## 1 Introduction
However, Evolutionary Dynamic Optimization (EDO) approaches include an explicit or implicit mechanisms to detect and correctly react to the dynamic change. A change detection mechanism can be maintained through detectors using a feasible search population, such as the current best solutions, memory of optimal solutions or some predefined sub-population. Furthermore, this can be assumed separately to the search space using a set of random selected solutions, a fixed point, a regular grid of solutions or a set of determined points. In addition, the algorithm behaviors have considered a robust detection strategy based on the average of best-found solutions, time-varying observation of different sub-swarms, diversity of the solutions compared to the success rate, time-varying distributions and statistical methods. Increasing the mutation rate (hyper-mutation) or adding a randomly new member and relocating some useful solutions are the main mechanisms used to manage the loss of diversity in a dynamic search space which may fall within undetected regions of potential solutions. The efficiency of standard MOEAs significantly decreases when dealing with Many-Objective Optimization Problems (MaOPs) where the number of objectives that need to be satisfied is higher than 3. Furthermore, three main issues are introduced when solving MaOPs, including: (i) the inutility of the dominance operator when dealing with a large number of objectives, (ii) the loss of diversity and premature convergence, and (iii) the exponentially increase of the population size. The Crow Search Algorithm (CSA) [9] is a meta-heuristic that simulates the social behavior of crows for food-searching. Crows are characterized by their ability to memorize food sources, as well as sources that other member of the flock may hold or hide. The CSA algorithm was first proposed as a mono-objective optimization technique and then extended to solve static Multi-Objective Problem (MOP) and constrained engineering optimization problems, in which the algorithm showed a relative effectiveness in comparison with techniques such as the harmony search (HS) [10], GA [1] and PSO approach. The main contribution is as follows:  
* This contribution presents a novel Distributed Bi-behaviours Crow Search Algorithm (DB-CSA) to solve both Dynamic Multi-Objective Optimization Problems (DMOPs) and static Many-Objective Optimization Problems (MaOPs), which have not yet been performed using the standard CSA algorithm. * The main difference between the original CSA algorithm and the new DB-CSA algorithm is as follows: the proposed DB-CSA approach presents two new chasing profiles, denoted by Beta Distribution profiles over the large Gaussian Beta-1 function for diversity enhancement and the narrow Gaussian Beta-2 function for convergence improvements. * The proposed approach tends to achieve a dynamic balance between exploitation and exploration at each iteration during the optimization process, which makes it more suitable for both dynamic multi-objective optimization and many-objective optimization. * A dynamic optimization mechanism is considered within the proposed DB-CSA algorithm when solving DMOPs to detect the time-varying POS and POF, effectively reacts to the dynamic changes and is denoted by the second variant (DB-CSA-II). This process aims to manage and control the dynamic change in a time-varying search space. The reminder of this manuscript is organized as follows: Section 2 presents an overview of the best-known Dynamic Multi-Objective Optimization methods, Many-Objective Optimization Approaches and some existing Crow Search Algorithms based-methods. Section 3 presents the proposed Distributed Bi-behaviours Crow Search Algorithm (DB-CSA). Section 4 details the experimental evaluation, which is based on two comparative studies: one for DMOPs and the second for MaOPs. The results are presented in terms of their mean and standard deviation.