“…Conventionally, MOO problems are often converted into single-objective optimization problems by aggregating similar objectives or through the weighted sum method [18]. In most cases, objective functions conflict with each other, so multiple objectives are formulated for MOO problems so as to generate a set of Pareto-optimal solutions instead of one unique solution [2,19,20]. Pareto-optimal solution sets represent non-dominated solutions with varying degrees of trade-offs between the objective functions.…”
Section: How Multi-criteria Decision-making (Mcdm) Methods Can Be Lin...mentioning
confidence: 99%
“…Wan et al [81] integrated NSGA-II with differential evolution and named the method Non-dominated Sorting Differential Evolution (NSDE). NSGA-II was selected by the researchers mainly due to its computational speed and better performance in terms of maintaining the diversity/versatility among Pareto-optimal solutions, and better convergence efficiency [2,79,[82][83][84]. Mirghaderi and Modiri [84] applied the Strength Pareto Evolutionary Algorithm (SPEA) to identify an optimized and sustainable supply chain for construction materials and reported that the method outperformed NSGA-II and Pareto Envelope-Based Selection Algorithms for addressing real cases.…”
“…Outperforming or nondominated solutions refer to outcomes where it is not possible to improve one objective function's value without degrading one or more other objective functions' values. When the problem contains continuous objective functions with two or more conflicting goals, it is often considered to be a Multi-Objective Optimization (MOO) problem [2]. These objectives are designed to either minimize or maximize some functions related to, e.g., economic (i.e., cost, profit), technical (i.e., energy use efficiency, yield), environmental (i.e., GHG emissions, land use footprint), or other factors or decision/design variables.…”
“…Uncertainty can be included with MOO methods either a posteriori (sensitivity analysis) or a priori (during model development) [2]. On the other hand, uncertainty in MCDM methods is mostly addressed by using stochastic methods to consider the ambiguity in DMs' subjective preferences and the associated weights assigned to each criterion/objective function [27].…”
The integration of Multi-Objective Optimization (MOO) and Multi-Criteria Decision-Making (MCDM) has gathered significant attention across various scientific research domains to facilitate integrated sustainability assessment. Recently, there has been a growing interest in hybrid approaches that combine MCDM with MOO, aiming to enhance the efficacy of the final decisions. However, a critical gap exists in terms of providing clear methodological guidance, particularly when dealing with data uncertainties. To address this gap, this systematic review is designed to develop a generic decision tree that serves as a practical roadmap for practitioners seeking to perform MOO and MCDM in an integrated fashion, with a specific focus on accounting for uncertainties. The systematic review identified the recent studies that conducted both MOO and MCDM in an integrated way. It is important to note that this review does not aim to identify the superior MOO or MCDM methods, but rather it delves into the strategies for integrating these two common methodologies. The prevalent MOO methods used in the reviewed articles were evolution-based metaheuristic methods. TOPSIS and PROMETHEE II are the prevalent MCDM ranking methods. The integration of MOO and MCDM methods can occur either a priori, a posteriori, or through a combination of both, each offering distinct advantages and drawbacks. The developed decision tree illustrated all three paths and integrated uncertainty considerations in each path. Finally, a real-world case study for the pulse fractionation process in Canada is used as a basis for demonstrating the various pathways presented in the decision tree and their application in identifying the optimized processing pathways for sustainably obtaining pulse protein. This study will help practitioners in different research domains use MOO and MCDM methods in an integrated way to identify the most sustainable and optimized system.
“…Conventionally, MOO problems are often converted into single-objective optimization problems by aggregating similar objectives or through the weighted sum method [18]. In most cases, objective functions conflict with each other, so multiple objectives are formulated for MOO problems so as to generate a set of Pareto-optimal solutions instead of one unique solution [2,19,20]. Pareto-optimal solution sets represent non-dominated solutions with varying degrees of trade-offs between the objective functions.…”
Section: How Multi-criteria Decision-making (Mcdm) Methods Can Be Lin...mentioning
confidence: 99%
“…Wan et al [81] integrated NSGA-II with differential evolution and named the method Non-dominated Sorting Differential Evolution (NSDE). NSGA-II was selected by the researchers mainly due to its computational speed and better performance in terms of maintaining the diversity/versatility among Pareto-optimal solutions, and better convergence efficiency [2,79,[82][83][84]. Mirghaderi and Modiri [84] applied the Strength Pareto Evolutionary Algorithm (SPEA) to identify an optimized and sustainable supply chain for construction materials and reported that the method outperformed NSGA-II and Pareto Envelope-Based Selection Algorithms for addressing real cases.…”
“…Outperforming or nondominated solutions refer to outcomes where it is not possible to improve one objective function's value without degrading one or more other objective functions' values. When the problem contains continuous objective functions with two or more conflicting goals, it is often considered to be a Multi-Objective Optimization (MOO) problem [2]. These objectives are designed to either minimize or maximize some functions related to, e.g., economic (i.e., cost, profit), technical (i.e., energy use efficiency, yield), environmental (i.e., GHG emissions, land use footprint), or other factors or decision/design variables.…”
“…Uncertainty can be included with MOO methods either a posteriori (sensitivity analysis) or a priori (during model development) [2]. On the other hand, uncertainty in MCDM methods is mostly addressed by using stochastic methods to consider the ambiguity in DMs' subjective preferences and the associated weights assigned to each criterion/objective function [27].…”
The integration of Multi-Objective Optimization (MOO) and Multi-Criteria Decision-Making (MCDM) has gathered significant attention across various scientific research domains to facilitate integrated sustainability assessment. Recently, there has been a growing interest in hybrid approaches that combine MCDM with MOO, aiming to enhance the efficacy of the final decisions. However, a critical gap exists in terms of providing clear methodological guidance, particularly when dealing with data uncertainties. To address this gap, this systematic review is designed to develop a generic decision tree that serves as a practical roadmap for practitioners seeking to perform MOO and MCDM in an integrated fashion, with a specific focus on accounting for uncertainties. The systematic review identified the recent studies that conducted both MOO and MCDM in an integrated way. It is important to note that this review does not aim to identify the superior MOO or MCDM methods, but rather it delves into the strategies for integrating these two common methodologies. The prevalent MOO methods used in the reviewed articles were evolution-based metaheuristic methods. TOPSIS and PROMETHEE II are the prevalent MCDM ranking methods. The integration of MOO and MCDM methods can occur either a priori, a posteriori, or through a combination of both, each offering distinct advantages and drawbacks. The developed decision tree illustrated all three paths and integrated uncertainty considerations in each path. Finally, a real-world case study for the pulse fractionation process in Canada is used as a basis for demonstrating the various pathways presented in the decision tree and their application in identifying the optimized processing pathways for sustainably obtaining pulse protein. This study will help practitioners in different research domains use MOO and MCDM methods in an integrated way to identify the most sustainable and optimized system.
“…In this way, the created robot leg will be optimized with a larger step length in both horizontal and vertical direction. In addition, more advanced algorithms, such as genetic algorithms [30][31][32] , can be introduced to improve the performance of the proposed multi-objective process. Furthermore, we also plan to incorporate a geometrically nonlinear model into the proposed optimization algorithm to achieve large-displacement synthesis of compliant legs with specific motion curves.…”
Robotic legs are an important component of the quadruped robot for achieving different motion gaits. Although the conventional rigid-link-based legs can generally perform robust motions, they still have the issues with poor sealing when operating in complex and liquid terrains. To cope with this problem, fully compliant legs with monolithic structure have been introduced in recent years to improve the system compactness and structural compliance of quadruped robots. In this article, we present a topology-optimization-based method to achieve efficient design of compliant robotic legs. In order to balance the structural stiffness and bending flexibility of the realized leg, a multi-objective optimization algorithm is utilized. A series of design cases are presented to illustrate the design principle and analytical procedure of the proposed method. In addition, experimental evaluation is also performed, and the results have demonstrated that, a quadruped robot with the optimized legs can successfully achieve stable and continuous straight-line walking motions.
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