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

Two-Dimensional Loading in Vehicle Routing Problem With Release and Due Dates

In this paper, we study a two-dimensional vehicle loading and routing problem, in which customer orders with deadlines become available for dispatch as per their release dates. The objective is to minimize the sum of transportation, inventory, and tardiness costs, while respecting various loading and routing constraints. This scenario allows us to study various tradeoffs that tend to arise due to temporal order aggregation across release dates. We thereby propose an integrated mathematical formulation to simultaneously model both the routing and loading requirements of the problem at hand. Specifically, as the problem is NP-hard, we propose a scatter search based heuristic approach to solve large-size instances. Further, its performance is enhanced using problem-specific procedures and strategic oscillation approaches. Additionally, the numerical experiments illustrate the influence of cost structures on both the optimal loading configurations along with the optimal routes. Importantly, our experiments also suggest that the proposed scatter search method can produce good quality solutions in less time.

Solving binary programming problems using homotopy theory ideas

PurposeThe aim of the study is to show that merging two areas of mathematics – topology and discrete optimization – could result in a viable option to solve classical or specialized integer problems.Design/methodology/approachIn the paper, discrete topology concepts are applied to propose a metaheuristic algorithm that is capable to solve binary programming problems. Particularly, some of the homotopy for paths principles are used to explore the solution space associated with four well-known NP-hard problems herein considered as follows: knapsack, set covering, bi-level single plant location with order and one-max.FindingsComputational experimentation confirms that the proposed algorithm performs in an effective manner, and it is able to efficiently solve the sets of instances used for the benchmark. Moreover, the performance of the proposed algorithm is compared with a standard genetic algorithm (GA), a scatter search (SS) method and a memetic algorithm (MA). Acceptable results are obtained for all four implemented metaheuristics, but the path homotopy algorithm stands out.Originality/valueA novel metaheuristic is proposed for the first time. It uses topology concepts to design an algorithmic framework to solve binary programming problems in an effective and efficient manner.

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.

Model-Based Simulation Approach for Pre-Front End Engineering Design Studies for Subsea Field Architecture Development

Summary Presented is a model-based methodology identifying subsea field architectures that satisfy prespecified multiphysics constraints. The proposed methodology prioritizes the identified subsea system using a multiobjective optimization approach considering two objective functions, which are minimizing pressure drop reflecting the maximization of production flow rates and minimizing capital expenditures. The architecture solutions produce manifolds positioning and optimal pipeline routing/sizing. A convex combination approach creates the multiobjective optimization criterion enabling weighting among constraints such as hydraulic, topological, structural, and flow assurance, as well as technical issues and financial limitations. The optimization problem is computationally solved using a hybrid method with a global multistart algorithm that combines a scatter search process with a gradient-based local nonlinear problem solver. A case study is provided to test the proposed methodology including the effect of varying the weights among the constraints. This deep-dive analysis demonstrates the potential offered by the proposed methodology, illustrated by the ability to perform several investigations such as wells-grouping analysis and insulation effect on the overall optimization procedure, as well as to provide a tracking tool for flow-assurance factors, namely erosion and corrosion rates along the subsea layout. Hence, we present a demonstration of the capabilities of the proposed model-based subsea field layout optimization procedure.

A Comprehensive Review on Scatter Search: Techniques, Applications, and Challenges

Recent years have witnessed the use of metaheuristic algorithms to solve the optimization problems that usually require extensive computations and time. Among others, scatter search is the widely used evolutionary metaheuristic algorithm. It uses the information of global optima, which is stored in a different and unique set of solutions. In this paper, an updated review of scatter search (SS) is given. SS has been successfully applied in a variety of research problems, namely, data mining, bioinformatics, and engineering design. This paper presents the modified and hybrid versions of SS with their applications. The control strategies are discussed to show their impact on the performance of SS. various issues and future directions related to SS are also discussed. It inspires innovative researchers to use this algorithm for their research domains.