scholarly journals Proximity measures based on KKT points for constrained multi-objective optimization

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Leo Warnow
Keyword(s):  
Evolutionary Algorithms ◽  
Optimal Solution ◽  
Necessary Optimality Conditions ◽  
Kkt Conditions ◽  
Test Problems ◽  
Numerical Verification ◽  
Termination Criteria ◽  
Continuity Properties ◽  
Optimal Solution Set ◽  
Proximity Measures

AbstractAn important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.

Applied Process Simulation-Driven Oil and Gas Separation Plant Optimization using Surrogate Modeling and Evolutionary Algorithms

2019 ◽  
Author(s):  
Anders Andreasen
Keyword(s):  
Evolutionary Algorithms ◽  
Gas Separation ◽  
Oil And Gas ◽  
Optimal Solution ◽  
Computer Experiment ◽  
Latin Hypercube Sampling ◽  
Surrogate Models ◽  
Inlet Temperature ◽  
Separation Plant ◽  
Separation Stage

In this article the optimization of a realistic oil and gas separation plant has been studied. Two different fluids are investigated and compared in terms of the optimization potential. Using Design of Computer Experiment (DACE) via Latin Hypercube Sampling (LHS) and rigorous process simulations, surrogate models using Kriging have been established for selected model responses. The surrogate models are used in combination with a variety of different evolutionary algorithms for optimizing the operating profit, mainly by maximizing the recoverable oil production. A total of 10 variables representing pressure and temperature various key places in the separation plant are optimized to maximize the operational profit. The optimization is bounded in the variables and a constraint function is included to ensure that the optimal solution allows export of oil with an RVP < 12 psia. The main finding is that, while a high pressure is preferred in the first separation stage, apparently a single optimal setting for the pressure in downstream separators does not appear to exist. In the second stage separator apparently two different, yet equally optimal, settings are revealed. In the third and final separation stage a correlation between the separator pressure and the applied inlet temperature exists, where different combinations of pressure and temperature yields equally optimal results.<br>

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

HIERARCHICAL GENETIC ALGORITHM FOR NEAR-OPTIMAL FEEDFORWARD NEURAL NETWORK DESIGN

2002 ◽  
Vol 12 (01) ◽  
pp. 31-43 ◽  
Author(s):  
GARY YEN ◽  
HAIMING LU
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Neural Networks ◽  
Cost Function ◽  
Design Procedure ◽  
Optimal Solution ◽  
Traditional Learning ◽  
Feed Forward Neural Network ◽  
Optimal Solution Set ◽  
Hierarchical Genetic Algorithm

In this paper, we propose a genetic algorithm based design procedure for a multi-layer feed-forward neural network. A hierarchical genetic algorithm is used to evolve both the neural network's topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi-objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey–Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi-layer Perceptron networks and radial-basis function networks. Based upon the chosen cost function, a linear weight combination decision-making approach has been applied to derive an approximated Pareto-optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two-objective optimization problem.

scholarly journals Automation of the one-storey underground parking space organization

2021 ◽  
Vol 284 ◽  
pp. 06012
Author(s):  
Natalia Knyazeva ◽  
Anastasia Kolosova
Keyword(s):  
Evolutionary Algorithms ◽  
Urban Area ◽  
Optimal Solution ◽  
Parking Space ◽  
Space Planning ◽  
Parking Lots ◽  
Legal Documents ◽  
Space Organization ◽  
Big Cities ◽  
The One

With the growing car population in big cities, the problem of its keeping in conditions of a compact urban area has happened. The organisation of parking space in a different way has resolved this issue. Underground parking was in demand in many countries even in the XX century. By the way, they are becoming more and more popular now. The design of car parking is based on legal documents, which regulate the size of car parking seats and the width of the passage inside the garage. It is expedient to use evolutionary algorithms as one of the tools of algorithmic modelling for automation of design the car parking lots and for identifying the most effective and profitable way of the car parking space planning. So, the process of looking for the most optimal solution in underground car parking designing.

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 Performance of Resource Allocation in Device-to-Device Communication Systems Based on Evolutionally Optimization Algorithms

2018 ◽  
Author(s):  
Hsu-Tan Tan ◽  
Bor-An Chen ◽  
Yung-Fa Huang
Keyword(s):  
Particle Swarm Optimization ◽  
Evolutionary Algorithms ◽  
Communication Systems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
System Capacity ◽  
Swarm Optimization ◽  
Device To Device ◽  
Simulation Results ◽  
Capacity Performance

In this study, the resource blocks (RB) are allocated to user equipment (UE) according to the evolutional algorithms for long term evolution (LTE) systems. Particle Swarm Optimization (PSO) algorithm is one of the evolutionary algorithms, based on the imitation of a flock of birds foraging behavior through learning and grouping the best experience. In previous work, the Simple Particle Swarm Optimization (SPSO) algorithm was proposed for RB allocation to enhance the throughput of Device-to-Device (D2D) communications and improve the system capacity performance. In simulation results, with less population size of M = 10, the SPSO can perform quickly convergence to sub-optimal solution in the 100th generation and obtained sub-optimum performance with more 2 UEs than the Rand method. Genetic algorithm (GA) is one of the evolutionary algorithms, based on Darwinian models of natural selection and evolution. Therefore, we further proposed a Refined PSO (RPSO) and a novel GA to enhance the throughput of UEs and to improve the system capacity performance. Simulation results show that the proposed GA with 100 populations, in 200 generations can converge to suboptimal solutions. Therefore, with comparing with the SPSO algorithm the proposed GA and RPSO can improve system capacity performance with 1.8 and 0.4 UEs, respectively.

Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms

2003 ◽  
Vol 11 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Andrea Toffolo ◽  
Ernesto Benini
Keyword(s):  
Genetic Diversity ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Selection Pressure ◽  
Evaluation Method ◽  
State Of The Art ◽  
Search Space ◽  
Test Problems ◽  
Multi Objective ◽  
Diversity Evaluation

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a dual selection pressure towards the exploitation of current non-dominated solutions and the exploration of the search space. We also introduce a new multi-objective evolutionary algorithm, the Genetic Diversity Evolutionary Algorithm (GDEA), strictly designed around GeDEM and then we compare it with other state-of-the-art algorithms on a well-established suite of test problems. Experimental results clearly indicate that the performance of GDEA is top-level.

Comparison of Multi-Objective Evolutionary Algorithms to Prioritize Regression Test Cases

2021 ◽  
Vol 9 (12) ◽  
pp. 1445-1454
Keyword(s):  
Fault Detection ◽  
Evolutionary Algorithms ◽  
Fitness Function ◽  
Optimal Solution ◽  
Test Suite ◽  
Test Case ◽  
Test Cases ◽  
Nsga Ii ◽  
Multi Objective ◽  
Regression Test

Regression testing is one of the most critical testing activities among software product verification activities. Nevertheless, resources and time constraints could inhibit the execution of a full regression test suite, hence leaving us in confusion on what test cases to run to preserve the high quality of software products. Different techniques can be applied to prioritize test cases in resource-constrained environments, such as manual selection, automated selection, or hybrid approaches. Different Multi-Objective Evolutionary Algorithms (MOEAs) have been used in this domain to find an optimal solution to minimize the cost of executing a regression test suite while obtaining maximum fault detection coverage as if the entire test suite was executed. MOEAs achieve this by selecting set of test cases and determining the order of their execution. In this paper, three Multi Objective Evolutionary Algorithms, namely, NSGA-II, IBEA and MoCell are used to solve test case prioritization problems using the fault detection rate and branch coverage of each test case. The paper intends to find out what’s the most effective algorithm to be used in test cases prioritization problems, and which algorithm is the most efficient one, and finally we examined if changing the fitness function would impose a change in results. Our experiment revealed that NSGA-II is the most effective and efficient MOEA; moreover, we found that changing the fitness function caused a significant reduction in evolution time, although it did not affect the coverage metric.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

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