A new uncertain multi-objective programming model with chance-entropy constraint for advertising promotion

Abstract

The COVID-19 outbreak has forced people to stay at home to prevent the spread of the virus. In this case, social media platforms have become the main communication venue for people. Online sales platforms have also become the main field for people’s daily consumption. So, how to make full use of social media to carry out online advertising promotion, and then achieve better marketing, is one of the core issues that the marketing industry must pay attention to and solve. Therefore, this study takes the advertiser as the decision-maker, maximizes the number of full playing, likes, comments and forwarding, and minimizes the cost of advertising promotion as the decision-making goals, and Key Opinion Leader (KOL) selection as the decision vector. Based on this, a multi-objective uncertain programming model of advertising promotion is constructed. Among them, the chance-entropy constraint is proposed by combining the entropy constraint and the chance constraint. In addition, the multi-objective uncertain programming model is transformed into a clear single-objective model through mathematical derivation and linear weighting of the model. Finally, the practicability and effectiveness of the model are verified by numerical simulation, and decision-making suggestions for advertising promotion are put forward.

Adaptive Sampling Immune Algorithm for Multi-Objective Probabilistic Optimization

“…Eq. (11) shows that if CM is smaller, the convergence of A ′ will be better, where d (x, X * ) is the Hausdorff distance between x and X * in the objective space.…”

“…Multi-Objective Probabilistic Optimization Problem (MOPOP) is a class of stochastic programming problems with extensive engineering application background 1 , where there are multiple conflicting objective functions to be optimized that satisfy probabilistic constraints. MOPOPs have been applied in many practical engineering areas, such as water resource operations 2,3 , airborne ground operations 4 , coordinated power grid and electricity dispatch 5,6 , electric vehicle charging stations 7 , service resource scheduling 8 , distributed energy 9 , bi-level optimal dispatching 10 , advertising promotion 11 , and so on. These engineering problems usually contain random parameters or random variables (referred to as noise), and are characterized by complex model structure, unknown noise distribution information, multiple conflicting objective functions, non-linearity, and multimodality, which make MOPOPs very challenging to solve.…”