# A Hybrid Strategy Improved SPEA2 Algorithm for Multi-Objective Web Service Composition
## 2 Related Work  
In this section, we discuss existing articles with reference to algorithms and problem models. To the best of our knowledge, there has been limited research conducted on the IOM-based WSCP. Therefore, we combine the discussions on SooA and MooA into discussions on IOM-based problems. Non-heuristic algorithms: Non-heuristic algorithms solve web service composition problems optimally by using an exhaustive search. [PERSON] et al. proposed a 0-1 linear programming-based optimal approach for QoS and transactional-aware service composition [14]. [PERSON] et al. proposed a parameterized search algorithm based on multiple QoS parameters, achieving a balance between search time and solution quality [15]. [PERSON] et al. proposed a functionality-oriented composition technique for composing web services, which helped reach the extreme functionality of each web service in the composition to achieve customer satisfaction [16]. Although non-heuristic algorithms can obtain optimal solutions, their time complexity is exceptionally high, often unacceptably so to users as the number of services increases. Single-objective heuristic algorithms based on the WM: Heuristic algorithms are semi-automated approaches that require customized optimization of the problem. They can provide feasible solutions within an acceptable time and space but do not guarantee the best solution. [PERSON] et al. filtered unreliable component services and constructed a convex hull based on trust-based selection methods, reducing the search space during the service composition process. Heuristic global optimization methods were applied to find near-optimal solutions to the problem [17]. Many works have applied evolution algorithms to the WSCP, such as the intelligent water drops algorithm [18], artificial bee colony optimization [19; 20], genetic programming [21; 22], particle swarm optimization [23], grey wolf optimizer [24; 25], and ant colony optimization [26; 27]. To overcome the limitations of single evolutionary algorithms, some studies have utilized hybrid heuristic algorithms. [PERSON] et al. employed a hybrid approach SFGA combining the frog leaping algorithm and genetic programming on top of an energy-aware mechanism to optimize mobile cloud service composition [28]. [PERSON] et al. addressed the issue of slow or premature convergence to some extent by integrating the mutation process from genetic programming into the whale algorithm [29]. Multiple-objective heuristic algorithms based on the WM: However, single-target heuristic algorithms, even when QoS includes multiple attributes, are highly dependent on the weights of each attribute, providing users with limited options. [PERSON] et al. proposed a multi-objective meme algorithm (MO-MA) that combined LS and GA methods, effectively utilizing the potential area generated by genetic algorithms [30]. [PERSON] et al. treated service cost and multi-cloud risk perspectives as a dual-objective optimization problem. They proposed a dual-objective time-varying particle swarm optimization algorithm, achieving a good balance between exploration and optimization [31]. [PERSON] et al. applied the multi-objective grey wolf algorithm to web service composition. The issues of easily falling into local optima and poor stability were improved through a nonlinear adjustment strategy of control parameters and an enhanced search strategy [32]. Heuristic algorithms based on the IOM: The IOM-based WSCP is more complex than the WM-based WSCP, since the combination results need to encode and decode input-output dependency. [PERSON] et al. proposed an indirect particle swarm optimization (PSO)-based approach. A forward algorithm and backward algorithm were used to decode solutions [33]. [PERSON] et al. proposed a hybrid approach based on genetic programming. The greedy algorithm was utilized to generate valid and locally optimized individuals to populate the initial generation [34]. [PERSON] et al. applied NSGA2 for a multi-objective problem in an IOM.