# A Novel Multi-Objective Five-Elements Cycle Optimization Algorithm
## 1 Introduction  
In real-world applications, commonly Multiple-Objective Optimization (MOO) problems are applied to many situations such as biology, engineering, medical and economics, and so forth [1]. Usually this kind of optimization problem contains multiple objectives which conflict with each other, hence no single optimal solution can be derived. As a result, a set of solutions should be found to trade off the multiple conflicting goals. In the past few decades, Evolutionary Algorithms (EAs), and some population-based meta-heuristic algorithms, have been verified to effectively solve MOO problems and they can also get an optimal Pareto solution set in one run [2]. Therefore, the application of EAs to MOO problems has received considerable attention, which led to the emergence of a new research issue named Multi-Objective Evolutionary Algorithms (MOEAs). Since then, a large number of MOEAs have been developed and widely used, which have become an important research hotspot in evolutionary optimization. The purpose of researching MOEAs is to make the population converge quickly and widely, and in the meanwhile distribute uniformly in the non-inferior optimal domain of the problem, which means the convergence and diversity of the solution set should be considered simultaneously [3]. In order to achieve these two goals, quite a few well-performed MOEAs have been proposed in the literature. Some of the most representative ones and some of their applications are listed as follows. The Non-dominated Sorting Genetic Algorithm (NSGA)was proposed by [PERSON] and [PERSON] [4] and based on this, an improved version Non-dominated Sorting Genetic Algorithm II(NSGA-II) was proposed by [PERSON] et al. [5]. NSGA-II was applied to carry out the integer optimized design of the Methyl Acetate Hydrolysis Process [6]. [PERSON] and [PERSON] proposed the Strength Pareto Evolutionary Algorithms (SPEA) [7] and its improved version Strength Pareto Evolutionary Algorithms II (SPEA-II) [8]. In the optimization of the microgrid energy dispatch, considering the economic costs, energy utilization rate and environmental benefits as multi-objective, the literature [9] established the microgrid energy allocation model and used the PSEA to solve the MOO problem. [PERSON] et al. proposed the Pareto Envelope-based Selection Algorithm (PESA) [10] and its successor Pareto Envelope-based Selection Algorithm II (PESA-II) [11]; [PERSON] et al. proposed the Multi-Objective Particle Swarm Optimization algorithm (MOPSO) [12], which was effectively applied to the design of water distribution systems in Reference [13] and minimizing the total signaling overhead of location management in Long-term Evolution (LTE) networks to solve the signaling overhead in accessing the network in the literature [14]. In recent years, there has also been a considerable amount of newly presented multi-objective optimization algorithms showing their competitiveness in the field of multi-objective optimization. [PERSON] proposed Non-dominated Sorting and Local Search (NSLS) [15], which was used to solve high-dimensional big data and it turned out that NSLS could find a better spread of solutions and better convergence to the true Pareto-optimal front [16]. Bi-Criterion Evolution for Indicator-Based Evolutionary Algorithm (BCE-IBEA) [17] and Multi-Objective Evolutionary Algorithm based on an enhanced Inverted Generational Distance metric (MOEA/IGD-NS) [18], and so forth, also show great potential for solving MOO problems. In the literature [19], a new Five-Elements Cycle Model (FECM) derived from ancient Chinese philosophy which is based on the Yin-Yang theory and Five Elements (metal, wood, water, fire, earth) is proposed. FECM was established based on the relationship of generation and restriction among the five elements. In FECM, the fitness value of each element is measured by calculating the interaction between elements, and then the element is updated according to its strengths and weaknesses.