An Efficient Benchmark Generator for Dynamic Optimization Problems
A number of benchmark generators have been proposed for dynamic single objective optimization problems. The moving peaks benchmark and the GDBG benchmark are widely used to test the performance of an evolutionary algorithm. The two benchmarks construct a
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Abstract. A number of benchmark generators have been proposed for dynamic single objective optimization problems. The moving peaks benchmark and the GDBG benchmark are widely used to test the performance of an evolutionary algorithm. The two benchmarks construct a fitness landscape with a number of peaks that can change heights, widths, and locations. The two benchmarks are simple and easy to understand. However, they exist two major issues: (1) the time complexity is high for evaluating a solution and (2) peaks may become invisible when changes occur. To address the two issues, this paper proposes an efficient generator with enriched features. The generator applies the k-d tree to partition the search space and sets a simple unimodal function in each sub-space. The properties of the proposed benchmark are discussed and verified by a set of evolutionary algorithms. Keywords: Dynamic optimization problem
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Introduction
In recent years, there has been a growing interest in developing evolutionary algorithms in dynamic environments. To comprehensively evaluate the performance of an evolutionary algorithm (EA), an important task is to develop a good benchmark generator. Over the years, a number of benchmark generators for dynamic optimization problems (DOPs) have been proposed. Generally speaking, these benchmark generators can be classified to the following three classes in terms of the way to construct problems. Note that, this paper focuses on only dynamic continuous unconstrained single objective optimization problems. The first class of generators switch the environment between several stationary problems or several states of a problem. Early generators normally belong to this class. A generator based on two static landscapes A and B was proposed in [7]. Changes can occur in three ways: (1) linear translation of peaks in landscape A; (2) only the global optimum randomly moves in landscape A; (3) switching landscapes between A and B. In [15], the environment oscillates among a set of fixed landscapes. Like the first class of generators, the second class of generators also consist of a number of basic functions. However, the environment normally takes the form c Springer Nature Singapore Pte Ltd. 2016 M. Gong et al. (Eds.): BIC-TA 2016, Part II, CCIS 682, pp. 60–72, 2016. DOI: 10.1007/978-981-10-3614-9 8
An Efficient Benchmark Generator for Dynamic Optimization Problems
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f (x) = max{gi (x)}, i = 1, . . . , N to construct the fitness landscape and it does not switch among the basic functions. The environmental changes are caused by the changes of every g(x). Many generators fall into this class. The moving peaks benchmark (MPB) [15] is one of the widely used generators. The MPB consist of a number of peaks. Each peak is constructed by a simple unimodal function which can change in height, width, and location. The DF1 generator [15] and the rotation dynamic benchmark generator (RDBG) [10] use a similar way to construct the fitness landscape. The DF1 generator uses the logistic function to change the height,
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