Giter VIP home page Giter VIP logo

rveaa's Introduction

RVEAa: Reference vector-guided evolution algorithm embedded with the reference vector regeneration strategy

Reference: Cheng R, Jin Y, Olhofer M, et al. A reference vector guided evolutionary algorithm for many-objective optimization[J]. IEEE Transactions on Evolutionary Computation, 2016, 20(5): 773-791.
RVEAa is an improved version of RVEA which can solve many-objective optimization problems (MaOPs) with irregular Pareto front.
Variables Meaning
npop Population size
iter Iteration number
lb Lower bound
ub Upper bound
nobj The dimension of objective space (default = 3)
eta_c Spread factor distribution index (default = 30)
eta_m Perturbance factor distribution index (default = 20)
alpha The parameter to control the change rate of APD (default = 2)
fr Reference vector adaption parameter (default = 0.1)
nvar The dimension of decision space
pop Population
objs Objectives
V0 Original reference vectors
V Reference vectors
gamma The smallest angle value of each reference vector to the others
APD Angle-penalized distance
dom Domination matrix
pf Pareto front

Test problem: DTLZ5

$$ \begin{aligned} & \theta_i = \frac{\pi}{4(1 + g(x_M))}(1 + 2g(x_M)x_i), \quad i = 1, \cdots, n \\ & g(x_M) = \sum_{x_i \in x_M} (x_i - 0.5) ^ 2 \\ & \min \\ & f_1(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \cos(\theta_{M-2} \pi /2) \cos(\theta_{M - 1} \pi /2) \\ & f_2(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \cos(\theta_{M-2} \pi /2) \sin(\theta_{M - 1} \pi /2) \\ & f_3(x) = (1 + g(x_M)) \cos(\theta_i \pi / 2) \cdots \sin(\theta_{M-2} \pi /2) \\ & \vdots \\ & f_M(x) = (1 + g(x_M)) \sin(\theta_1 \pi /2) \\ & \text{subject to} \\ & x_i \in [0, 1], \quad \forall i = 1, \cdots, n \end{aligned} $$

Example

if __name__ == '__main__':
    main(105, 500, np.array([0] * 12), np.array([1] * 12))
Output:

It can be seen that RVEAa performs betters on MaOPs with irregular Pareto fronts than the original RVEA.

rveaa's People

Contributors

xavier-mayiming avatar

Stargazers

 avatar Xinyi avatar

Watchers

 avatar

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    ๐Ÿ–– Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. ๐Ÿ“Š๐Ÿ“ˆ๐ŸŽ‰

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google โค๏ธ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.