# Support Vector Machine-Assisted Importance Sampling for Optimal Reliability Design
## 1 Introduction
GA is an evolutionary-based optimization technique, which was proposed by mimicking the natural selection and genetic mechanism [10]. Selection, crossover, and mutation are cores of GA. Examples of papers applying GA to solve ORD are [11; 12; 13]. Particle swarm optimization (PSO) is a random search algorithm based on group cooperation [14]. PSO is initialized as a group of random particles within the feasible domain. In each iteration, the particles update themselves by tracking the optimal solution found by the particle itself (i.e., individual best or personal best) and the optimal solution found by the whole population (i.e., global best). For papers that apply PSO to solve ORD, see [15; 16; 17]. Ant colony optimization (ACO) is a probabilistic algorithm used to find the optimal decision scheme [18]. It utilizes the walking path of ants to represent the feasible solution of the optimization problem. For applications of ACO for solving ORD, see [19; 20]. There are also some other metaheuristics for solving ORD, such as in [21; 22]. Nonconvex optimization problems can present many discontinuous discrete feasible regions and local optima. This may trap the algorithm's iterations and make the algorithm of poor quality to tackle the problem at hand. Therefore, global optimization methods must be sought to escape local optima. Revisiting the collected literature, we can see intuitively that most population-based intelligent approaches are greedy algorithms. These explore the optimal solution gradually and iteratively. The decision of each iteration is usually made according to a certain criterion based on the current situation, without considering all possible situations. It makes successive greedy choices until the optimal solution is emerged. In this process, the generation (or renewal) of the next-generation population (or particle position, etc.) is a crucial operation. For example, SA draws new candidate solutions by simulating an ergodic Markov chain whose stationary distribution is the target distribution: GA produces new individuals through selection, crossover, and mutation; and PSO updates the positions of particles in terms of particle velocity, local optimum, and global optimum. Despite the benefits of intelligent algorithms, there are still many issues associated with implementing these approaches. For example, it is difficult to determine the initial temperature and temperature gradient in SA; GA may require long processing for a feasible solution to evolve; and PSO is easy to be caught into local optima and lacks of strict mathematical study. In an attempt to reduce the processing time and improve the quality of solutions, particularly to escape local optima, this paper proposes a new population-based greedy algorithm that is able to reach the (near) global optimum in a relatively short time. The key ingredients of the proposed algorithm include importance sampling (IS) [23] and support vector machine (SVM) [24; 25]. Starting from an initial group of individuals uniformly generated from the design domain, a new population is produced based on the existing information about the feasible/infeasible domains and the fitness values of feasible individuals. New populations will be generated iteratively until the optimal solution appears. To generate the new population in each iteration, a quasi-optimal IS probability density function (PDF) is constructed as the target distribution to draw samples for the new-generation population, leveraging the information of the constraint boundary and the fitness values of feasible individuals. To alleviate the computational burden, SVM is utilized to manage the information that is used to construct IS PDF, so as to avoid repeatedly invoking the objective and constraint functions numerous times. Obviously, this advantage is of great significant for complex problems. Furthermore, to speed up the convergence, a number of candidate solutions are generated at each iteration. The merits of the proposed algorithm are twofold.