## 1 Introduction
One of the most effective methods for improving the performance of metaheuristic algorithms is to use chaos maps, which generate bounded random numbers based on initial conditions. In the literature, there are various chaos maps, such as the piecewise map, iterative map, logistic map, sine map, Tent map, and so on [44]. Chaos has been used in the self-adaptive chaos differential evolution (SACDE) [45], where the mutation factor is controlled using chaos maps and dynamically changing weighting factors and crossover factors are also introduced. Recently, a new hybrid optimization method based on differential evolution (DE) and chaos theory was made [46]. This method uses chaotic sequences to change DE parameters automatically in order to help the algorithm to escape local minimums and improve global convergence. For the purpose of tackling three engineering optimization problems, [PERSON] and [PERSON] [36] suggested an enhanced butterfly optimization technique with several chaotic maps. Here, three chaotic BOA algorithms were created. The first one used chaos maps to generate initial solutions, the second used chaos to control switch probability \(p\), and the third was a combination of the previous two. The results showed that BOA modified with chaotic maps shows improved performance in terms of avoiding local optima and accelerating convergence. To prove that the suggested chaotic BOA is correct, engineering design issues, benchmark test functions, and both multimodal and unimodal benchmarks are used. As a result, the pseudo-randomness, ergodicity, and irregularity of chaos maps make them an ideal addition to EAs, helping to boost the efficiency of optimization and the quality of the solutions they provide [36; 47]. Motivated by the above considerations, we recognise the importance of passive localization, especially in the indoor environment, where the traditional techniques cannot be applied with the required accuracy. By also looking at the above strengths and weaknesses of the BOA and DE algorithms, we can see that the DE algorithm has a good ability to explore, which depends on the mutation scheme chosen, and that the BOA algorithm has a good ability to search locally. Therefore, in this study, we suggest ICDEBOA, a hybridization between BOA and DE, to effectively tackle the passive target localization problem. In the suggested approach, we add a new composite roulette wheel-based mutation operator into the DE algorithm. To take advantage of the BOA algorithm's good local search ability, a hybrid algorithm is created by using BOA expressions for particle movement to produce a mutant vector in the DE algorithm. Furthermore, an adaptive technique incorporating chaos map is used to update the BOA algorithm's sensory fragrance. In the context of range-based target localization, the CRLB is usually utilised to access the statistical performance of various localization algorithms. As a result, determining CRLB as an optimality criterion for the considered localization problem is a critical issue [48]. In this aspect, the CRLB establishes the physical impossibility of an unbiased estimator's variance being less than the given bound. Consequently, in this research, we define the CRLB for the investigated localization problem and use it to evaluate the root-mean-square error (RMSE) of the presented ICDEBOA technique and compare against that of several other widely used methods. Given the aforementioned information, the primary goals of this work were as follows:* To formulate a new problem of localization of a passive target using the obtained TDOA measurements. * To present a new global optimization method that is a hybridization of BOA and DE algorithms, named ICDEBOA, so that the passive target localization problem can be solved successfully. * To validate the proposed algorithm's performance on benchmark test functions by comparing simulation results to a number of state-of-the-art methods.