Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Cuate, Oliver; Schütze, Oliver

doi:10.3390/math8101651

Cited by 18 publications

(7 citation statements)

References 55 publications

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“…Conversely, for actual implementation, only one solution is required. Thus, the most suitable solution can be selected in various ways [54][55][56]. For example, in [57] an iterative Pareto fuzzy method is proposed to determine a suitable balance between all objective functions.…”

Section: Solution Selection Criterionmentioning

confidence: 99%

Multiobjective Optimization of Fuzzy System for Cardiovascular Risk Classification

Villamil,

Espitia,

Bejarano

2023

Computation

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Since cardiovascular diseases (CVDs) pose a critical global concern, identifying associated risk factors remains a pivotal research focus. This study aims to propose and optimize a fuzzy system for cardiovascular risk (CVR) classification using a multiobjective approach, addressing computational aspects such as the configuration of the fuzzy system, the optimization process, the selection of a suitable solution from the optimal Pareto front, and the interpretability of the fuzzy logic system after the optimization process. The proposed system utilizes data, including age, weight, height, gender, and systolic blood pressure to determine cardiovascular risk. The fuzzy model is based on preliminary information from the literature; therefore, to adjust the fuzzy logic system using a multiobjective approach, the body mass index (BMI) is considered as an additional output as data are available for this index, and body mass index is acknowledged as a proxy for cardiovascular risk given the propensity for these diseases attributed to surplus adipose tissue, which can elevate blood pressure, cholesterol, and triglyceride levels, leading to arterial and cardiac damage. By employing a multiobjective approach, the study aims to obtain a balance between the two outputs corresponding to cardiovascular risk classification and body mass index. For the multiobjective optimization, a set of experiments is proposed that render an optimal Pareto front, as a result, to later determine the appropriate solution. The results show an adequate optimization of the fuzzy logic system, allowing the interpretability of the fuzzy sets after carrying out the optimization process. In this way, this paper contributes to the advancement of the use of computational techniques in the medical domain.

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Section: Solution Selection Criterionmentioning

confidence: 99%

Multiobjective Optimization of Fuzzy System for Cardiovascular Risk Classification

Villamil,

Espitia,

Bejarano

2023

Computation

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“…Then, the solution with the most extended length from itself perpendicular to the hyperplane is the knee solution. Several knee searching algorithms are based on this technique, e.g., [39][40][41].…”

Section: Itinerary Selection From Pareto Frontmentioning

confidence: 99%

Multi-Objective Trip Planning With Solution Ranking Based on User Preference and Restaurant Selection

2022

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The tourist trip design problem (TTDP) helps the trip planners, such as tourists, tour companies, and government agencies, automate their trip planning. TTDP solver chooses and sequences an optimal subset of point of interest (POIs), which adhere to the POIs attributes and tourist preferences, and then generates a travel itinerary that maximizes their pleasure. However, the traditional TTDP does not include the lunch period at a local restaurant, which causes the rest of the itinerary in the afternoon to shift, nor compulsory POIs that the trip planners must be included in the itinerary. Moreover, as tourism contributes to high greenhouse gas emissions, especially from its transportation, minimizing the itinerary's total distance is also considered. Unfortunately, this objective conflicts with the profit scores; no single itinerary can optimize both objectives simultaneously. Hence, the multi-objective technique and the results of non-dominated itineraries can be organized as a Pareto front. The trip planners can choose one suitable itinerary from the Pareto front based on their preferences. To address these real-world issues, we formulate a new variant of the well-known orienteering problem with time windows (OPTW) called the multi-objective orienteering problem with Time Windows, Restaurant Selection, and Compulsory POIs (MOPTW-RSCP). The proposed problem is provided with a mathematical formulation and two exact algorithms for solving them, i.e., greedy and branch-and-cut Pareto-based techniques. The algorithms' performance is tested against the Rattanakosin island (the old city of Bangkok) dataset. We conduct 24 test cases, and the computational results confirm the algorithms' efficiency.INDEX TERMS branch-and-cut algorithm, greedy algorithm, knee solution, low carbon tourism, multiobjective optimization, orienteering with time windows, point-of-interests, recommendation, solution ranking, tourist trip design problem

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“…Some novel ideas to rank the potential solutions obtained by evolutionary algorithms in application to engineering problems are exposed in [32]. Likewise, an approach to the knee solution of the Pareto Front approximation for optimization problems with many objectives is addressed in [33].…”

Section: Multicriteria Decision Makingmentioning

confidence: 99%

“…These data were initially fitted to functions of the normalized delay τ. Afterwards, the resulting expressions were scaled to obtain the LADRC tuning rules applicable to the control of the general FOPDT system (33).…”

Section: Tuning Rules For Ladrcmentioning

confidence: 99%

“…In addition, the tuning rules for the second-order LADRC from [11] (ADRC H ) were also taken into account. The latter are proposed for the control of high order plants, but can be used for self-regulatory FOPDT systems with nominal delay (τ/T) above 0.46 by approximating the plant into the form K/(Ts + 1) n (Note that K and T have a different meaning than in (33)). Figures 14 and 15 show the closed loop time response of G 2 (s) with the LADRC and the PID controllers, respectively.…”

Section: Example 2: a Delay-dominated Systemmentioning

confidence: 99%

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Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness

et al. 2021

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A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives.

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Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Cited by 18 publications

References 55 publications

Multiobjective Optimization of Fuzzy System for Cardiovascular Risk Classification

Multiobjective Optimization of Fuzzy System for Cardiovascular Risk Classification

Multi-Objective Trip Planning With Solution Ranking Based on User Preference and Restaurant Selection

Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness

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