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Evolutionary Manytasking Optimization Based on Symbiosis in Biocoenosis

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Evolutionary Manytasking Optimization Based on Symbiosis in Biocoenosis The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19) Evolutionary Manytasking Optimization Based on Symbiosis in Biocoenosis Rung-Tzuo Liaw, Chuan-Kang Ting Department of Power Mechanical Engineering National Tsing Hua University Hsinchu 30013, Taiwan [email protected], [email protected] Abstract Evolutionary multitasking introduces the new concept of simultaneously solving multiple problems through a single Evolutionary multitasking is a significant emerging search run of EA (Gupta, Ong, and Feng 2016). The multi-factorial paradigm that utilizes evolutionary algorithms to concur- rently optimize multiple tasks. The multi-factorial evolution- evolutionary algorithm (MFEA) has proved effective at real- ary algorithm renders an effectual realization of evolution- izing evolutionary multitasking by leveraging the synergy of ary multitasking on two or three tasks. However, there re- fitness landscapes among different problems. By regarding mains room for improvement on the performance and ca- each problem as a task, MFEA seeks the optima for all tasks pability of evolutionary multitasking. Beyond three tasks, in a unified decision space, where the search space of mul- this paper proposes a novel framework, called the symbio- tiple problems are unified by a transformation function. The sis in biocoenosis optimization (SBO), to address evolution- solution information of different tasks is exchanged through ary many-tasking optimization. The SBO leverages the notion skill factor and mating. MFEA has achieved several promis- of symbiosis in biocoenosis for transferring information and ing results in dealing with two or three tasks. However, there knowledge among different tasks through three major com- exists room for improving EAs in multitasking. ponents: 1) transferring information through inter-task indi- vidual replacement, 2) measuring symbiosis through inter- This paper aims to address three issues at evolutionary task paired evaluations, and 3) coordinating the frequency multitasking. First, information transfer plays a crucial role and quantity of transfer based on symbiosis in biocoenosis. in solving multiple tasks concurrently. In MFEA, informa- The inter-task individual replacement with paired evaluations tion is transferred through recombination of individuals that caters for estimation of symbiosis, while the symbiosis in bio- are good at some specific tasks under the user-defined ran- coenosis provides a good estimator of transfer. This study ex- dom mating probability (rmp). Nevertheless, MFEA does amines the effectiveness and efficiency of the SBO on a suite not control the rmp during evolution; that is, it lacks a mech- of many-tasking benchmark problems, designed to deal with anism for controlling the quantity and frequency of informa- 30 tasks simultaneously. The experimental results show that SBO leads to better solutions and faster convergence than the tion transfer. Second, MFEA is inapplicable to the model- state-of-the-art evolutionary multitasking algorithms. More- based EAs, such as estimation of distribution algorithm over, the results indicate that SBO is highly capable of identi- (Hauschild and Pelikan 2011) and ant colony optimization fying the similarity between problems and transferring infor- (Dorigo, Maniezzo, and Colorni 1996), in that these EAs mation appropriately. seldom adopt recombination of individuals. The information transfer among tasks is therefore disabled. Third, evolution- ary multitasking is focused on two or three tasks, whereas 1 Introduction concurrently solving more tasks is highly desirable but has Evolutionary algorithms (EAs) (Holland 1975; Goldberg not been investigated yet. In particular, appropriate transfer 1989; Schwefel 1995) have shown their great capability of becomes even harder as the number of tasks increases due to tackling search and optimization problems. Inspired from m the squared number 2 of possible transfers. Therefore, the Darwinian evolution theory (Darwin 1859), EAs mimic nat- increase of tasks intensifies the importance of balancing the ural evolution to search for the optimal solutions by ma- exploitation within a task and the exploration among multi- nipulating a population of candidate solutions. There have ple tasks. been various EAs proposed for different problems (Eiben This paper proposes a novel framework for evolutionary and Smith 2003; Gen and Cheng 1997). In EA, a population multitasking, called the symbiosis in biocoenosis optimiza- of individuals evolves for searching the optimal solution, tion (SBO), which manipulates multiple EAs and each one is where a solution is encoded as chromosome, and the fitness responsible for a task. In SBO, the collection of EA popula- implies the quality of a solution. The principle of “survival tions constitutes the biocoenosis, while the transfer of infor- of the fittest” drives the population towards better and opti- mation between populations caters to the symbiosis. Specifi- mal solutions. cally, the inter-task individual replacement is proposed for Copyright c 2019, Association for the Advancement of Artificial information transfer; hence, SBO enables the use of EAs Intelligence (www.aaai.org). All rights reserved. without recombination for evolutionary multitasking. For 4295 measuring the symbiosis, we combine the inter-task individ- ual replacement with paired evaluations. Furthermore, SBO Species A Species F controls the quantity and frequency of information transfer Biocoenosis through symbiosis to balance exploitation within single task and exploration between different tasks. The effectiveness Symbiosis of SBO is verified on the suite of many-tasking problems Species B Species E (MaTPs), in which each problem comprises 30 test func- tions of CEC 2017 competition. A series of experiments is conducted on the MaTPs to investigate the effects and ad- vantages of SBO in evolutionary many-tasking. Species C Species D The main contributions of this study are summarized as follows: • A novel framework SBO for evolutionary multitasking. Figure 1: An illustration of SBO framework • Three features of SBO: transferring information through inter-task individual replacement, measuring symbiosis et al. (2015) incorporated a nested bi-level EA into MFEA through inter-task paired evaluations, and coordinating for tackling bi-level optimization problems. Sagarna and the frequency and quantity of transfer based on symbiosis Ong (2016) used MFEA to solve the software testing prob- in biocoenosis. lems. Chandra et al. (2016) utilized MFEA to optimize the • Empirical study on the effectiveness and efficiency of architecture and parameters of feed forward neural network. SBO, in comparison with single-task optimization and Zhou et al. (2016) adopted MFEA on a combinatorial opti- multitask optimization methods. mization problem, i.e., the capacitated vehicle routing prob- • Comprehensive analysis of transfer behavior for SBO and lem. In (Gupta et al. 2016b), MFEA tackled multi-objective MFEA. optimization problem by treating two performance metrics for multi-objective optimization problem, i.e., the nondomi- The remainder of this paper is organized as follows. Sec- nated front and crowding distance, as different tasks. tion 2 reviews the related work about evolutionary multi- Some studies focus on improving or analyzing the ef- tasking. Section 3 elucidates the proposed SBO framework fect of transfer. The synergy of fitness landscapes affects and its components. Section 4 presents the experimental re- the effectiveness and efficiency of MFEA. That is, a bet- sults. Finally, we draw conclusions in Section 5. ter movement in decision space for one task can be good for the other task. Gupta et al. (2016a) analyzed the syn- 2 Related Work ergy of fitness landscapes on some test functions. Wen and Evolutionary multitasking establishes a new class of EAs ca- Ting (2017) designed a parting ways strategy based on the pable of solving multiple problems simultaneously. MFEA survival rate of transferred individuals; such strategy aims is a renowned EA for evolutionary multitasking (Gupta et at terminating information transfer between tasks if transfer al. 2017; Gupta, Ong, and Feng 2018; Ong and Gupta 2016; is useless. Li et al. (2018) enabled multiple rmp to deter- Strasser et al. 2016). MFEA utilizes a single population for mine the frequency of transfer, where each rmp is adapted optimizing multiple tasks. The main ideas behind MFEA are according to the survival rate after genetic transfer. Cheng et the designs of scalar fitness serving as a unified fitness func- al. (2017) applied the scheme of co-evolution to evolution- tion for survival selection and the assortative mating opera- ary multitasking, yet the performance is similar to MFEA tor for information transfer. The skill factor of an individual in bi-tasking test problems. Ding et al. (2017) improved represents the task index with the best rank over all tasks, the transfer mechanism in MFEA by learning the decision while the scalar fitness is the reciprocal of the rank of the space transformation, including the location and permuta- most talented task. The assortative mating operator performs tion of decision vector. Feng et al. (2018) proposed transfer- crossover in two cases: the two parents have the same skill ring knowledge through task mapping, where the mapping is factor or the predefined random mating probability (rmp) learnt by a denoising autoencoder. Some studies utilize the is met. The offspring generated by crossover operator ran- transfer from past experience
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