Technical Note—A Further Note on One-Dimensional Space Allocation

The layout positioning problem of facilities on a straight line is known as Single Row Facility Layout Problem (SRFLP). The objective of SRFLP, categorized as NP-Complete problem, is to arrange the layout such that the sum of distances between all facilities’ pairs can be minimized. Extended Artificial Chromosome Genetic Algorithm (eACGA) is a promising algorithm that has been proposed recently. eACGA extends the probabilistic model in Estimation of Distribution Algorithms (EDAs) and then hybridize it with Genetic Algorithms (GAs). eACGA is proven to produce an excellent solution for scheduling problem. In this paper, we modify the eACGA to solve SRFLP. Computational results on benchmark problems show the effectiveness of eACGA for solving SRFLP. Key Words: single row facility layout, estimation distribution algorithm, genetic algorithm.

The Single-Row Facility Layout Problem (SRFLP) is one of the most studied facility layout problems in the literature. It asks for an optimal arrangement of departments with given lengths on a row such that the weighted sum of all centre-to-centre distances between department pairs is minimised. Real-world facility layouts may require taking different restrictions on the placement of departments into account, such as arrangement on a fixed position, pairwise placement, or precedence considerations. Therefore, we consider the constrained Single-Row Facility Layout Problem (cSRFLP) that additionally considers positioning, ordering, and relation constraints on single-row facility layouts. In this work, we suggest a new Integer Linear Programming (ILP) formulation for the cSRFLP, which outperforms the best available exact approach in literature. In an extensive computational study, we apply our ILP approach as well as an LP-based cutting plane algorithm on SRFLP and cSRFLP instances from the literature. We provide optimal cSRFLP layouts as well as strong lower bounds for instances with up to 42 departments. Further, we present new results for SRFLP instances from the literature. Additionally, we demonstrate the individual impact of the constraint sets on the run times of cSRFLP instances to emphasise further research on this rarely studied practice-oriented Facility Layout Problem.

The single row facility layout is the NP-Hard problem of arranging facilities with given lengths on a line, so as to minimize the weighted sum of the distances between all pairs of facilities. Owing to its computational complexity, researchers have developed several heuristics to obtain good quality solutions. In this paper, we present a genetic algorithm called GENALGO to solve large single row facility layout problem instances. Our algorithm uses standard genetic operators and periodically improves the fitness of all individuals. Our computational experiments show that our genetic algorithm yields high quality solutions in spite of starting with an initial population that is randomly generated. Our algorithm improves the previously best known solutions for the 19 instances of 58 benchmark instances and is competitive for most of the remaining ones.

A parallel ordering problem in facilities layout

Differential evolution is an efficient evolutionary optimization paradigm that has shown a good ability to solve a variety of practical problems, including combinatorial optimization ones. Single row facility layout problem is an NP-hard permutation problem often found in facility design, factory construction, production optimization, and other areas. Real-world problems can be cast as large single row facility location problem instances with different high-level properties and efficient algorithms that can solve them efficiently are needed. In this work, the differential evolution is used to solve the single row facility location problem and the ability of three different variants of the algorithm to evolve solutions to various problem instances is studied.

In this paper, an artificial immune system (AIS) algorithm is proposed to solve single row facility layout problem (SRFLP) for obtaining a best layout design of machines, which simultaneously minimises the multiple objectives. The multi-product environment with multiple objectives is considered in this work and it is a non-polynomial hard problem too. Total number of machines in the layout, total flow distance of products, total length of the flow line and total material handling cost are considered as objectives. Four problems are taken from Lenin et al. (2018) and four problems are randomly generated to obtain the best layout using AIS. The reduction in objective values is good by the proposed AIS algorithm compared with Lenin et al. (2018). In addition, the computational time for all the eight problems by the proposed AIS method is less compared with Lenin et al. (2018).

The Algebraic Differential Evolution for Permutations (ADEP) has been recently proposed as an effective evolutionary algorithm for permutation-based optimization problems. ADEP is built upon a framework that exploits the rich algebraic structure of the permutations search space. In this paper we further explore the abilities of ADEP by presenting an implementation for the Single Row Facility Layout Problem (SRFLP): a permutation problem with interesting real-world applications ranging from designing the layouts of machines in certain manufacturing systems to optimally arranging rooms in hospitals. An experimental investigation was conducted on a set of commonly adopted benchmarks and different settings ADEP were compared among them and with respect to the other methods in the literature. Interestingly, the experimental results confirm the validity of ADEP by showing its competitiveness with respect to the state-of-the-art results for the SRFLP.

Single-Row Facility Layout Problem (SRFLP) is a special class of facility layout problems, consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line. In this research, we first present a theorem to find the optimal solution of a special case of SRFLP. The results obtained by this theorem are very useful in reducing the computational efforts when, later on, a new algorithm based on tabu search is presented for SRFLP. Computational results of the proposed algorithm on benchmark problems show the efficiency of the algorithm compared to the other heuristics. The proposed algorithm can easily find near-optimal solutions in less than one minute for instances consist of 200 departments. However, the largest instances reported to be solved by the other methods had only 80 departments and took more than 10 hours to reach the solution.

This paper focuses on solving the Continuous Facility Layout Problem (CFLP), which aims to minimize material handling costs by strategically placing facilities in a known or unknown area. The objective is to find optimal or near-optimal facility arrangements while adhering to non-overlapping and spatial constraints, thus enhancing the efficiency of production systems. The study addresses various layout scenarios, including single-row facility layout (with and without clearance), continuous layout, and unequal-area facility layout problems. To achieve this, the authors propose a mixed-integer nonlinear programming (MINLP) model tailored for continuous layouts. Two meta-heuristic algorithms are developed to optimize this model: a hybrid Simulated Annealing-Genetic Algorithm (SA-GA), which leverages genetic crossover operations, and an Enhanced Harmony Search Algorithm (EHSA), featuring dynamic parameters and a novel improvisation technique. The proposed methods provide flexible and efficient solutions for both small and large-scale layout problems, offering decision-makers practical tools for real-world applications.

The Single-Row Facility Layout Problem (SRFLP) is a well-known combinatorial optimization problem. The objective of SRFLP is to find out the arrangement of facilities with given lengths on a line so that the weighted sum of the distances between all pairs of facilities is minimized. This problem is known to be NP-hard. Hence, a population-based improvement heuristic algorithm with local search is presented in this article to solve SRFLP. The proposed algorithm works well also for the Single-Row Equidistant Facility Layout Problem (SREFLP), where the length of each facility is equal. The computational efficiency of the proposed algorithm is checked with the instances of sizes ranging from 5 to 300 available in the literature for SRFLP and SREFLP. The obtained results are compared to those from different state-of-the-art algorithms. The proposed algorithm achieves best known solutions to date for every instance considered in this article in reasonable computational time.

Contributors

CV. Tempe Suryadi Sentosa is a company engaged in the manufacture of tempeh, a traditional food of Tangerang, which is spread across almost all areas of Tangerang, namely Tangerang City, Tangerang Regency, South Tangerang City, and parts of Serang. Therefore, the company's Operational Research at CV. Tempe Suryadi Sentosa must be carried out smoothly, and its layout must not be frequently obstructed. Various facilities and spaces must be in accordance with the various activities carried out to ensure that the process runs smoothly and worker comfort is maintained. In this study, the identification of relationships between facilities was carried out using the Activity Relationship Chart (ARC). Each facility is categorized into work stations. After determining the relationships between facilities, the next step is to design the facility layout using the BLOCPLAN method, which produces five alternative proposed facility layouts. The results of the facility layout design research using the BLOCPLAN method Each alternative facility layout has an Adjacency Score, R-Score, and Rel-dist Score which will be used as criteria for selecting the best alternative facility layout. And the latest layout is 13 with a layout score of 0.5

Contributors

My research in optimization at the Department of Systems and Computer Engineering at Carleton University has brought me into contact with researchers in the Department of Electronics, our sister department in the general field of Electrical and Computer Engineering (ECE), which has a major research thrust in computer-aided design (CAD) of very large scale integrated (VLSI) circuits. I have come to realize that the design of VLSI systems consists in large part of solving incredibly massive mixed-integer nonlinear optimization problems, together with enormous circuit simulations. This is impossible without the use of CAD techniques. Over time, ECE-CAD researchers have both borrowed useful standard techniques from operations research (OR) and have invented their own, often to deal with the sheer scale and complexity of the design problems they face. Interaction between the OR and ECE-CAD communities would seem to be a natural development. Coincidentally, the INFORMS Journal on Computing had an area entitled “High Performance Computation” that covered (i) the solution of OR problems using new computing technologies, (ii) the application of OR techniques in the design and use of highperformance computing and communication systems, and (iii) solution methods for ultra-large-scale OR applications. The viability of this area was debated during 2003 as some of its aspects migrated to other areas (e.g., the new “Telecommunications and Electronic Commerce” area), and the number of submissions declined. The area was eventually closed, although I argued that the overlap between OR and ECE-CAD, essentially covering items (ii) and (iii), was a very active research area. This Special Cluster of papers was conceived as a way to test that argument. I was recruited at the same time to prepare a tutorial on ECE-CAD for the 2004 INFORMS Annual Meeting (see John W. Chinneck, Michel Nakhla, and Q. J. Zhang 2004. Computer-aided design for electrical and computer engineering. H. J. Greenberg, ed. Tutorials on Emerging Methodologies and Applications in Operations Research. Springer, New York, 6-1 to 6-44). The preparation of the article reinforced my observation about the research overlap between OR and ECE-CAD. A search of the electrical engineering literature for 2000 through early 2004 turned up 46,725 papers mentioning “simulate” or “simulation” as keywords in the abstract, 14,216 papers mentioning “optimization” or “optimize,” and relatively smaller numbers for specific techniques such as “neural network” (6,251), “genetic algorithm” (2,603), “linear programming” (576), “simulated annealing” (448), and “branch and bound” (199). One surprise was the relatively small number of papers using the generic keywords “mathematical programming” (68) or “operations research” (37). The general conclusion of the tutorial article is that the OR and the ECE-CAD communities have much to offer each other. This is certainly the case for the papers gathered in this Special Cluster. We see known OR techniques adapted for use in ECECAD. In “Integer Linear Programming Models for Global Routing,” Behjat et al. apply integer linear programming in a heuristic to solve enormous NPhard connection routing problems for VLSI circuits. In “Task Scheduling in a Finite-Resource, Reconfigurable Hardware/Software Codesign Environment,” Loo and Wells use simulated annealing, genetic algorithms, and random search techniques to solve scheduling problems in hardware-software co-design. We also see new techniques specifically developed by the ECE-CAD community to deal with problems of extreme scale. In “A Projection-Based Reduction Approach to Computing Sensitivity of Steady-State Response of Nonlinear Circuits,” Pai et al. develop methods for sensitivity analysis in extremely large nonlinear programs, especially those in which the objective function is very costly to evaluate. The methods have special relevance for simulation-based

About Our Authors