Application Analysis on PSO Algorithm in the Discrete Optimization Problems

Particle Swarm Optimization (PSO) is kind of algorithm that can be used to solve optimization problems. In practice, many optimization problems are discrete but PSO algorithm was initially designed to meet the requirements of continuous problems. A lot of researches had made efforts to handle this case and varieties of discrete PSO algorithms were proposed. However, these algorithms just focus on the specific problem, and the performance of it significantly degrades when extending the algorithm to other problems. For now, there is no reasonable unified principle or method for analyzing the application of PSO algorithm in discrete optimization problem, which limits the development of discrete PSO algorithm. To address the challenge, we first give an investigation of PSO algorithm from the perspective of spatial search, then, try to give a novel analysis of the key feature changes when PSO algorithm is applied to discrete optimization, and propose a classification method to summary existing discrete PSO algorithms.

A Discrete Crow Search Algorithm for Mining Quantitative Association Rules

Association rules are the specific data mining methods aiming to discover explicit relations between the different attributes in a large dataset. However, in reality, several datasets may contain both numeric and categorical attributes. Recently, many meta-heuristic algorithms that mimic the nature are developed for solving continuous problems. This article proposes a new algorithm, DCSA-QAR, for mining quantitative association rules based on crow search algorithm (CSA). To accomplish this, new operators are defined to increase the ability to explore the searching space and ensure the transition from the continuous to the discrete version of CSA. Moreover, a new discretization algorithm is adopted for numerical attributes taking into account dependencies probably that exist between attributes. Finally, to evaluate the performance, DCSA-QAR is compared with particle swarm optimization and mono and multi-objective evolutionary approaches for mining association rules. The results obtained over real-world datasets show the outstanding performance of DCSA-QAR in terms of quality measures.

H-PSO Routing Optimization Model for Zoomlion Ghana Limited

This research combines Particle Swarm Optimization (PSO) with Crossover and Mutation Operators of Genetic Algorithm (GA) to produce a hybrid optimization algorithm to solve a routing problem identified at Zoomlion Ghana Limited, Sekondi Takoradi branch. PSO is known to converge prematurely and can be trapped into a local minimum especially with complex problems. On the other hand, GA is a robust and works well with discrete and continuous problems. The Crossover and Mutation operations of GA makes the iterations converges faster and are reliable. The hybrid algorithm therefore merges these operators into PSO to produce a more reliable optimal solution. The hybrid algorithm was then used to solve the routing problem identified at Zoomlion Ghana Limited, Sekondi Takoradi branch. A total of 160 public waste bin centers scattered in the metropolis and the distance between them were considered. The main aim was to determine the best combination of the set of routes connecting all the bin centers in the municipality that will produce the shortest optimal route for the study. MATLAB simulation was run of the list of distances to determine the optimal route. After 10,000 iterations, PSO produced an optimal result of 81.6 km, GA produced an optimal result of 88.9 km and the proposed hybrid model produced an optimal result of 79.9 km

Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E , 55:R3844–R3846, 1997] and studied mathematically by the authors in [C. Canc\`es, D. Matthes, and F. Nabet. Arch. Ration. Mech. Anal. , 233(2):837-866, 2019]. The scheme is shown to preserve the key properties of the continuous model, namely mass conservation, positivity of the concentrations, the decay of the energy and the control of the entropy dissipation rate. This allows to establish the existence of a solution to the nonlinear algebraic system corresponding to the scheme. Further, we show thanks to compactness arguments that the approximate solution converges towards a weak solution of the continuous problems as the discretization parameters tend to 0. Numerical results illustrate the behavior of the numerical model.

Representative Solutions for Bi-Objective Optimisation

Bi-objective optimisation aims to optimise two generally competing objective functions. Typically, it consists in computing the set of nondominated solutions, called the Pareto front. This raises two issues: 1) time complexity, as the Pareto front in general can be infinite for continuous problems and exponentially large for discrete problems, and 2) lack of decisiveness. This paper focusses on the computation of a small, “relevant” subset of the Pareto front called the representative set, which provides meaningful trade-offs between the two objectives. We introduce a procedure which, given a pre-computed Pareto front, computes a representative set in polynomial time, and then we show how to adapt it to the case where the Pareto front is not provided. This has three important consequences for computing the representative set: 1) does not require the whole Pareto front to be provided explicitly, 2) can be done in polynomial time for bi-objective mixed-integer linear programs, and 3) only requires a polynomial number of solver calls for bi-objective problems, as opposed to the case where a higher number of objectives is involved. We implement our algorithm and empirically illustrate the efficiency on two families of benchmarks.