A characterization of weakly efficient points

Ruı́z-Canales, P.; Rufián-Lizana, A.

doi:10.1007/bf01585765

Cited by 46 publications

(11 citation statements)

References 3 publications

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“…In our case, the emissions bounds go from Em to E*, so finding a solution is guaranteed. In general, the solutions obtained using the ε‐constraint method are weak Pareto‐optimal and every weak Pareto‐optimal point can be obtained if the feasible region is convex and all the objective functions are explicitly quasi‐convex (Ruíz‐Canales and Rufian‐Lizana, ). If the solution is unique, then it is Pareto optimal.…”

Section: Resultsmentioning

confidence: 99%

Analysing the factors that influence the Pareto frontier of a bi‐objective supply chain design problem

Palacio

Adenso‐Díaz

Lozano

2017

Int Trans Operational Res

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In this paper a bi-objective multi-product model for the design of a production/distribution supply chain logistic network with four echelons is considered. The proposed optimization model minimizes the total cost of the network (including the fixed cost to open facilities and the transportation costs between them) and the total CO 2 emissions. Five factors (network size, product complexity, cost variability, CO 2 emissions generation and over-capacity) are considered for the experimental framework. The problem is solved using the ε-constraint method and the resulting Pareto frontiers (PF) are characterized using five new metrics specifically developed for analysing how those factors affect the resulting optimal configurations. The results show that over-capacity and product complexity are the two most influential factors regarding the characteristics of the PF, and that their effects are in the same direction: more complexity and capacity mean a wider set of optima alternatives, some close to the ideal point, and in general with a smaller number of links used.

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Section: Resultsmentioning

confidence: 99%

Analysing the factors that influence the Pareto frontier of a bi‐objective supply chain design problem

Palacio

Adenso‐Díaz

Lozano

2017

Int Trans Operational Res

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“…There also exist other scalarization methods, such as the ǫ-constraint method [1,37], the lexicographic method [7,22]. We refer to [6,10,36,38,51] for different scalarizations.…”

Section: Introductionmentioning

confidence: 99%

The Multi-Objective Polynomial Optimization

Nie,

Yang

2021

Preprint

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The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies multi-objective optimization problems that are given by polynomial functions. First, we study the convex geometry for (weakly) Pareto values and give a convex representation for them. Linear scalarization problems (LSPs) and Chebyshev scalarization problems (CSPs) are typical approaches for getting (weakly) Pareto points. For LSPs, we show how to use tight relaxations to solve them, how to detect existence or nonexistence of proper weights. For CSPs, we show how to solve them by moment relaxations. Moreover, we show how to check if a given point is a (weakly) Pareto point or not and how to detect existence or nonexistence of (weakly) Pareto points. We also study how to detect unboundedness of polynomial optimization, which is used to detect nonexistence of proper weights or (weakly) Pareto points.

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“…Steuer and Choo [24] proposed an interactive weighted Tchebycheff procedure to find efficient solutions. By using kth-objective ε-constraint method, Ruíz-Canales and Rufián-Lizana [23] established a characterization of weakly efficient solutions for multi-objective optimization problems. In order to generate all weakly efficient solutions of a convex multi-objective optimization problem, Luc et YUAN-MEI XIA, XIN-MIN YANG AND KE-QUAN ZHAO al.…”

Section: Introductionmentioning

confidence: 99%

A combined scalarization method for multi-objective optimization problems

Xia¹,

Yang²,

Ke-quan³

2021

JIMO

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In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and the generalized Tchebycheff norm and then use it to obtain some equivalent scalarization characterizations of (weakly, strictly, properly) efficient solutions by adjusting the range of parameters. These scalarization results do not need any convexity assumption conditions of objective functions. Furthermore, we establish some scalarization results of approximate solutions by means of the method. Moreover, we also present some examples to illustrate the main results.

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A characterization of weakly efficient points

Cited by 46 publications

References 3 publications

Analysing the factors that influence the Pareto frontier of a bi‐objective supply chain design problem

Analysing the factors that influence the Pareto frontier of a bi‐objective supply chain design problem

The Multi-Objective Polynomial Optimization

A combined scalarization method for multi-objective optimization problems

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