_algorithms_  
_Editorial_  
**\"Multi-Objective and Multi-Level Optimization: Algorithms and Applications\": 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]  
Decision making in real-world applications frequently calls for taking into account multiple goals to come up with viable solutions. Multi-objective optimization is frequently the result of the association of (conflicting) objectives defined by either a single decision maker or a group of decision makers. In this case, optimal solutions do not have the same image values as in single-objective optimization but are rather non-dominated, equivalent, and enable the definition of the Pareto front. We enter the realm of game theory when objectives belong to several non-cooperative decision makers; furthermore, when goals and/or decision makers are hierarchically arranged, this necessitates dealing with nested optimization problems and, consequently, multi-level optimization. All these problems are computationally difficult to solve, and their resolution typically involves reformulating them into several single-objective problems or one single-objective problem, introducing additional constraints. Moreover, to limit the computational burden, before their resolution, it is worthwhile to reduce the number of objectives to a very limited (significative) number by applying proper methodologies. This Special Issue, \"Multi-Objective and Multi-Level Optimization: Algorithms and Applications\", presents original articles focused on multi-objective and multi-level optimization. Five papers have been collected which present innovative applications and theory development, as reported in the following. Attainment surfaces, which were first described by [PERSON] and [PERSON] more than 25 years ago, give multi-objective optimization researchers a way to precisely visualize the region dominated by a Pareto Optimal Front. Many studies link the non-dominated solutions with curves to depict approximated Pareto Optimal Fronts (POFs). It is incorrect to utilize a curve to unite these non-dominated solutions, according to [PERSON] and [PERSON]'s reasoning. Intermediate solutions between any two non-dominated solutions identified using curves suggest that these solutions may exist; however, there is no assurance they do. Non-dominated solutions, according to [PERSON] and [PERSON], can be used to create an envelope that divides dominated and non-dominated regions rather than a curve. The envelope formed by the non-dominated solutions is referred to as an attainment surface. Attainment surfaces have not been widely applied. The first article [1] of this Special Issue investigates some of the drawbacks that might have prevented this performance measure from being adopted, wherein the quantitative Knowles and Corne measure is analyzed based on attainment surfaces. The analysis demonstrates that the attainment surface's shape influences the outcomes of the Knowles and Corne technique. An improved Knowles and Corne method for bi-objective POF comparisons is proposed. In addition, assuming \(m\) objective functions, the porcupine measure, an \(m\)-dimensional attainment-surface-based quantitative metric, is suggested for comparing the effectiveness of multi-objective optimization techniques. A computationally and empirically improved version of the porcupine measure is devised by the authors. To identify pores and fractures (both natural and induced, even at the micro-level) in the wells of a hydrocarbon reservoir, the authors of the second paper [2] of this Special Issue propose a novel meta-heuristic image analysis method using multi-objective optimization. The algorithm is called \"Pixel-wise \(k\)-Immediate Neighbors\", and offers better identification accuracy in the presence of grayscale sample rock images.