Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map

Solving optimization problems is an ever-growing subject with an enormous number of algorithms. Examples of such algorithms are Scatter Search (SS) and genetic algorithms. Modifying and improving of algorithms can be done by adding diversity and guidance to them. Chaotic maps are quite sensitive to the initial point, which means even a very slight change in the value of the initial point would result in a dramatic change of the sequence produced by the chaotic map Arnold's Cat Map. Arnold's Cat Map is a chaotic map technique that provides long non-repetitive random-like sequences. Chaotic maps play an important role in improving evolutionary optimization algorithms and meta-heuristics by avoiding local optima and speeding up the convergence. This paper proposes an implementation of the scatter search algorithm with travelling salesman as a case study, then implements and compares the developed hyper Scatter Arnold's Cat Map Search (SACMS) method against the traditional Scatter Search Algorithm. SACMS is a hyper Scatter Search Algorithm with Arnold's Cat Map Chaotic Algorithm. Scatter Arnold's Cat Map Search shows promising results by decreasing the number of iterations required by the Scatter Search Algorithm to get an optimal solution(s). Travelling Salesman Problem, which is a popular and well-known optimization example, is implemented in this paper to demonstrate the results of the modified algorithm Scatter Arnold's Cat Map Search (SACMS). Implementation of both algorithms is done with the same parameters: population size, number of cities, maximum number of iterations, reference set size, etc. The results show improvement by the modified algorithm in terms of the number of iterations required by SS with an iteration reduction of 10–46 % and improvements in time to obtain solutions with 65 % time reduction

A Scatter Search Algorithm for Multi-Criteria Inventory Classification with Maximize the Satisfaction Level

Inventory management requires thousands or millions of individual transactions each year. Classification of the items influences the results of inventory management. Traditionally, this is usually classified with considering an annual dollar usage criterion but maybe other criterias such as lead time, criticality, perishability, inventory cost, and demand type can be affected on that classification. The objective of this study is to determine the multi-criteria inventory classification (MCIC) of the inventory items to minimize the total inventory cost and also dissimilarity of classes. Because of the two objectives is considered to solve with together, the maximization of satisfaction level is described to solve the multi-objective problem. This study introduces a Mixed Integer Nonlinear Programming (MINLP) model of the MCIC problem by giving two objectives. A Scatter Search Algorithm (SSA) is used to solve the MINLP model for obtaining high-quality solutions within reasonable computation times. Finally, we illustrate an example and compare our results with other studies in previous literature.

Optimum contributions of hydropower reservoirs to the minimum flow of Vu Gia – Thu Bon river basin

Upstream hydropower development has a great impact on downstream flows. According to the Regulation of Multi-reservoir Operation in Vu Gia – Thu Bon River Basin (Regulation 15371), four large-scale upstream reservoirs must discharge certain flow during the dry season to increase water levels at downstream hydrological stations named Ai Nghia and Giao Thuy. These stations are used as the control points for the downstream water supply. An optimizing-simulation based model was developed that both maximizes total electricity production and ensures minimum flow downstream as required. A thousand combinations of the reservoir inflows were generated by Monte Carlo simulation, considering the correlation between tributaries. Then, the Scatter search algorithm available in the Optquest module of Crystal Ball was used to find the optimal release from the reservoirs. The results show that the current Regulation 1537 can be improved for more efficient water resources management.