Evolutionary multiobjective optimization in dynamic environments: A set of novel benchmark functions

Abstract

Time varying nature of the constraints, objectives and parameters that characterize several practical optimization problems have led to the field of dynamic optimization with Evolutionary Algorithms. In recent past, very few researchers have concentrated their efforts on the study of Dynamic multiobjective Optimization Problems (DMOPs) where the dynamicity is attributed to multiple objectives of conflicting nature. Considering the lack of a somewhat diverse and challenging set of benchmark functions, in this article, we discuss some ways of designing DMOPs and propose some general techniques for introducing dynamicity in the Pareto Set and in the Pareto Front through shifting, shape variation, slope variation, phase variation, and several other types. We introduce 9 benchmark functions derived from the benchmark suite used for the 2009 IEEE Congress on Evolutionary Computation competition on bound-constrained and static MO optimization algorithms. Additionally a variant of multiobjective EA based on decomposition (MOEA/D) have been put forward and tested along with peer algorithms to evaluate the newly proposed benchmarks.

A survey of swarm intelligence for dynamic optimization: Algorithms and applications

“…Recently, benchmark generators for continuous dynamic constrained optimization [77,78,26,14] and continuous dynamic multiobjective optimization [25,61,79,80,81,82,83,84,85] are proposed. But, constrained and multi-objective optimization under the discrete space has not attracted much attention yet and deserves future consideration.…”

A Scalable Test Suite for Continuous Dynamic Multiobjective Optimization

“…We noticed that some existing test suites, i.e., UDF [3] and GTA [11], also recognise the importance of several SDP features, including variable linkage, degeneration, and unpredictability. Thus, we compared SDP against the test suites with these features (settings for comparison are detailed in the supplementary material), and the comparison is illustrated in Fig.…”

“…Five different DMO algorithms are employed for studying the proposed benchmarks, each representing a type of [10] s ZDT/DTLZ DIMP [26] s,d ZDT DSW [33] s dMOP [14] s ZDT T [17] s M,n DTLZ ZJZ [52] s FDA/LZ HE [16] s,d FDA/LZ/WFG UDF [3] s,d ZDT JY [20] s,d GTA [11] s,d ZDT/DTLZ CLY [5] s M T/DTLZ 's', 'ns', or 's' in the column of PF connectivity denote DMOPs exist having a simply-connected, non-simply connected, or disconnected PF, respectively. 'M' or 'n' in column of 'dynamic M/n' means DMOPs exist having a time-varying number of objectives or variables, respectively.…”

A Steady-State and Generational Evolutionary Algorithm for Dynamic Multiobjective Optimization

“…Twenty-one test problems, including five FDA [15] problems, three dMOP [18] problems, six ZJZ problems (F5-F10) [54], and seven UDF [4] problems, are used to assess our proposed algorithm in comparison with other algorithms. The time instance t involved in these problems is defined as t = (1/n t ) (τ/τ t ) (where n t , τ t , and τ represent the severity of change, the frequency of change, and the iteration counter, respectively).…”

“…Many real-life problems in nature are DMOPs, such as planning [8], scheduling [12], [35], and control [15], [50]. There have been a number of contributions made to several important aspects of this field, including dynamism classification [15], [41], test problems [4], [15], [20], [23]- [26], performance metrics [9], [15], [17]- [19], [41], [55], and algorithm design [9], [12], [15], [18], [21], [28], [54], [55]. Among these, algorithm design is the most important issue as it is the problem-solving tool for DMOPs.…”