JOURNAL OF L A T E X CLASS FILES, VOL. 14, NO. 8, AUGUST 2015 1 A Unified Framework of Graph-based Evolutionary Multitasking Hyper-heuristic Xingxing Hao, Rong Qu, Senior Member, IEEE, and Jing Liu, Senior Member, IEEE Abstract—In recent research, hyper-heuristics have attracted increasing attention among researchers in various fields. The most appealing feature of hyper-heuristics is that they aim to provide more generalized solutions to optimization problems by searching in a high-level space of heuristics instead of direct problem domains. Despite the good generalities of hyper- heuristics, the design of more general search methodologies is still an emerging challenge. Evolutionary multitasking is a relatively new evolutionary paradigm that attempts to solve multiple optimization problems simultaneously. It exploits the underlying similarities among different optimization tasks by allowing the transmission of information among them, thus accel- erating the optimization of all tasks. Inherently, hyper-heuristics and evolutionary multitasking share similarities in three ways. (1) They both operate on third-party search spaces. (2) High- level search methodologies are universal. (3) They both conduct cross-domain optimization. To integrate their advantages, i.e., the knowledge-transfer and the cross-domain optimization abilities of the evolutionary multitasking and the search in the heuristic spaces of hyper-heuristics, in this paper, a unified framework of evolutionary multitasking graph-based hyper-heuristic (EMHH) is thereby proposed. To assess the generality and effectiveness of EMHH, the integration of the population-based graph-based hyper-heuristics with the evolutionary multitasking for solving exam timetabling and graph-coloring problems, separately and simultaneously, is studied. The experimental results demonstrate the effectiveness, efficiency, and increased generality of the proposed unified framework compared with single-tasking hyper- heuristics. Index Terms—Hyper-heuristics, evolutionary multitasking, exam timetabling, graph coloring. I. I NTRODUCTION M ETA-heuristics have shown to be highly effective in solving various combinational optimization problems [1], [2]. They quite often concern one particular problem, however, tend to perform poorly on other problems or even other instances of the same problem. The performance of these approaches also strongly depends on domain-specific knowl- edge and expertise such as complicated parameter tunings [3]– [5]. Such tailor-made settings limit the generality of meta- heuristics, making them expensive to develop and adapt to other problems. This work was supported in part by the General Program of NSFC under Grant 61773300, in part by the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province, China under Grant 2017JZ017, and in part by the Doctoral Students’ Short-Term Study Abroad Scholarship Fund of Xidian University. X. Hao and J. Liu are with the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an 710071, China (e-mail: ystar1991@126.com; neouma@163.com). R. Qu is with the Computational Optimisation and Learning (COL) Lab, School of Computer Science, University of Nottingham, United Kingdom (e- mail: rong.qu@nottingham.ac.uk) Motivated by this, more recent research concerns general- ized and adaptive algorithms [6]. Hyper-heuristics, which are heuristics that choose heuristics, can be regarded as such general algorithms [3], [6]–[10]. Instead of searching directly in the solution space like meta-heuristics, hyper-heuristics work at the higher-level search space of a set of low-level heuristics. The goal is to solve the problem at hand by selecting existing low-level heuristics or generating new low- level heuristics. The only requirement for developing a hyper- heuristic for a problem is a set of low-level heuristics that are easy-to-implement and a problem-specific objective function. These are used at the low-level in hyper-heuristics which are general addressing different problems. After the term was first proposed in [4], hyper-heuristic approaches have been successfully used to solve a range of combinational optimization problems, such as Boolean satis- fiability problems [11], [12], vehicle routing problems [13], [14], packing problems [15], [16], educational timetabling problems [9], and many more [8], [10]. The search space of hyper-heuristics either comprises of existing low-level heuristics or a set of components and operators that are used to construct low-level heuristics. Based on these properties, hyper-heuristics can be categorized into heuristic selection and heuristic generation hyper-heuristics, respectively [17]. Heuristic selection hyper-heuristics select a given set of low- level heuristics to construct or improve solutions; while heuris- tic generation hyper-heuristics generate new heuristics using a given set of components and operators. Furthermore, in both of the heuristic selection and heuristic generation hyper- heuristics, constructive and perturbative low-level heuristics can be used to build solutions step by step; or modify and improve complete solutions. This paper concerns a new framework of selection constructive hyper-heuristic. The paradigm of evolutionary multitasking optimization (EMO) was first proposed in [18] for solving multifacto- rial optimization (MFO) problems, which are categorized as the third category of optimization problems besides single- objective and multi-objective optimization problems. EMO has been successfully extended since then to several domains including continuous optimization, discrete optimization, com- binational optimization, and multi-objective optimization [18]– [26]. EMO can optimize two or more tasks simultaneously instead of evaluating every task at each step of evaluation. Under the assumption that each individual is at least skilled at one task, the population in EMO is split into different skill groups. The success of EMO lies in the knowledge transfer among different skill groups; that is, the genetic experience within one group can be transferred to other groups, thus to