## 1 Introduction
The _WOA_ is a simple method as it uses a small number of parameters to control the search process, which makes it a good candidate for new modifications. In this paper, we propose combining the _WOA_[17] with _TS_ for fast computation of almost optimal solutions of _MOPs_ (_MOWOATS_). _MOWOATS_ is proposed to find solutions of _MOPs_ that are very near the true _PF_ of the problems and evenly distributed over the solution space. This comes as a result from using the mature memory elements of _TS_ to provide a better guidance to swarm members while covering the solution space. Another technique is proposed to overcome the drawbacks of _PSO_ and its rivals, which is the new diversification method that is used to improve the coverage of solution space. _MOWOATS_ uses the crossover operator inspired form Genetic Algorithm (_GA_) [19] to improve the diversity of the population. These modifications ensure that _MOWOATS_ can cover solution space and obtain high-quality solutions for _MOPs_ in real time. _MOWOATS_ uses _EL_ to store the non-dominated solutions about the search space. Then, these solutions are used to guide the search by the swarm members to escape from local extreme points. This technique avoids the _MOWOATS_ to get trapped in local optima as it selects the best solution randomly each time from solutions stored in _EL_. To ensure covering the promising regions in search space, _MOWOATS_ applies a crossover operator among swarm members and solutions in _EL_. _MOWOATS_, too, is a modified diversification step that positions the swarm members in their vicinity rather than the vicinity of the prey. This technique provides a better coverage of search space and eliminates the need to local search methods. The crossover operator is also applied among swarm members to improve the diversity of the population. The contributions of this paper can be summarized into:  
* Design a simple and hybrid multi-objective optimization algorithm that attains more accurate solutions than common _SI_-based optimization heuristics. It uses the _EL_ memory component to store non-dominated solutions. These solutions are used to guide swarm members during the search process, which eliminates the need for local search methods. * A new diversification step is proposed to ensure an effective coverage of search space. The method ensures the balance between local optima and global optimization. * Since _SI_ methods need to enhance the diversity of swarm members [7; 10], _MOWOATS_ uses a crossover operator to broaden the diversity of swarm members. Crossover is also used to enhance the evolution of swarm members by applying it over solutions kept in the _EL_. * _MOWOATS_ uses the Pareto dominance criterion to evaluate the solutions. This method allows _MOWOATS_ to optimize the whole objectives simultaneously and ensures obtaining solutions that are evenly distributed over solution space. * _MOWOATS_ is tested over different benchmark multi-objective test functions, such as Zitzler-Deb Thiele (_ZDT_) [20] test functions proposed by [PERSON] et al., Deb-Thiele-Laumanns Zitzler (_DTLZ_) [20] test functions proposed by [PERSON] et al., and _CEC2009_ test functions proposed by [PERSON] et al. [21]. The Inverted Generational Distance (_IGD_) metric [13] is used for the comparison. The paper is organized as follows. Section 2 presents previous methods proposed to solve _MOPs_. Section 3 presents a mathematical description of _MOPs_ and provides a short description for both _WOA_ and _TS_ algorithms. Section 4 describes the proposed algorithm and explains in detail some of its major components. Section 5 reports a performance analysis for _MOWOATS_. Section 6 summarizes the main points of our work and future work.