A Study on Greedy Technique in Container Loading Problem and Knapsack Problem

The main aim of the paper is to use application of greedy algorithm in container loading problem and Knapsack problem. Greedy method gives an optimal solution to the problem by considering the inputs one at a time, checking to see if it can be included in the set of values which give an optimal solution and then check if it is the feasible solution. The Greedy algorithm could be understood very well with a well-known problem referred to as container loading problem and Knapsack problem. The basic Container Loading Problem can be defined as the problem of placing a set of boxes into the container respecting the geometric constraints: the boxes cannot overlap and cannot exceed the dimensions of the container. The knapsack problem is in combinatorial optimization problem. It appears as a sub problem in many, more complex mathematical models of real world problems.

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A Hybrid Greedy Algorithm and Simulated Annealing for Single Container Loading Problem: A Case Study

Jurnal Teknik Industri ◽

10.9744/jti.20.2.89-94 ◽

2019 ◽

Vol 20 (2) ◽

pp. 89

Author(s):

Gede A Widyadana ◽

Audrey Tedja Widjaja ◽

Kun Jen Wang

Keyword(s):

Greedy Algorithm ◽

Three Dimensional ◽

Computation Time ◽

Computational Time ◽

Container Loading ◽

Flexible Packaging ◽

Loading Problem ◽

And Performance ◽

Container Loading Problem

A single container loading problem is a problem to effectively load boxes in a three-dimensional container. There are many researchers in this problem try to find the best solution to solve the problem with feasible computation time and to develop some models to solve real case problem. Heuristics are the most method used to solve this problem since the problem is an NP-hard. In this paper, we introduce a hybrid greedy algorithm and simulate annealing algorithm to solve a real container loading problem in one flexible packaging company in Indonesia. Validation is used to show that the method can be applied practically. We use seven real cases to check the validity and performance of the model. The proposed method outperformed the solution developed by the company in all seven cases with feasible computational time.

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Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

ACM Journal on Emerging Technologies in Computing Systems ◽

10.1145/3451209 ◽

2021 ◽

Vol 17 (4) ◽

pp. 1-20

Author(s):

Serena Wang ◽

Maya Gupta ◽

Seungil You

Keyword(s):

Optimization Problem ◽

Optimal Solution ◽

Combinatorial Optimization Problem ◽

Joint Optimization ◽

Early Stopping ◽

Time Approximation ◽

Approximation Bound ◽

Evaluation Time ◽

Speed Up ◽

Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

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