Authors: Amgad Naiem, Mohammed El-Beltagy INTRODUCTION The linear sum assignment problem (LSAP) is a classical combinatorial optimization problems that is found in many applications.The assignment problem deals with the question of how to assign n persons to n objects in the best possible way.
DGS was developed to fulfill these requirement and in our context it sacrificed a mere 0.6% of the optimal solution obtained by the auction algorithm while attaining a substantial speedup in terms of computational time.
A plethora of greedy heuristics have been developed for different optimization problems.
Due to the dynamic nature of many applications, as well as the expansion of problem sizes, where a solution needs to be found under tight time constraints, heuristics that give rise to solutions that are close to optimal solution are sought.
Our efforts in that regards lead us to the Deep Greedy Switching (DGS) algorithm.
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Parent Homework Tips - Linear Assignment Problem
Visit Stack Exchange I wonder if there is any literature on the following problem $$\begin \underset & \displaystyle\sum_ C_ X_\ \text & \displaystyle\sum_ X_ = \displaystyle\sum_ X_ = 1\ & X_ \geq 0\end$$ The closest related problem might be Rectangular Linear Assignment Problem (RLAP)$^\dagger$, as RLAP further constrains $X_ \in $.I understand that the proposed problem is a relaxed version of the RLAP.But my intuition is that the optimum for the relax problem should occur at "vertex".The linear sum assignment problem can be found in many real world problems; from simple personnel to tasks assignment in a factory or an organization to more complex applications such as peer-to-peer (P2P) satellite refueling.It occurs in fields as varied as bioinformatics and computer vision.Even as the auction is considered one of the fastest algorithms, for large-scale and complex instances of the assignment problem the auction algorithm can take a lot of time to find the optimal solution. discussed five types of the assignment problem instances which are Geometric, Fixed-Cost, High-Cost, Low-Cost and Uniformly Random.It was shown that for the first two problem types the auction algorithm performs poorly in terms of the running time in comparison with the other three problem types.I.e., the Square Assignment Problem can be solved as a Continuous Linear Program and will produce the correct optimal objective value for the Assignment Problem constrained to have integer (binary) solutions.Therefore, the Rectangular Assignment Problem can also be solved as a Continuous Linear Program and will produce the correct optimal objective value.The fact that the auction algorithm only gives a partial assignment if interrupted makes it more unsuitable.We deduced that the auction algorithm would be impractical for our system and other applications where execution time is strictly constrained and a solution needs to be found before a certain deadline.