Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs

2015 ◽  
Vol 168 (3) ◽  
pp. 864-883 ◽  
Author(s):  
Kazhal Khaledian ◽  
Esmaile Khorram ◽  
Majid Soleimani-damaneh
2019 ◽  
Author(s):  
Sabrine Drira ◽  
Frida Ben Rais Lasram ◽  
Tarek Hattab ◽  
Yunne Jai Shin ◽  
Amel Ben Rejeb Jenhani ◽  
...  

AbstractSpecies distribution models (SDMs) have been proposed as a way to provide robust inference about species-specific sites suitabilities, and have been increasingly used in systematic conservation planning (SCP) applications. However, despite the fact that the use of SDMs in SCP may raise some potential issues, conservation studies have overlooked to assess the implications of SDMs uncertainties. The integration of these uncertainties in conservation solutions requires the development of a reserve-selection approach based on a suitable optimization algorithm. A large body of research has shown that exact optimization algorithms give very precise control over the gap to optimality of conservation solutions. However, their major shortcoming is that they generate a single binary and indivisible solution. Therefore, they provide no flexibility in the implementation of conservation solutions by stakeholders. On the other hand, heuristic decision-support systems provide large amounts of sub-optimal solutions, and therefore more flexibility. This flexibility arises from the availability of many alternative and sub-optimal conservation solutions. The two principles of efficiency and flexibility are implicitly linked in conservation applications, with the most mathematically efficient solutions being inflexible and the flexible solutions provided by heuristics suffering sub-optimality. In order to avoid the trade-offs between flexibility and efficiency in systematic conservation planning, we propose in this paper a new reserve-selection framework based on mathematical programming optimization combined with a post-selection of SDM outputs. This approach leads to a reserve-selection framework that might provide flexibility while simultaneously addressing efficiency and representativeness of conservation solutions and the adequacy of conservation targets. To exemplify the approach we a nalyzed an experimental design crossing pre- and post-selection of SDM outputs versus heuristics and exact mathematical optimizations. We used the Mediterranean Sea as a biogeographical template for our analyses, integrating the outputs of 8 SDM techniques for 438 fishes species.


2003 ◽  
Vol 45 (1) ◽  
pp. 75-89 ◽  
Author(s):  
B. Jiménez ◽  
V. Novo

AbstractIn this paper we define two types of proper efficient solutions in the Borwein sense for vector optimisation problems and we compare them with the notions of local Borwein, Ishizuka-Tuan, Kuhn-Tucker and strict efficiency. A sufficient condition for a proper solution is also proved.


Author(s):  
Bo Huang ◽  
Pierre Fery ◽  
Liangpei Zhang

This research attempted to build a framework for determining optimal routes for hazardous materials transportation. Previous work has suggested the incorporation of many conflicting objectives in the analysis, such as travel cost, population exposure, environmental risk, and security concerns. Multiplying the number of objectives leads to complex shortest path problems that often have several efficient solutions. The present study emphasizes an overview of possible trade-offs among routes without generating all of them. A simple characterization of the efficient routes is used to select the best ones with no need for input from the decision maker. A case study with eight objective functions was performed on a road network in Singapore. A geographical information system was used to quantify road link attributes, which are assumed linear and deterministic for the sake of simplicity. The proposed algorithm derives four significantly different routes, which conform to intuition.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hongwei Liang ◽  
Zhongping Wan ◽  
Litao Zhang

AbstractIn this paper, we provide the connectedness of the sets of weak efficient solutions, Henig efficient solutions and Benson proper efficient solutions for set-valued vector equilibrium problems under improvement sets.


2020 ◽  
Vol 54 (4) ◽  
pp. 949-959
Author(s):  
Xiaoyan Zhang ◽  
Qilin Wang

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.


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