the feasibility probability is higher than a userdefined constant in uncertain environments not given the mathematical expressions of objective functions and constraints explicitly. In BBCCFO, only objective function values of solutions and their feasibilities are available because the algebra expressions of objective functions and constraints cannot be used. In approaches to BBCCFO, a method based on an evolutionary algorithm proposed by Loughlin and Ranjithan shows relatively good performance in a realworld application, but this conventional method has a problem in that it requires many samples to obtain a good solution because it estimates the expectation of the objective function and the feasibility probability of an individual by sampling the individual plural times. In this paper, we propose a new evolutionary algorithm that estimates the expectation of the objective function and the feasibility probability of an individual by using the other individuals in the neighborhood of the individual. We show the effectiveness of the proposed method through experiments both in benchmark problems and in the problem of a inverted pendulum balancing with a neural network controller.

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.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2011 ◽  
Vol 4 (2) ◽  
pp. 43-60
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

Pareto Artificial Life Algorithm for Multi-Objective Optimization

2013 ◽  
pp. 100-115
Author(s):  
Jin-Dae Song ◽  
Bo-Suk Yang
Keyword(s):  
Objective Function ◽  
Artificial Life ◽  
Pareto Set ◽  
Function Optimization ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Function ◽  
Artificial Life Algorithm ◽  
Single Objective

Most engineering optimization uses multiple objective functions rather than single objective function. To realize an artificial life algorithm based multi-objective optimization, this paper proposes a Pareto artificial life algorithm that is capable of searching Pareto set for multi-objective function solutions. The Pareto set of optimum solutions is found by applying two objective functions for the optimum design of the defined journal bearing. By comparing with the optimum solutions of a single objective function, it is confirmed that the single function optimization result is one of the specific cases of Pareto set of optimum solutions.

scholarly journals Multi-Objective Function for SWIPT System by SADDE

2020 ◽  
Vol 10 (9) ◽  
pp. 3124
Author(s):  
Wei Chien ◽  
Chien-Ching Chiu ◽  
Yu-Ting Cheng ◽  
Wei-Lin Fang ◽  
Eng Hock Lim
Keyword(s):  
Objective Function ◽  
Path Loss ◽  
Wireless Power Transfer ◽  
Function Optimization ◽  
Multiple Objective ◽  
Power Transfer ◽  
Objective Functions ◽  
Wireless Power ◽  
Real Environment ◽  
Single Objective

Simultaneous wireless information and power transfer (SWIPT) optimization with multiple objective function optimization is presented in the millimeter band in this paper. Three different objective functions that are used for harvest power (HP), capacity, and bit error rate (BER) were studied. There are three different nodes in real environment for wireless power transfer (WPT) and SWIPT. The channel estimation calculated by shooting and bouncing ray/image techniques includes multi-path, fading effect, and path-loss in the real environment. We applied beamforming techniques at the transmitter to focus the transmitter energy in order to reduce the multi-path effect and adjust the length of the feed line on each array element in order to find the extremum of the objective functions by the self-adaptive dynamic differential evolution (SADDE) method. Numerical results showed that SWIPT node cannot achieve good performance by single objective function, but wireless power transfer (WPT) can. Nevertheless, both WPT and SWIPT nodes can meet the criteria by the multiple objective function. The harvesting power ratio as well as the BER and capacity can be improved by the multiple objective function to an acceptable level by only reducing a little harvesting energy compared to the best harvesting energy for the single objective function. Finally, the multiple optimization function cannot merely provide good information quality for SWIPT node but achieve good total harvesting power for WPT and SWIPT node as well.

scholarly journals Graph-Based Upper Bounds for the Probability of the Union of Events

10.37236/752 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Pierangela Veneziani
Keyword(s):  
Objective Function ◽  
Upper Bounds ◽  
Linear Program ◽  
Graph Structures ◽  
Basic Feasible Solutions ◽  
Objective Function Values ◽  
Feasible Solutions ◽  
The Individual

We consider the problem of generating upper bounds for the probability of the union of events when the individual probabilities of the events as well as the probabilities of pairs of these events are known. By formulating the problem as a Linear Program, we can obtain bounds as objective function values corresponding to dual basic feasible solutions. The new upper bounds are based on underlying bipartite and threshold type graph structures.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals Intramax and other objective functions: The case of Slovenia

2016 ◽  
Vol 24 (2) ◽  
pp. 12-25 ◽  
Author(s):  
Samo Drobne ◽  
Mitja Lakner
Keyword(s):  
Objective Function ◽  
The Other ◽  
Objective Functions ◽  
Interaction Index ◽  
Functional Regions ◽  
Hierarchical Aggregation ◽  
Administrative Units

Abstract The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and Killian’s interaction index. The results of the functional regionalisation have been evaluated by self-containment statistics, and they show that the use of the original Intramax procedure tends to delineate operationally the most persuasive and balanced regions that, regarding the intra-regional flows, homogeneously cover the analysed territory. The other objective functions give statistically better but operationally less suitable results. Functional regions modelled using the original Intramax procedure were compared to the regions at NUTS 2 and NUTS 3 levels, as well as to administrative units in Slovenia. We conclude that there are some promising directions for further research on functional regionalisation using hierarchical aggregation procedures.

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