scholarly journals Semicontinuity of multifunctions connected with optimization with respect to cones

1986 ◽  
Vol 40 (2) ◽  
pp. 183-193 ◽  
Author(s):  
Alicja Sterna-Karwat
Keyword(s):  
Lower Semicontinuity ◽  
Optimization Problems ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Upper And Lower Semicontinuity

AbstractThis paper studies topological upper and lower semicontinuity of the minimal value multifunction and the solution multifunction for optimization problems, which are defined in terms of cones, subject to perturbations in constraints. It extends the results of Tanino and Sawaragi to finite dimensions and one of Berge to multiple objective optimization problems.

scholarly journals Fresa: A Plant Propagation Algorithm for Black-Box Single and Multiple Objective Optimization

2021 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Mathematical Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Population Based ◽  
Black Box ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Plant Propagation ◽  
Propagation Algorithm ◽  
Multiple Dispatch

Fresa implements a nature inspired plant propagation algorithm for the solution of single and multiple objective optimization problems. The method is population based and evolutionary. Treating the objective function as a black box, the implementation is able to solve problems exhibiting behaviour that is challenging for mathematical programming methods. Fresa is easily adapted to new problems which may benefit from bespoke representations of solutions by taking advantage of the dynamic typing and multiple dispatch capabilities of the Julia language. Further, the support for threads in Julia enables an efficient implementation on multi-core computers.

INTERACTIVE ROBUST CONE CONTRACTION METHOD FOR MULTIPLE OBJECTIVE OPTIMIZATION PROBLEMS

2012 ◽  
Vol 11 (02) ◽  
pp. 327-357 ◽  
Author(s):  
MIŁOSZ KADZIŃSKI ◽  
ROMAN SŁOWIŃSKI
Keyword(s):  
Optimization Problems ◽  
Pairwise Comparison ◽  
Multiple Objective ◽  
Multiple Objective Optimization ◽  
Nondominated Solutions ◽  
Nondominated Points ◽  
Current Sample ◽  
Evaluation Space ◽  
Problem Setting ◽  
A Current

We introduce a new interactive procedure for multiple objective optimization problems. The identification of the most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he specifies pairwise comparisons of nondominated solutions from a current sample. We represent this preference information by a compatible form of the achievement scalarizing function, i.e., we are searching for weights of objectives which ensure that the reference solutions are compared by the function in the same way as by the DM. Directions of the isoquants of all compatible achievement scalarizing functions create a cone in the evaluation space, with the origin in a reference point. In successive iterations, each new pairwise comparison of solutions contracts the cone which is zooming on a subregion of nondominated points of greatest interest for the DM. The procedure ends when at least one satisfactory solution is selected or when the DM comes to conclusion that there is no such solution for the current problem setting.

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