A Lin-Kernighan Heuristic for Single Row Facility Layout

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is known to be NP-hard. In this paper, we present a neighborhood search heuristic called LK-INSERT which uses a Lin-Kernighan neighborhood structure built on insertion neighborhoods. To the best of our knowledge this is the first such heuristic for the SRFLP. Our computational experiments show that LK-INSERT is competitive and improves the best known solutions for several large sized benchmark SRFLP instances.

Facility layout problem: Bibliometric and benchmarking analysis

Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems

The single row layout problem with clearances

The single row layout problem (SRLP) is a specially structured instance of the classical facility layout problem, especially used in flexible manufacturing systems. The SRLP consists of finding the most efficient arrangement of a given number of machines along one side of the material handling path with the purpose of minimising the total weighted sum of distances among all machine pairs. To reflect real manufacturing situations, a minimum space (so-called clearances) between machines may be required by observing technological constraints, safety considerations and regulations. This thesis intends to outline the different concepts of clearances used in literature and analyse their effects on modelling and solution approaches for the SRLP. In particular the special characteristics of sequence-dependent, asymmetric clearances are discussed and finally extended to large size clearances (machine-spanning clearances). For this, adjusted and novel model formulations and solution approaches are presented. Furthermore, a comprehensive survey of articles published in this research area since 2000 is provided which identify recent developments and emerging trends in SRLP

An investigation of multilevel refinement in routing and location problems

Multilevel refinement is a collaborative hierarchical solution technique. The multilevel technique aims to enhance the solution process of optimisation problems by improving the asymptotic convergence in the quality of solutions produced by its underlying local search heuristics and/or improving the convergence rate of these heuristics. To these aims, the central methodologies of the multilevel technique are filtering solutions from the search space (via coarsening), reducing the amount of problem detail considered at each level of the solution process and providing a mechanism to the underlying local search heuristics for efficiently making large moves around the search space. The neighbourhoods accessible by these moves are typically inaccessible if the local search heuristics are applied to the un-coarsened problems. The methodologies combine to meet the multilevel technique's aims, because, as the multilevel technique iteratively coarsens, extends and refines a given problem, it reduces the possibility of the local search heuristic becoming trapped in local optima of poor quality. The research presented in this thesis investigates the application of multilevel refinement to classes of location and routing problems and develops numerous multilevel algorithms. Some of these algorithms are collaborative techniques for metaheuristics and others are collaborative techniques for local search heuristics. Additionally, new methods of coarsening for location and routing problems and enhancements for the multilevel technique are developed. It is demonstrated that the multilevel technique is suited to a wide array of problems. By extending the investigations of the multilevel technique across routing and location problems, the research was able to present generalisations regarding the multilevel technique's suitability, for these and similar types of problems. Finally, results on a number of well known benchmarking suites for location and routing problem are presented, comparing equivalent single-level and multilevel algorithms. These results demonstrate that the multilevel technique provides significant gains over its single-level counterparts. In all cases, the multilevel algorithm was able to improve the asymptotic convergence in the quality of solutions produced by the standard (single-level) local search heuristics or metaheuristics. The multilevel technique did not improve the convergence rate of the single-level's local search heuristics in all cases. However, for large-scale problems the multilevel variants scaled in a manner superior to the single-level techniques. The research also demonstrated that for sufficiently large problems, the multilevel technique was able to improve the asymptotic convergence in the quality of solutions at a sufficiently fast rate, such that the multilevel algorithms were able to produce superior results compared to the single-level versions, without refining the solution down to the most detailed level

Метод вычисления дельта-составляющих со сложностью O(1) в квадратичной задаче о назначениях

Квадратична задача про призначення по праву вважається однією із самих складних проблем комбінаторної оптимізації. У зв’язку з цим, знайти її розв’язок, близький до оптимального, за розумний час можна тільки з використанням евристичних алгоритмів. Однією з найбільш ефективних евристик є алгоритм Robust Tabu Search, який лежить в основі багатьох наступних метаэвристических алгоритмів. У роботі описано новий підхід до сканування околиці поточного розв’язку, який дозволяє зменшити наполовину число обчислень дельта-складових, які обчислювалися зі складністю O(N) у більшості метаэвристик, що застосовуються для розв’язку квадратичної задачі про призначення. Дослідження взаємозв’язку між колишніми й новими значеннями дельта-складових, дозволило отримати нову формулу складності O(1) для їхнього обчислення, що приводить до збільшення до 25% швидкодії алгоритму в порівнянні Robust Tabu Search у випадку задач великої розмірності. Формула, отримана в роботі, може бути успішно застосована в інших евритстиках, що використовують повне сканування околиці розв'язку.The quadratic assignment problem is rightfully considered to be one of the most challenging problems of combinatorial optimization. Since this problem is NP-hard, the use of heuristic algorithms is the only way to find in a reasonable time a solution that is close to optimal. One of the most effective heuristic algorithms is the Robust Tabu Search, which is the basis of many subsequent metaheuristic algorithms. The paper describes a novel approach to scanning the neighborhood of the current solution that allows reducing by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation between the old and new delta values, obtained in this work, a new formula of complexity O(1) is proposed. The results obtained leads up to 25% performance increase as compared to such well-known algorithms as the Robust Tabu Search and others based on it. The formula obtained in this paper may be successfully applied to other heuristics using a full scan of the solution neighborhood.Квадратичная задача о назначениях по праву считается одной из самых сложных проблем комбинаторной оптимизации. В этой связи, найти ее решение, близкое к оптимальному, за разумное время можно только с использованием эвристических алгоритмов. Одной из наиболее эффективных эвристик является алгоритм Robust Tabu Search, который лежит в основе многих последующих метаэвристических алгоритмов. В работе описан новый подход к сканированию окрестности текущего решения, позволяющий уменьшить наполовину число вычислений дельта-составляющих, которые вычислялись со сложностью O(N) в большинстве метаэвристик, применяемых для решения квадратичной задачи о назначениях. Исследование взаимосвязи между прежними и новыми значениями дельта-составляющих, позволило получить новую формулу сложности O(1) для их вычисления, что приводит к увеличению до 25% быстродействия алгоритма по сравнению Robust Tabu Search в случае задач большой размерности. Формула, полученная в работе, может быть успешно применена в других эвристиках, использующих полное сканирование окрестности решения

Revisiting the Evolution and Application of Assignment Problem: A Brief Overview

The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on   a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc

Facility layout planning. An extended literature review

[EN] Facility layout planning (FLP) involves a set of design problems related to the arrangement of the elements that shape industrial production systems in a physical space. The fact that they are considered one of the most important design decisions as part of business operation strategies, and their proven repercussion on production systems' operation costs, efficiency and productivity, mean that this theme has been widely addressed in science. In this context, the present article offers a scientific literature review about FLP from the operations management perspective. The 232 reviewed articles were classified as a large taxonomy based on type of problem, approach and planning stage and characteristics of production facilities by configuring the material handling system and methods to generate and assess layout alternatives. We stress that the generation of layout alternatives was done mainly using mathematical optimisation models, specifically discrete quadratic programming models for similar sized departments, or continuous linear and non-linear mixed integer programming models for different sized departments. Other approaches followed to generate layout alternatives were expert's knowledge and specialised software packages. Generally speaking, the most frequent solution algorithms were metaheuristics.The research leading to these results received funding from the European Union H2020 Program under grant agreement No 958205 `Industrial Data Services for Quality Control in Smart Manufacturing (i4Q)'and from the Spanish Ministry of Science, Innovation and Universities under grant agreement RTI2018-101344-B-I00 `Optimisation of zerodefectsproduction technologies enabling supply chains 4.0 (CADS4.0)'Pérez-Gosende, P.; Mula, J.; Díaz-Madroñero Boluda, FM. (2021). Facility layout planning. An extended literature review. International Journal of Production Research. 59(12):3777-3816. https://doi.org/10.1080/00207543.2021.189717637773816591

Facility layout problem: Bibliometric and benchmarking analysis

Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems

O(1) delta part computation technique for the quadratic assignment problem

The quadratic assignment problem is rightfully considered to be one of the most challenging problems of combinatorial optimization. Since this problem is NP-hard, the use of heuristic algorithms is the only way to find in a reasonable time a solution that is close to optimal. One of the most effective heuristic algorithms is the Robust Tabu Search, which is the basis of many subsequent metaheuristic algorithms. The paper describes a novel approach to scanning the neighborhood of the current solution that allows reducing by half the number of delta values that were required to be computed with complexity O(N) in most of the heuristics for the quadratic assignment problem. Using the correlation between the old and new delta values, obtained in this work, a new formula of complexity O(1) is proposed. The results obtained leads up to 25% performance increase as compared to such well-known algorithms as the Robust Tabu Search and others based on it. The formula obtained in this paper may be successfully applied to other heuristics using a full scan of the solution neighborhood.Квадратична задача про призначення по праву вважається однією із самих складних проблем комбінаторної оптимізації. У зв’язку з цим, знайти її розв’язок, близький до оптимального, за розумний час можна тільки з використанням евристичних алгоритмів. Однією з найбільш ефективних евристик є алгоритм Robust Tabu Search, який лежить в основі багатьох наступних метаэвристических алгоритмів. У роботі описано новий підхід до сканування околиці поточного розв’язку, який дозволяє зменшити наполовину число обчислень дельта-складових, які обчислювалися зі складністю O(N) у більшості метаэвристик, що застосовуються для розв’язку квадратичної задачі про призначення. Дослідження взаємозв’язку між колишніми й новими значеннями дельта-складових, дозволило отримати нову формулу складності O(1) для їхнього обчислення, що приводить до збільшення до 25% швидкодії алгоритму в порівнянні Robust Tabu Search у випадку задач великої розмірності. Формула, отримана в роботі, може бути успішно застосована в інших евритстиках, що використовують повне сканування околиці розв'язку.Квадратичная задача о назначениях по праву считается одной из самых сложных проблем комбинаторной оптимизации. В этой связи, найти ее решение, близкое к оптимальному, за разумное время можно только с использованием эвристических алгоритмов. Одной из наиболее эффективных эвристик является алгоритм Robust Tabu Search, который лежит в основе многих последующих метаэвристических алгоритмов. В работе описан новый подход к сканированию окрестности текущего решения, позволяю- щий уменьшить наполовину число вычислений дельта-составляющих, которые вычислялись со сложностью O(N) в большинстве метаэвристик, применяемых для решения квадратичной задачи о назначениях. Исследование взаимосвязи между прежними и новыми значениями дельта-составляющих, позволило получить новую формулу сложности O(1) для их вычисления, что приводит к увеличению до 25% быстродействия алгоритма по сравнению Robust Tabu Search в случае задач большой размерности. Формула, полученная в работе, может быть успешно применена в других эвристиках, использующих полное сканирование окрестности решения