## 1 Introduction  
In recent years, numerous real-life issues have been formulated as MOPs, involving different fields such as manufacturing process optimization [1, 2]. In fact, in single-objective optimization problems, the only challenge is covering a single optimal solution. On the other hand, MOPs have multiple contradictory objectives which need to be optimized synchronously [3, 4]. Therefore, two goals commonly known as convergence and diversity are set forth. As it is well-known, several population-based algorithms have been developed for MOP solving, a popular one of which is the NSGAII [5]. In this method, the population is classified via the non-dominated sorting procedure through which a rank of non-dominance is attributed to each individual. Moreover, to assess the density of the region around a given individual, the ones in the same rank are classified based on the crowding distance operator. Moreover, to improve diversity, the SPEA II was proposed in [6], which includes new fitness assignment based on a density estimator, using a truncation technique when updating a predefined archive size. However, several attempts have been made towards the success of such approaches. For example, Pareto solutions were stored in an external repository in multiple objective PSO (MOPSO) [7]. An effective selection strategy of Gbest, in which the objective space is divided in adaptive grids, has also been employed to maintain the diversity of solutions. In addition, to improve both convergence and diversity, the \(\epsilon\)-dominance multiple objective evolutionary algorithm (\(\epsilon\)-MOEA) was developed, using the \(\epsilon\)-dominance relation [8]. However, in another example, to decompose the master multi-objective problem into several weighted sub-problems and, subsequently, to solve them simultaneously, the MOEA/D framework was proposed based on decomposition [9]. In multi-objective optimal processing, the preference-inspired co-evolutionary algorithm using goal vectors (PICEA-g) [10] is utilized to address a problem. Based on NN-DNSGA-II [11], an artificial neural network is combined with the NSGA II algorithm. However, the Indicator-Based Evolutionary Algorithm (IBEA) [12] adopts a new approach, in which indicators are directly used in the optimization process. Moreover, to solve multi-objective scheduling problems, the Chaotic PICEA-g-based algorithm was introduced in [10]. In recent years, new multi-objective methods have emerged mainly based on the swarm intelligence algorithm. Similar to MOPSO, the multi-objective Grey Wolf Optimizer (MOGWO) was proposed by [13]. Moreover, the multi-objective AntLion Optimizer (MOALO) was set forth by [14], in which a reference frame and a solution-coverage-based roulette selection are used to store the Pareto solutions and to continue the circulation of solutions, respectively. Based on the chicken swarm optimizer, it was combined with the external population in [15], using crowding calculations and \(\varepsilon\)-dominance to continue diversity to solve MOPs. In this context, in order to achieve the engineering design problem, the whale optimization algorithm was used in [16]. Moreover, the sorting and updating method was adopted based on NSGA II crowding distance to guide the population to the region with good diversity in the search space. Other well-known proposals can also be referred to, among which are the multi-objective Spotted Hyena Optimizer (MOSHO) [17], the hybrid multi-objective firefly (HMOFA) [18], the hybrid multi-objective cuckoo search (HMOCS) [19], the multi-objective Salp Swarm Algorithm (MSSA) [20], the multi-objective Artificial Sheep Algorithm (MOASA) [21] and the multi-objective Seagull Optimization Algorithm (MOSOA) [22]. Most of the MOEs mentioned above suffer from fitness allocation problems. In their application, the efficiency of the search engine is substantially low unless fitness allocation is properly designed. To avoid this issue, [PERSON] et al.