_algorithms_  
_Editorial_  
_\"Algorithms in Multi-Objective Optimization\": Foreword by the Guest Editor_  
**[PERSON]**  
Dipartimento di Ingegneria Dell'Impresa, University of Rome \"Tor Vergata\"--Via del Politecnico, 1,  
00133 Rome, Italy; [EMAIL_ADDRESS]  
Many real-world optimization problems typically involve multiple (conflicting) objectives. In such problems, the aim is to find the set of non-dominated (Pareto-optimal) solutions, producing different image vectors that are indifferent to each other when no other selection criterion is available [1]. Determining the whole set of Pareto-optimal solutions, as well as its image, i.e., the Pareto-front, is a difficult problem even though objectives and constraints are linear. Some algorithms (e.g., the Weighting method and the \(\varepsilon\)-Constraints method), in the attempt to (fully or partially), accomplish this task, rely on iteratively solving proper single-objective mathematical formulations derived from the original problem, each one returning a non-dominated solution, possibly requiring a large computing time when such a single-objective problem is NP-hard. Other solution approaches, such as Evolutionary Algorithms, due to their inherent parallelism, have the potential of finding multiple Pareto-optimal solutions in a single run. Other classes of algorithms (e.g., the Utility Function method, Lexicographic method, and Goal Programming), even more differently, try to overcome the burden hidden behind finding the Pareto-front by reducing the multi-objective problem into a unique single-objective problem, assuming the knowledge of additional information, e.g., a utility value for each solution or a ranking among the objectives. This Special Issue aimed to collect original manuscripts dealing with algorithms and applications in a Multi-Objective Optimization (MOO) environment. Four papers have been collected, each one touching an important field of application of MOO, as reported in the following paragraphs. Production planning and scheduling are among the most studied applications when it comes to multi-objective optimization, as witnessed, e.g., by the recent survey by [PERSON] et al. [2]. Related to this field of research is the first paper of this Special Issue, \"A Multi-Objective Model and Algorithms of Aggregate Production Planning of Multi-Product with Early and Late Delivery\" by [PERSON] and [PERSON] [3]. Here, the authors dealt with production planning and tackled a scenario where, due to the influence of insufficient production capacity or a shortage of production materials, production enterprises may produce products in advance or on backorder. To improve the adaptability of enterprises and reduce production costs, the authors analyzed the impacts of early delivery and delayed delivery and proposed a method to determine the loss threshold. Moreover, the maximum allowable shortage of customers with different tardiness is calculated, and the cost of delayed delivery and loss of sales is determined. Considering the production cost, raw material cost, inventory cost, staff cost, stockout, and lost sales cost, an early/delay multi-objective optimization model is developed for an aggregate production planning problem to minimize total production costs and instability in the workforce. Three algorithms and three different hybrid strategies were designed and tested to solve the model. Another important field of application of multi-objective optimization is cloud computing. As per the forecast report by Moore [4], Gartner predicted that 41% of global IT spending will shift from traditional services to public cloud services in 2022. By 2025, this percentage will increase to 51%. In the booming cloud market, cloud providers are facing the challenge of optimizing both the cost and performance of cloud services. Cloud service brokering plays an important role in finding suitable cloud services for application providers to deploy their applications in cloud data centers [5].