Artificial immune system in dynamic environments solving time-varying non-linear constrained multi-objective problems

Abstract

A bio-inspired artificial immune system is developed to track dynamically the Pareto fronts of timevarying constrained multi-objective problems with changing variable dimensions. It executes in order T-module, B-module, and M-module within a run period. The first module is designed to examine dynamically whether the environment changes or whether a change takes place in the optimization problem, while creating an initial population by means of the history information. Thereafter, the second one is a loop of optimization that searches for the desired non-dominated front of a given environment, in which the evolving population is sorted into several subpopulations. Each of such subpopulations, relying upon the population diversity, suppresses its redundant individuals and evolves the winners. The last one stores temporarily the resultant non-dominated solutions of the environment that assist T-module to create some initial candidates helpful for the coming environment. These dynamic characteristics, along with the comparative experiments guarantee that the artificial immune system can track adaptively the time-varying environment and maintain the diversity of population while being of potential use for complex dynamic constrained multi-objective problems.

Dynamic Multi-objective Optimization: A Survey of the State-of-the-Art

“…All of the test problems are unconstrained or domain constrained although it should be noted that dynamic constrained multi-objective test problems have already been designed such as extending a static constrained optimization problem [36]. In general, the source of dynamism comes mostly from the changing objective function.…”

Immune Optimization Approach for Dynamic Constrained Multi-Objective Multimodal Optimization Problems

“…More recently, we also studied immune-based optimization techniques for such kind of problem [9]. Subsequently, we handled one general kind of DCMO by developing an immune agent-based artificial immune system (DCMOAIS) [10]. In this approach, the interactive mechanism between B-cell and T-cell is our major bio-inspiration.…”

“…Dynamic multi-objective optimization (DMO) has become active in the recent years. Many researchers in the fields of evolutionary computation and immune optimization have made their efforts to study how the search procedure can adaptively track the environmental change and rapidly find the desired Pareto front [1][2][3][4][5][6][7][8][9][10]. DCMMO is one particular kind of DMO, presenting complex dynamic behaviors such as dynamics and multimodality.…”

“…Although immune optimization, a popular research branch, was proved to be potential for dynamic problems because of the inherent diversity and adaptation, more studies on it are concentrated on solving non-constrained dynamic single or multi-objective optimization problems [10][11][12]. It is not clear whether bio-immune inspirations are valuable for handling DCMMO.…”

Performance measures for dynamic multi-objective optimisation algorithms

“…Zhang and Qian [68] introduced the coverage scope (CS) measure to quantify the average width or coverage of the non-dominated set. CS is calculated by averaging the maximum distance between each solution in POF * and the other solutions in POF * .…”