scholarly journals An iterative vertex enumeration method for objective space based vector optimization algorithms

2020 ◽  
Author(s):  
Firdevs Ulus ◽  
İrfan Caner Kaya
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Pareto Frontier ◽  
Recession Cone ◽  
Vertex Enumeration ◽  
Convex Vector Optimization ◽  
Multiobjective Optimization Problems ◽  
Objective Space ◽  
Enumeration Problem

An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex vector optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP, which is defined in the objective space, is solved in each iteration and it has a special structure. Namely, the recession cone of the polyhedron to be generated is the ordering cone. We consider and give a detailed description of a vertex enumeration procedure, which iterates by calling a modified `double description (DD) method' that works for such unbounded polyhedrons. We employ this procedure as a function of an existing objective space based vector optimization algorithm (Algorithm 1); and test the performance of it for randomly generated linear multiobjective optimization problems. We compare the efficiency of this procedure with another existing DD method as well as with the current vertex enumeration subroutine of Algorithm 1. We observe that the modified procedure excels the others especially as the dimension of the vertex enumeration problem (the number of objectives of the corresponding multiobjective problem) increases.

scholarly journals A Hybrid Predictive Strategy Carried through Simultaneously from Decision Space and Objective Space for Evolutionary Dynamic Multiobjective Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Peng Xu ◽  
Xiaoming Wu ◽  
Man Guo ◽  
Shuai Wang ◽  
Qingya Li ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Ideal Point ◽  
Dynamic Environment ◽  
Decision Space ◽  
Center Point ◽  
Multiobjective Optimization Problems ◽  
Objective Space ◽  
Adaptive Diversity ◽  
Dynamic Multiobjective Optimization

There are many issues to consider when integrating 5G networks and the Internet of things to build a future smart city, such as how to schedule resources and how to reduce costs. This has a lot to do with dynamic multiobjective optimization. In order to deal with this kind of problem, it is necessary to design a good processing strategy. Evolutionary algorithm can handle this problem well. The prediction in the dynamic environment has been the very challenging work. In the previous literature, the location and distribution of PF or PS are mostly predicted by the center point. The center point generally refers to the center point of the population in the decision space. However, the center point of the decision space cannot meet the needs of various problems. In fact, there are many points with special meanings in objective space, such as ideal point and CTI. In this paper, a hybrid prediction strategy carried through from both decision space and objective space (DOPS) is proposed to handle all kinds of optimization problems. The prediction in decision space is based on the center point. And the prediction in objective space is based on CTI. In addition, for handling the problems with periodic changes, a kind of memory method is added. Finally, to compensate for the inaccuracy of the prediction in particularly complex problems, a self-adaptive diversity maintenance method is adopted. The proposed strategy was compared with other four state-of-the-art strategies on 13 classic dynamic multiobjective optimization problems (DMOPs). The experimental results show that DOPS is effective in dynamic multiobjective optimization.

A DYNAMIC POLYNOMIAL MUTATION FOR EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION ALGORITHMS

2011 ◽  
Vol 20 (01) ◽  
pp. 209-219 ◽  
Author(s):  
MOHAMMAD HAMDAN
Keyword(s):  
Performance Metrics ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Local Optima ◽  
Multi Objective ◽  
Multiobjective Optimization Problems ◽  
Evolutionary Optimization Algorithms ◽  
Dynamic Version ◽  
Polynomial Mutation ◽  
Multiobjective Algorithms

Polynomial mutation is widely used in evolutionary optimization algorithms as a variation operator. In previous work on the use of evolutionary algorithms for solving multi-objective problems, two versions of polynomial mutations were introduced. The first is non-highly disruptive that is not prone to local optima and the second is highly disruptive polynomial mutation. This paper looks at the two variants and proposes a dynamic version of polynomial mutation. The experimental results show that the proposed adaptive algorithm is doing well for three evolutionary multiobjective algorithms on well known multiobjective optimization problems in terms of convergence speed, generational distance and hypervolume performance metrics.

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