Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO

Abstract: An illustration of different shapes of the time-varying transfer function with different values of the control parameter Display Omitted Analyse how transfer function in BPSO affects the balance between exploration and exploitationPropose a time-varying transfer function for BPSO to achieve a better such balanceValidate the advantage of the new transfer function on knapsack instances and a truss design problem Many real-world problems belong to the family of discrete optimization problems Most of these problems are NP-hard and difficult to solve efficiently using classical linear and convex optimization methods In addition, the computational difficulties of these optimization tasks increase rapidly with the increasing number of decision variables A further difficulty can be also caused by the search space being intrinsically multimodal and non-convex In such a case, it is more desirable to have an effective optimization method that can cope better with these problem characteristics Binary particle swarm optimization (BPSO) is a simple and effective discrete optimization method The original BPSO and its variants have been used to solve a number of classic discrete optimization problems However, it is reported that the original BPSO and its variants are unable to provide satisfactory results due to the use of inappropriate transfer functions More specifically, these transfer functions are unable to provide BPSO a good balance between exploration and exploitation in the search space, limiting their performances To overcome this problem, this paper proposes to employ a time-varying transfer function in the BPSO, namely TVT-BPSO To understand the search behaviour of the TVT-BPSO, we provide a systematic analysis of its exploration and exploitation capability Our experimental results demonstrate that TVT-BPSO outperforms existing BPSO variants on both low-dimensional and high-dimensional classical 01 knapsack problems, as well as a 200-member truss problem, suggesting that TVT-BPSO is able to better scale to high dimensional combinatorial problems than the existing BPSO variants and other metaheuristic algorithms

Set-Based Discrete Particle Swarm Optimization Based on Decomposition for Permutation-Based Multiobjective Combinatorial Optimization Problems

Abstract: This paper studies a specific class of multiobjective combinatorial optimization problems (MOCOPs), namely the permutation-based MOCOPs. Many commonly seen MOCOPs, e.g., multiobjective traveling salesman problem (MOTSP), multiobjective project scheduling problem (MOPSP), belong to this problem class and they can be very different. However, as the permutation-based MOCOPs share the inherent similarity that the structure of their search space is usually in the shape of a permutation tree, this paper proposes a generic multiobjective set-based particle swarm optimization methodology based on decomposition, termed MS-PSO/D. In order to coordinate with the property of permutation-based MOCOPs, MS-PSO/D utilizes an element-based representation and a constructive approach. Through this, feasible solutions under constraints can be generated step by step following the permutation-tree-shaped structure. And problem-related heuristic information is introduced in the constructive approach for efficiency. In order to address the multiobjective optimization issues, the decomposition strategy is employed, in which the problem is converted into multiple single-objective subproblems according to a set of weight vectors. Besides, a flexible mechanism for diversity control is provided in MS-PSO/D. Extensive experiments have been conducted to study MS-PSO/D on two permutation-based MOCOPs, namely the MOTSP and the MOPSP. Experimental results validate that the proposed methodology is promising.

Distributed Parallel Particle Swarm Optimization for Multi-Objective and Many-Objective Large-Scale Optimization

Abstract: With the advent of big data era, complex optimization problems with many objectives and large numbers of decision variables are constantly emerging. Traditional research about multi-objective particle swarm optimization (PSO) focuses on multi-objective optimization problems (MOPs) with small numbers of variables and less than four objectives. At present, MOPs with large numbers of variables and many objectives (greater than or equal to four) are constantly emerging. When tackling this type of MOPs, the traditional multi-objective PSO algorithms have low efficiency. Aiming at these multi-objective large-scale optimization problems (MOLSOPs) and many-objective large-scale optimization problems (MaOLSOPs), we need to explore thoroughly parallel attributes of the particle swarm, and design the novel PSO algorithms according to the characteristics of distributed parallel computation. We survey the related research on PSO: multi-objective large-scale optimization, many-objective optimization, and distributed parallelism. Based on the aforementioned three aspects, the multi-objective large-scale distributed parallel PSO and many-objective large-scale distributed parallel PSO methodologies are proposed and discussed, and the other future research trends are also illuminated.