DeepAI
Log In Sign Up

Novel bi-objective optimization algorithms minimizing the max and sum of vectors of functions

09/06/2022
by   Hamidreza Khaleghzadeh, et al.
0

We study a bi-objective optimization problem, which for a given positive real number n aims to find a vector X = {x_0,⋯,x_k-1}∈ℝ^k_≥ 0 such that ∑_i=0^k-1 x_i = n, minimizing the maximum of k functions of objective type one, max_i=0^k-1 f_i(x_i), and the sum of k functions of objective type two, ∑_i=0^k-1 g_i(x_i). This problem arises in the optimization of applications for performance and energy on high performance computing platforms. We first propose an algorithm solving the problem for the case where all the functions of objective type one are continuous and strictly increasing, and all the functions of objective type two are linear increasing. We then propose an algorithm solving a version of the problem where n is a positive integer and all the functions are discrete and represented by finite sets with no assumption on their shapes. Both algorithms are of polynomial complexity.

READ FULL TEXT

page 2

page 3

04/21/2018

Best subset selection in linear regression via bi-objective mixed integer linear programming

We study the problem of choosing the best subset of p features in linear...
09/18/2018

Branch-and-bound for bi-objective integer programming

In bi-objective integer optimization the optimal result corresponds to a...
11/27/2014

Bi-objective Optimization for Robust RGB-D Visual Odometry

This paper considers a new bi-objective optimization formulation for rob...
09/16/2019

Multitype Integer Monoid Optimization and Applications

Configuration integer programs (IP) have been key in the design of algor...
03/20/2022

Convergence rates of the stochastic alternating algorithm for bi-objective optimization

Stochastic alternating algorithms for bi-objective optimization are cons...