A Novel Continuous Optimization Approach for the 0-1 Knapsack Problem

2015 ◽  
Author(s):  
Felipe Ferreira Lopes ◽  
Alireza Mohebi Ahstiani
Keyword(s):  
Knapsack Problem ◽  
Continuous Optimization ◽  
Optimization Approach

scholarly journals The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 17 ◽  
Author(s):  
Yanhong Feng ◽  
Haizhong An ◽  
Xiangyun Gao
Keyword(s):  
Transfer Function ◽  
Knapsack Problem ◽  
Transfer Functions ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Continuous Optimization ◽  
Search Space ◽  
Discrete Search ◽  
Continuous Optimization Problems

Moth search (MS) algorithm, originally proposed to solve continuous optimization problems, is a novel bio-inspired metaheuristic algorithm. At present, there seems to be little concern about using MS to solve discrete optimization problems. One of the most common and efficient ways to discretize MS is to use a transfer function, which is in charge of mapping a continuous search space to a discrete search space. In this paper, twelve transfer functions divided into three families, S-shaped (named S1, S2, S3, and S4), V-shaped (named V1, V2, V3, and V4), and other shapes (named O1, O2, O3, and O4), are combined with MS, and then twelve discrete versions MS algorithms are proposed for solving set-union knapsack problem (SUKP). Three groups of fifteen SUKP instances are employed to evaluate the importance of these transfer functions. The results show that O4 is the best transfer function when combined with MS to solve SUKP. Meanwhile, the importance of the transfer function in terms of improving the quality of solutions and convergence rate is demonstrated as well.

Robust optimization approach for a chance-constrained binary knapsack problem

2015 ◽  
Vol 157 (1) ◽  
pp. 277-296 ◽  
Author(s):  
Jinil Han ◽  
Kyungsik Lee ◽  
Chungmok Lee ◽  
Ki-Seok Choi ◽  
Sungsoo Park
Keyword(s):  
Robust Optimization ◽  
Knapsack Problem ◽  
Optimization Approach

Computational Object-Wrapping Rope Nets

2022 ◽  
Vol 41 (1) ◽  
pp. 1-16
Author(s):  
Jian Liu ◽  
Shiqing Xin ◽  
Xifeng Gao ◽  
Kaihang Gao ◽  
Kai Xu ◽  
...  
Keyword(s):  
Continuous Optimization ◽  
Optimization Approach ◽  
Construction Process ◽  
Topological Constraints ◽  
3D Objects ◽  
Physical Experiments ◽  
Discrete Phase ◽  
Anchor Points ◽  
3D Shapes ◽  
Easy Operation

Wrapping objects using ropes is a common practice in our daily life. However, it is difficult to design and tie ropes on a 3D object with complex topology and geometry features while ensuring wrapping security and easy operation. In this article, we propose to compute a rope net that can tightly wrap around various 3D shapes. Our computed rope net not only immobilizes the object but also maintains the load balance during lifting. Based on the key observation that if every knot of the net has four adjacent curve edges, then only a single rope is needed to construct the entire net. We reformulate the rope net computation problem into a constrained curve network optimization. We propose a discrete-continuous optimization approach, where the topological constraints are satisfied in the discrete phase and the geometrical goals are achieved in the continuous stage. We also develop a hoist planning to pick anchor points so that the rope net equally distributes the load during hoisting. Furthermore, we simulate the wrapping process and use it to guide the physical rope net construction process. We demonstrate the effectiveness of our method on 3D objects with varying geometric and topological complexity. In addition, we conduct physical experiments to demonstrate the practicability of our method.

scholarly journals Binary social group optimization algorithm for solving 0-1 knapsack problem

2022 ◽  
Vol 11 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Anima Naik ◽  
Pradeep Kumar Chokkalingam
Keyword(s):  
Knapsack Problem ◽  
Social Group ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
High Dimensional ◽  
The Social ◽  
Social Group Optimization ◽  
Low Dimensional ◽  
Continuous Optimization Problems

In this paper, we propose the binary version of the Social Group Optimization (BSGO) algorithm for solving the 0-1 knapsack problem. The standard Social Group Optimization (SGO) is used for continuous optimization problems. So a transformation function is used to convert the continuous values generated from SGO into binary ones. The experiments are carried out using both low-dimensional and high-dimensional knapsack problems. The results obtained by the BSGO algorithm are compared with other binary optimization algorithms. Experimental results reveal the superiority of the BSGO algorithm in achieving a high quality of solutions over different algorithms and prove that it is one of the best finding algorithms especially in high-dimensional cases.

A new natural-inspired continuous optimization approach

2018 ◽  
Vol 35 (3) ◽  
pp. 3267-3283 ◽  
Author(s):  
Mohamad Nabi Omidvar ◽  
Samad Nejatian ◽  
Hamid Parvin ◽  
Vahideh Rezaie
Keyword(s):  
Continuous Optimization ◽  
Optimization Approach

scholarly journals Deformable Registration with Discontinuity Preservation using Multi-Scale MRF

2014 ◽  
Author(s):  
Dohyung Seo ◽  
Jeroen Van Baar
Keyword(s):  
Discrete Optimization ◽  
Medical Image ◽  
Optimization Problem ◽  
Continuous Optimization ◽  
Deformable Registration ◽  
Optimization Approach ◽  
Smoothness Assumption ◽  
Breathing Motion ◽  
Multi Scale ◽  
3D Data

Deformable (2D or 3D) medical image registration is a challenging problem. Existing approaches assume that the underlying deformation is smooth. This smoothness assumption allows for solving the deformable registration at a coarse resolution and interpolate for finer resolutions. However, sliding of organs and breathing motion, exhibit discontinuities. We propose a discrete optimization approach to preserve these discontinuities. Solving continuous deformations using discrete optimization requires a fine distribution of the discrete labels. Coupled with the typical size of medical image datasets, this poses challenges to compute solutions efficiently. In this paper we present a practical, multi-scale formulation. We describe how discontinuities can be preserved, and how the optimization problem is solved. Results on synthetic 2D, and real 3D data show that we can well approximate the smoothness of continuous optimization, while accurately maintaining discontinuities.

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