Netgen-II: A System for Generating Structured Network-Based Mathematical Programming Test Problems

1982 ◽  
pp. 16-23 ◽  
Author(s):  
Joyce J. Elam ◽  
Darwin Klingman
Keyword(s):  
Mathematical Programming ◽  
Test Problems

An Improved Direct Search Mathematical Programming Algorithm

1975 ◽  
Vol 97 (4) ◽  
pp. 1305-1310 ◽  
Author(s):  
M. Pappas ◽  
J. Y. Moradi
Keyword(s):  
Mathematical Programming ◽  
Direction Finding ◽  
Direct Search ◽  
Pattern Search ◽  
New Method ◽  
Programming Algorithm ◽  
Test Problems ◽  
Feasible Direction ◽  
Search Termination

An improved, nonlinear, constrained algorithm is presented, coupling a rotating coordinate pattern search with a feasible direction finding procedure used at points of pattern search termination. The procedure is compared with eighteen algorithms, including most of the popular methods, on ten test problems. These problems are such that the majority of codes failed to solve more than half of them. The new method proved superior to all others in the overall generality and efficiency rating, being the only one solving all problems.

Independent strong weak domination: A mathematical programming approach

2020 ◽  
Vol 12 (05) ◽  
pp. 2050062
Author(s):  
Murat Erşen Berberler ◽  
Onur Uğurlu ◽  
Zeynep Nihan Berberler
Keyword(s):  
Mathematical Programming ◽  
Dominating Set ◽  
Domination Number ◽  
Minimum Size ◽  
Stable Set ◽  
Programming Approach ◽  
Test Problems ◽  
Minimum Cardinality ◽  
Mathematical Programming Approach ◽  
Independent Domination

Let [Formula: see text] be a graph. A subset [Formula: see text] of vertices is a dominating set if every vertex in [Formula: see text] is adjacent to at least one vertex of [Formula: see text]. The domination number is the minimum cardinality of a dominating set. Let [Formula: see text]. Then, [Formula: see text] strongly dominates [Formula: see text] and [Formula: see text] weakly dominates [Formula: see text] if (i) [Formula: see text] and (ii) [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a strong (weak) dominating set of [Formula: see text] if every vertex in [Formula: see text] is strongly (weakly) dominated by at least one vertex in [Formula: see text]. The strong (weak) domination number of [Formula: see text] is the minimum cardinality of a strong (weak) dominating set. A set [Formula: see text] is an independent (or stable) set if no two vertices of [Formula: see text] are adjacent. The independent domination number of [Formula: see text] (independent strong domination number, independent weak domination number, respectively) is the minimum size of an independent dominating set (independent strong dominating set, independent weak dominating set, respectively) of [Formula: see text]. In this paper, mathematical models are developed for the problems of independent domination and independent strong (weak) domination of a graph. Then test problems are solved by the GAMS software, the optima and execution times are implemented. To the best of our knowledge, this is the first mathematical programming formulations for the problems, and computational results show that the proposed models are capable of finding optimal solutions within a reasonable amount of time.

scholarly journals An Investigation into Mathematical Programming for Finite Horizon Decentralized POMDPs

2010 ◽  
Vol 37 ◽  
pp. 329-396 ◽  
Author(s):  
R. Aras ◽  
A. Dutech
Keyword(s):  
Mathematical Programming ◽  
Approximate Solutions ◽  
Mixed Integer ◽  
Test Problems ◽  
Theoretic Approach ◽  
Optimal Solutions ◽  
Uncertain Environments ◽  
Decision Theoretic Approach ◽  
Markov Decision ◽  
Novel Algorithms

Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, solving them is a task with an overwhelming complexity that can be doubly exponential. In this paper, we study an alternate formulation of DEC-POMDPs relying on a sequence-form representation of policies. From this formulation, we show how to derive Mixed Integer Linear Programming (MILP) problems that, once solved, give exact optimal solutions to the DEC-POMDPs. We show that these MILPs can be derived either by using some combinatorial characteristics of the optimal solutions of the DEC-POMDPs or by using concepts borrowed from game theory. Through an experimental validation on classical test problems from the DEC-POMDP literature, we compare our approach to existing algorithms. Results show that mathematical programming outperforms dynamic programming but is less efficient than forward search, except for some particular problems. The main contributions of this work are the use of mathematical programming for DEC-POMDPs and a better understanding of DEC-POMDPs and of their solutions. Besides, we argue that our alternate representation of DEC-POMDPs could be helpful for designing novel algorithms looking for approximate solutions to DEC-POMDPs.

Mathematical Programming for Industrial Engineers

1997 ◽  
Vol 48 (3) ◽  
pp. 334-0334
Author(s):  
M Avriel ◽  
B Golany
Keyword(s):  
Mathematical Programming
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