Dynamic Test Functions Research Articles

Designing Benchmark Generator for Dynamic Optimization Algorithm

Real-world problems always change over time. In the past two decades, many researchers have become increasingly interested in studying evolutionary optimization algorithms for dynamic problems owing to their great importance in real-world applications. Currently, there are no unified and mature test functions for dynamic problems, and the existing dynamic test functions are incapable of simulating a real dynamic environment. This study constructs a new benchmark test function generator for simulating dynamic environments that combine existing static benchmark functions and their related properties to form new dynamic test functions. It is simple to construct and conveniently control the dynamic properties by adjusting the corresponding parameters. Through a series of comparisons with the dynamic benchmark of the generalized dynamic benchmark generator (GDBG), the simulation results show that the dynamic test functions constructed by this generator can reflect different types of changing intensity.

Quantum particles-enhanced multiple Harris Hawks swarms for dynamic optimization problems

Dynamic optimization problems (DOPs) have been a subject of considerable research interest mainly due to their widespread application potential. In the literature, various mechanisms have been reported to cope with the challenges of DOPs. The proposed mechanisms have usually been adopted by well-known population-based optimization algorithms, such as genetic algorithms or particle swarm optimization. Although new generation swarm-intelligence algorithms are continuously being developed and have much to offer in DOPs, their performance is usually tested on stationary optimization problems. In this study, a recently introduced optimization algorithm, Harris Hawk Optimizer, is redesigned as a multi-population based algorithm to deal with possible multiple optima. Thus, the proposed modification is allowed to search diverse parts of the search space more efficiently, particularly in multimodal environments. Next, it is further enhanced by using quantum particles to tackle with diversification and intensification challenges in DOPs. As shown in the present work, this mechanism can maintain population diversity and intensification depending on a user-supplied parameter. Finally, based on different algorithmic components, four different variants of HHO are proposed. The performances of the developed algorithms are tested on both stationary and dynamic test problems. Dynamic test functions introduced in the IEEE Congress on Evolutionary Computation 2009 (CEC 2009) are used and further extended to test the proposed algorithms' performances. Finally, appropriate statistical analysis is conducted to demonstrate significant improvements over the existing algorithms.

A dual-population multi operators harmony search algorithm for dynamic optimization problems

Abstract Dynamic optimization problems (DOPs) have been widely researched in recent years. This is due to its numerous practical applications in real-life conditions. To solve DOPs, the optimizer should be able to track the changes and simultaneously seek for global optima in the search space. This paper proposes a dual population multi operators harmony search algorithm for DOPs to deal with changes in the problem landscape. The main difference between the proposed algorithm and other techniques are twofold: dual population for exploring and exploiting the search space, and the use of multi operators at different points of the search. Extensive experiments were conducted on the Moving Peaks Benchmark (MPB) and six dynamic test functions proposed in the IEEE Congress on Evolutionary Computation (CEC 2009) were used to evaluate the performance of the proposed algorithm. Empirical results indicate the superiority of the proposed algorithm when compared to state-of-the-art algorithms from the literature.

Systems with distributions and viability theorem

The approach to the consideration of the ordinary differential equations with distributions in the classical space D ′ of distributions with continuous test functions has certain insufficiencies: the notations are incorrect from the point of view of distribution theory, the right-hand side has to satisfy the restrictive conditions of equality type. In the present paper we consider an initial value problem for the ordinary differential equation with distributions in the space of distributions with dynamic test functions T ′ , where the continuous operation of multiplication of distributions by discontinuous functions is defined [V. Derr, D. Kinzebulatov, Distributions with dynamic test functions and multiplication by discontinuous functions, preprint, arXiv: math.CA/0603351, 2006], and show that this approach does not have the aforementioned insufficiencies. We provide the sufficient conditions for viability of solutions of the ordinary differential equations with distributions (a generalization of the Nagumo Theorem), and show that the consideration of the distributional (impulse) controls in the problem of avoidance of encounters with the set (the maximal viability time problem) allows us to provide for the existence of solution, which may not exist for the ordinary controls.