ILS-ESP: An efficient, simple, and parameter-free algorithm for solving the permutation flow-shop problem

From a managerial point of view, the more e cient, simple, and parameter-free (ESP) an algorithm is, the more likely it will be used in practice for solving real-life problems. Following this principle, an ESP algorithm for solving the Permutation Flowshop Sequencing Problem (PFSP) is proposed in this article. Using an Iterated Local Search (ILS) framework, the so-called ILS-ESP algorithm is able to compete in performance with other well-known ILS-based approaches, which are considered among the most e cient algorithms for the PFSP. However, while other similar approaches still employ several parameters that can a ect their performance if not properly chosen, our algorithm does not require any particular fine-tuning process since it uses basic ‘common sense’ rules for the local search, perturbation, and acceptance criterion stages of the ILS metaheuristic. Our approach defines a new operator for the ILS perturbation process, a new acceptance criterion based on extremely simple and transparent rules, and a biased randomization process of the initial solution to randomly generate di erent alternative initial solutions of similar quality -which is attained by applying a biased randomization to a classical PFSP heuristic. This diversification of the initial solution aims at avoiding poorly designed starting points and, thus, allows the methodology to take advantage of current trends in parallel and distributed computing. A set of extensive tests, based on literature benchmarks, has been carried out in order to validate our algorithm and compare it against other approaches. These tests show that our parameter-free algorithm is able to compete with state-of-the-art metaheuristics for the PFSP. Also, the experiments show that, when using parallel computing, it is possible to improve the top ILS-based metaheuristic by just incorporating to it our biased randomization process with a high-quality pseudo-random number generator.Preprin

Stochastic local search: a state-of-the-art review

The main objective of this paper is to provide a state-of-the-art review, analyze and discuss stochastic local search techniques used for solving hard combinatorial problems. It begins with a short introduction, motivation and some basic notation on combinatorial problems, search paradigms and other relevant features of searching techniques as needed for background. In the following a brief overview of the stochastic local search methods along with an analysis of the state-of-the-art stochastic local search algorithms is given. Finally, the last part of the paper present and discuss some of the most latest trends in application of stochastic local search algorithms in machine learning, data mining and some other areas of science and engineering. We conclude with a discussion on capabilities and limitations of stochastic local search algorithms

Local Optima Networks of the Permutation Flow-Shop Problem

International audienceThis article extracts and analyzes local optima networks for the permutation flow-shop problem. Two widely used move operators for permutation representations, namely, swap and insertion, are incorporated into the network landscape model. The performance of a heuristic search algorithm on this problem is also analyzed. In particular, we study the correlation between local optima network features and the performance of an iterated local search heuristic. Our analysis reveals that network features can explain and predict problem difficulty. The evidence confirms the superiority of the insertion operator for this problem

HYBRID GENETIC AND PENGUIN SEARCH OPTIMIZATION ALGORITHM (GA-PSEOA) FOR EFFICIENT FLOW SHOP SCHEDULING SOLUTIONS

This paper presents a novel hybrid approach, fusing genetic algorithms (GA) and penguin search optimization (PSeOA), to address the flow shop scheduling problem (FSSP). GA utilizes selection, crossover, and mutation inspired by natural selection, while PSeOA emulates penguin foraging behavior for efficient exploration. The approach integrates GA's genetic diversity and solution space exploration with PSeOA's rapid convergence, further improved with FSSP-specific modifications. Extensive experiments validate its efficacy, outperforming pure GA, PSeOA, and other metaheuristics

Two-Stage Vehicle Routing Problems with Profits and Buffers: Analysis and Metaheuristic Optimization Algorithms

This thesis considers the Two-Stage Vehicle Routing Problem (VRP) with Profits and Buffers, which generalizes various optimization problems that are relevant for practical applications, such as the Two-Machine Flow Shop with Buffers and the Orienteering Problem. Two optimization problems are considered for the Two-Stage VRP with Profits and Buffers, namely the minimization of total time while respecting a profit constraint and the maximization of total profit under a budget constraint. The former generalizes the makespan minimization problem for the Two-Machine Flow Shop with Buffers, whereas the latter is comparable to the problem of maximizing score in the Orienteering Problem. For the three problems, a theoretical analysis is performed regarding computational complexity, existence of optimal permutation schedules (where all vehicles traverse the same nodes in the same order) and potential gaps in attainable solution quality between permutation schedules and non-permutation schedules. The obtained theoretical results are visualized in a table that gives an overview of various subproblems belonging to the Two-Stage VRP with Profits and Buffers, their theoretical properties and how they are connected. For the Two-Machine Flow Shop with Buffers and the Orienteering Problem, two metaheuristics 2BF-ILS and VNSOP are presented that obtain favorable results in computational experiments when compared to other state-of-the-art algorithms. For the Two-Stage VRP with Profits and Buffers, an algorithmic framework for Iterative Search Algorithms with Variable Neighborhoods (ISAVaN) is proposed that generalizes aspects from 2BF-ILS as well as VNSOP. Various algorithms derived from that framework are evaluated in an experimental study. The evaluation methodology used for all computational experiments in this thesis takes the performance during the run time into account and demonstrates that algorithms for structurally different problems, which are encompassed by the Two-Stage VRP with Profits and Buffers, can be evaluated with similar methods. The results show that the most suitable choice for the components in these algorithms is dependent on the properties of the problem and the considered evaluation criteria. However, a number of similarities to algorithms that perform well for the Two-Machine Flow Shop with Buffers and the Orienteering Problem can be identified. The framework unifies these characteristics, providing a spectrum of algorithms that can be adapted to the specifics of the considered Vehicle Routing Problem.:1 Introduction 2 Background 2.1 Problem Motivation 2.2 Formal Definition of the Two-Stage VRP with Profits and Buffers 2.3 Review of Literature on Related Vehicle Routing Problems 2.3.1 Two-Stage Vehicle Routing Problems 2.3.2 Vehicle Routing Problems with Profits 2.3.3 Vehicle Routing Problems with Capacity- or Resource-based Restrictions 2.4 Preliminary Remarks on Subsequent Chapters 3 The Two-Machine Flow Shop Problem with Buffers 3.1 Review of Literature on Flow Shop Problems with Buffers 3.1.1 Algorithms and Metaheuristics for Flow Shops with Buffers 3.1.2 Two-Machine Flow Shop Problems with Buffers 3.1.3 Blocking Flow Shops 3.1.4 Non-Permutation Schedules 3.1.5 Other Extensions and Variations of Flow Shop Problems 3.2 Theoretical Properties 3.2.1 Computational Complexity 3.2.2 The Existence of Optimal Permutation Schedules 3.2.3 The Gap Between Permutation Schedules an Non-Permutation 3.3 A Modification of the NEH Heuristic 3.4 An Iterated Local Search for the Two-Machine Flow Shop Problem with Buffers 3.5 Computational Evaluation 3.5.1 Algorithms for Comparison 3.5.2 Generation of Problem Instances 3.5.3 Parameter Values 3.5.4 Comparison of 2BF-ILS with other Metaheuristics 3.5.5 Comparison of 2BF-OPT with NEH 3.6 Summary 4 The Orienteering Problem 4.1 Review of Literature on Orienteering Problems 4.2 Theoretical Properties 4.3 A Variable Neighborhood Search for the Orienteering Problem 4.4 Computational Evaluation 4.4.1 Measurement of Algorithm Performance 4.4.2 Choice of Algorithms for Comparison 4.4.3 Problem Instances 4.4.4 Parameter Values 4.4.5 Experimental Setup 4.4.6 Comparison of VNSOP with other Metaheuristics 4.5 Summary 5 The Two-Stage Vehicle Routing Problem with Profits and Buffers 5.1 Theoretical Properties of the Two-Stage VRP with Profits and Buffers 5.1.1 Computational Complexity of the General Problem 5.1.2 Existence of Permutation Schedules in the Set of Optimal Solutions 5.1.3 The Gap Between Permutation Schedules an Non-Permutation Schedules 5.1.4 Remarks on Restricted Cases 5.1.5 Overview of Theoretical Results 5.2 A Metaheuristic Framework for the Two-Stage VRP with Profits and Buffers 5.3 Experimental Results 5.3.1 Problem Instances 5.3.2 Experimental Results for O_{max R, Cmax≤B} 5.3.3 Experimental Results for O_{min Cmax, R≥Q} 5.4 Summary Bibliography List of Figures List of Tables List of Algorithm

Improved Firefly Algorithm with Variable Neighborhood Search for Data Clustering

من بين الخوارزميات الأدلة العليا (الميتاهيورستك)، تعد الخوارزميات القائمة على البحوث المتعددة (المجتمع) خوارزمية بحث استكشافية متفوقة كخوارزمية البحث المحلية من حيث استكشاف مساحة البحث للعثور على الحلول المثلى العالمية. ومع ذلك، فإن الجانب السلبي الأساسي للخوارزميات القائمة على البحوث المتعددة (المجتمع) هو قدرتها الاستغلالية المنخفضة، مما يمنع توسع منطقة البحث عن الحلول المثلى. خوارزمية اليَرَاعَة المضيئة (Firefly (FA هي خوارزمية تعتمد على المجتمع والتي تم استخدامها على نطاق واسع في مشاكل التجميع. ومع ذلك، فإن FA مقيد بتقاربها السابق لأوانه عندما لا يتم استخدام استراتيجيات بحث محلي لتحسين جودة حلول المجموعات في منطقة المجاورة واستكشاف المناطق العالمية في مساحة البحث. على هذا الأساس، فإن الهدف من هذا العمل هو تحسين FA باستخدام البحث المتغير في الأحياء (VNS) كطريقة بحث محلية (FA-VNS)، وبالتالي توفير فائدة VNS للمفاضلة بين قدرات الاستكشاف والاستغلال. يسمح FA-VNS المقترح لليراعات بتحسين حلول التجميع مع القدرة على تعزيز حلول التجميع والحفاظ على تنوع حلول التجميع أثناء عملية البحث باستخدام مشغلي الاضطراب في VNS. لتقييم أداء الخوارزمية، يتم استخدام ثماني مجموعات بيانات معيارية مع أربع خوارزميات تجميع معروفة. تشير المقارنة وفقًا لمقاييس التقييم الداخلية والخارجية إلى أن FA-VNS المقترحة يمكن أن تنتج حلول تجميع أكثر إحكاما من خوارزميات التجميع المعروفة.Among the metaheuristic algorithms, population-based algorithms are an explorative search algorithm superior to the local search algorithm in terms of exploring the search space to find globally optimal solutions. However, the primary downside of such algorithms is their low exploitative capability, which prevents the expansion of the search space neighborhood for more optimal solutions. The firefly algorithm (FA) is a population-based algorithm that has been widely used in clustering problems. However, FA is limited in terms of its premature convergence when no neighborhood search strategies are employed to improve the quality of clustering solutions in the neighborhood region and exploring the global regions in the search space. On these bases, this work aims to improve FA using variable neighborhood search (VNS) as a local search method, providing VNS the benefit of the trade-off between the exploration and exploitation abilities. The proposed FA-VNS allows fireflies to improve the clustering solutions with the ability to enhance the clustering solutions and maintain the diversity of the clustering solutions during the search process using the perturbation operators of VNS. To evaluate the performance of the algorithm, eight benchmark datasets are utilized with four well-known clustering algorithms. The comparison according to the internal and external evaluation metrics indicates that the proposed FA-VNS can produce more compact clustering solutions than the well-known clustering algorithms

The automatic design of hyper-heuristic framework with gene expression programming for combinatorial optimization problems

Hyper-heuristic approaches aim to automate heuristic design in order to solve multiple problems instead of designing tailor-made methodologies for individual problems. Hyper-heuristics accomplish this through a high level heuristic (heuristic selection mechanism and an acceptance criterion). This automates heuristic selection, deciding whether to accept or reject the returned solution. The fact that different problems or even instances, have different landscape structures and complexity, the design of efficient high level heuristics can have a dramatic impact on hyper-heuristic performance. In this work, instead of using human knowledge to design the high level heuristic, we propose a gene expression programming algorithm to automatically generate, during the instance solving process, the high level heuristic of the hyper-heuristic framework. The generated heuristic takes information (such as the quality of the generated solution and the improvement made) from the current problem state as input and decides which low level heuristic should be selected and the acceptance or rejection of the resultant solution. The benefit of this framework is the ability to generate, for each instance, different high level heuristics during the problem solving process. Furthermore, in order to maintain solution diversity, we utilize a memory mechanism which contains a population of both high quality and diverse solutions that is updated during the problem solving process. The generality of the proposed hyper-heuristic is validated against six well known combinatorial optimization problem, with very different landscapes, provided by the HyFlex software. Empirical results comparing the proposed hyper-heuristic with state of the art hyper-heuristics, conclude that the proposed hyper-heuristic generalizes well across all domains and achieves competitive, if not superior, results for several instances on all domains

Particle Swarm Optimization

Particle swarm optimization (PSO) is a population based stochastic optimization technique influenced by the social behavior of bird flocking or fish schooling.PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. This book represents the contributions of the top researchers in this field and will serve as a valuable tool for professionals in this interdisciplinary field