## 1 Introduction  
The development of computational intelligence approaches has allowed applying these methods in different areas nowadays. In particular, the evolutionary computation (EC) [1] methods and swarm-based algorithms proved themselves to be problem-independent and universal approaches for solving optimization tasks with different types of complexity. Most of these algorithms are developed to address stationary environments, where the objective function does not change over time. However, optimization in dynamic environments has become popular in the last three decades, which is indicated in several surveys of the state-of-the-art [2; 3; 4]. Many real-world applications can be formulated as a dynamic optimization problem (DOP), where the problem itself changes over time. The changing environment during the optimization process is a challenging task for most bio-inspired algorithms, as they are mainly developed under an assumption that a single best final solution should be found by the end of the computational resource, and the goal function does not change.  
In the non-stationary environment, the goal consists in tracking the optimum positions during the optimization process. The problems which are formulated as DOPs, are found in different areas of human activity such as path planning [4; 5], pollution control [6], searching for survivors with unmanned aerial vehicles (drones) [7], and others. The development of novel approaches for DOPs relies on well-established benchmarks, namely the classical Moving Peaks Benchmark (MPB) [8], Generalized Dynamic Benchmark Generator (GDBG) [9], or the recently proposed Generalized Moving Peaks Benchmark (GMPB) [10; 11] and the Deterministic Distortion and Rotation Benchmark (DDRB) [12].  
The dominating methods often applied for DOPs are the particle swarm optimization (PSO)-based algorithms and their modifications such as multi-swarm approaches [13; 14],however, certain studies used Differential Evolution (DE) [15] or, for example, Artificial Bee Colony (ABC) algorithm [16]. Yet little has been done for the development of hybrid approaches, which would use the advantages of different methods. Thus, the goal of this study is to establish the ways in which DE can be added to PSO-based approaches, improving the resulting performance.  
In this study, the multi-swarm Quantum Swarm Optimization (mQSO) [13] algorithm is modified with the Differential Evolution search operator. Several versions of the resulting mQSODE algorithm with different mutation operators are considered, and the sensitivity analysis for main parameters is conducted. The experiments are performed on the Generalized Moving Peaks Benchmark [10] with four scenarios. The main contributions of the current study can be summarized as follows:  
1. It is shown that applying differential mutation to current positions of the particles is inferior to the variant when it is applied to personal best positions;
2. The probability of applying differential evolution search should be relatively small, and the PSO should be the main search engine to achieve competitive results;
3. The scaling factor in differential mutation should be carefully chosen, as it significantly influences performance, whereas crossover rate does not seem to have any significant influence;
4. Applying differential mutation with a small probability results in higher diversity in the population compared to mQSO given the same population size;
5. The GMPB favors larger population sizes than recommended values, derived from testing on other benchmarks.  
The rest of the paper is organized as follows: the next section describes related work, i.e., algorithms and methods applied to dynamic optimization, after this the generalized moving peaks benchmark used in this study is given, next, the proposed approach is presented, after that, the experimental setup and results are provided, and finally, the conclusions are given.