Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems

Burachik, Regina S.; Kaya, C. Yalçın; Rizvi, M. M.

doi:10.1080/0305215x.2021.1939695

Cited by 32 publications

(16 citation statements)

References 54 publications

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“…These approaches are very effective when the problem has a small number of decision variables and of criteria to be optimized (up to two or three). Study [56] proposed the algorithm to address disconnected feasible domains that are characteristic of integer and mixed-integer programming problems. The approach proposed to approximate the convex hull was shown to be accurate, since the discrepancy between the points selected in the Pareto frontier and the real solution is small (less than 1%) and the execution times are acceptable, considering the problem size and complexity.…”

Section: Discussionmentioning

confidence: 99%

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Marques

Bushenkov

Лотов

et al. 2021

Forests

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Decision making in modern forest management planning is challenged by the need to recognize multiple ecosystem services and to address the preferences and goals of stakeholders. This research presents an innovative a posteriori preference modeling and multi-objective integer optimization (MOIP) approach encompassing integer programming models and a new technique for generation and interactive visualization of the Pareto frontier. Due to the complexity and size of our management problems, a decomposition approach was used to build the Pareto frontier of the general problem using the Pareto frontiers of its sub-problems. The emphasis was on the approximation of convex Edgeworth–Pareto hulls (EPHs) for the sub-problems by systems of linear inequalities; the generation of Edgeworth–Pareto hulls by the convex approximation of the Pareto frontier evinced a very small discrepancy from the real integer programming solutions. The results thus highlight the possibility of generating the Pareto frontiers of large multi-objective integer problems using our approach. This research innovated the generation of Pareto frontier methods using integer programming in order to address multiple objectives, locational specificity requirements and product even-flow constraints in landscape-level management planning problems. This may contribute to enhancing the analysis of tradeoffs between ecosystem services in large-scale problems and help forest managers address effectively the demand for forest products while sustaining the provision of services in participatory management planning processes.

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Section: Discussionmentioning

confidence: 99%

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Marques

Bushenkov

Лотов

et al. 2021

Forests

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show abstract

“…To study decision-making problems with multiple and conflicting objectives in the real world, multiobjective programming has been widely studied by researchers in a variety of fields, especially in the field of operational research, which can be referred to in the literature [1][2][3][4][5]. It can be seen that the above literature on multiobjective programming mainly focuses on the deterministic environment.…”

Section: Introductionmentioning

confidence: 99%

Research on Comparision between Deterministic Method and Uncertain Method for Solving Uncertain Multiobjective Programming

et al. 2022

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Since there are often few or no samples and asymmetry information in the problems, uncertainty theory is introduced to study uncertain multi-objective programming (UMP), which cannot be solved by probability theory. Generally speaking, there are two types of methods for solving the UMP problem: in deterministic method, using the numerical characteristics of an uncertain variable, the UMP problem is transformed into a deterministic multiobjective programming, and then solved by the weighting method and ideal point method; in the uncertain method, the UMP problem is transformed into an uncertain single-objective programming, and then is solved by the evaluation criteria of the uncertain variables. The theoretical analysis and the data results for numerical examples solved by the AC algorithm designed in the paper show that the two types of methods are obviously different. Further, using this comparison, the essential difference between the two methods is whether the uncertainty relation between objective functions sholud be considered. Therefore, when the uncertainty relation is closely related, the uncertain method is more appropriate; otherwise, the deterministic method should be chosen.

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“…Multi-objective Optimization (MOO) or Pareto Optimality is a technique used to solve a conflict of each objective and finds the optimal solution among each candidate [8], [9], [10], [11], [12], [13], [14]. Specifically, Pareto Optimality is a group of the best solution of each problem which no one solution is allowed to dominate; this is so called Pareto Front [15], [16], [17], [18], [19]. In this decade, many evolutionary algorithms have been proposed to appoint to MOO researches such as Vector Evolution Genetic Algorithm (VEGA) [20], [21], [22]; Nondominated Sorting Genetic Algorithm (NSGA) [23], [24], [25], [26]; Niched Pareto Genetic Algorithm (NPGA) [27], [28], [29]; Pareto Archived Evolution Strategy (PAES) [30], [31], [32], [33]; Strength Pareto Evolutionary Algorithm (SPEA) [34], [35], [36], [37]; and Particle Swarm Optimizer (PSO) [38], [39], [40], [41], [42], [43].…”

Section: Introductionmentioning

confidence: 99%

Optimization of Hue, Brightness, Luminance, and Saturation Parameters for Video Segmentation Based on Evolutionary Algorithms

Pensiri¹,

Visutsak²

2022

Preprint

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Video segmentation is crucial in a variety of practical applications especially in computer visions. Most of recent works in video segmentation are focusing on Deep learning based video segmentation, there are rooms for improvement in respect of the evolutionary algorithms. This paper aims to propose the novel method to video segmentation by using the optimization of segmentation parameters based on ensemble-based random forest and gradient boosting decision tree. The experimental results show Pareto front of segmentation parameters (hue, brightness, luminance, and saturation). Our optimization model yields accuracy: 85% +/-8.85 % (micro average: 85.00 %), average class precision: 84.88%, and average class recall: 85%. We also show the video segmentation results based on our optimization method and compare our results with Kinect-based video segmentation.

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Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems

Cited by 32 publications

References 54 publications

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Building Pareto Frontiers for Ecosystem Services Tradeoff Analysis in Forest Management Planning Integer Programs

Research on Comparision between Deterministic Method and Uncertain Method for Solving Uncertain Multiobjective Programming

Optimization of Hue, Brightness, Luminance, and Saturation Parameters for Video Segmentation Based on Evolutionary Algorithms

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