Genetic Algorithm for Solving Site Layout Problem with Unequal-Size and Constrained Facilities

This paper presents an investigation of the applicability of a genetic approach for solving the construction site layout problem. This problem involves coordinating the use of limited site space to accommodate temporary facilities so that transportation cost of materials is minimized. The layout problem considered in this paper is characterized by affinity weights used to model transportation costs between facilities and by geometric constraints that limit their relative positions on site. The proposed genetic algorithm generates an initial population of layouts through a sequence of mutation operations and evolves the layouts of this population through a sequence of genetic operations aiming at finding an optimal layout. The paper concludes with examples illustrating the strength and limitations of the proposed algorithm in the cases of ~1! loosely versus tightly constrained layouts with equal levels of interaction between facilities; ~2! loosely versus tightly packed layouts with variable levels of interactions between facilities; and ~3! loosely versus tightly constrained layouts. In most problems considered where the total-objects-to-site-area ratio did not exceed 60%, the algorithm returned close to optimal solutions in a reasonable time. DOI: 10.1061/~ASCE!0887-3801~2002!16:2~143! CE Database keywords: Algorithm; Construction sites; Workspace; Constraints. Introduction and Background Construction site layout involves coordinating the use of limited site space to accommodate temporary facilities ~such as fabrication shops, trailers, materials, or equipment! so that they can function efficiently on site. The layout problem is generally defined as the problem of ~1! identifying the shape and size of the facilities to be laid out; ~2! identifying constraints between facilities; and ~3! determining the relative positions of these facilities that satisfy the constraints between them and allow them to function efficiently. There are different classes of layout problems that have been studied in the literature. The variations stem from the assumptions made on the shape and size of facilities and on the constraints between them. Facilities may have a defined shape and size or a loose shape, in which case they will assume the shape of the site to which they have been assigned ~for example, bulk construction material!. The constraints can vary from simple nonoverlap constraints to other geometric constraints that describe orientation or distance constraints between facilities. In the layout problem addressed here, the shape and size of facilities are fixed. Facilities can have 2D geometric constraints on their relative positions Assistant Professor, Dept. of Industrial Engineering, Lebanese American Univ., Byblos, Lebanon. E-mail: [email protected] Assistant Professor, Dept. of Computer Science, Lebanese American Univ., Byblos, Lebanon. Graduate Research Assistant, Dept. of Computer Science, Lebanese American University, Byblos, Lebanon. Note. Discussion open until September 1, 2002. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on April 16, 2001; approved on September 4, 2001. This paper is part of the Journal of Computing in Civil Engineering, Vol. 16, No. 2, April 1, 2002. ©ASCE, ISSN 0887-3801/2002/2143–151/$8.001$.50 per page. JO along with proximity weights describing the level of interaction or flow between them. The layout problem is an NP-complete combinatorial optimization problem, that is, optimal solutions can be computed only for small or greatly restricted problems ~Kusiak and Heragu 1987!. Hence, layout planners often resort to using heuristics to reduce their search for acceptable solutions. These heuristics comprise strategic knowledge prescribing the order in which to select objects and to meet constraints, and have been modeled with various degrees of truthfulness, detail, and success in operations research and artificial intelligence applications for space planning ~Tommelein et al. 1991; Cheng 1992; Thabet 1992; Tommelein and Zouein 1993; Yeh 1995; Zouein 1995; Lin and Haas 1996; Feng et al. 1999; Zouein and Tommelein 1999!. The application of genetic algorithms ~GAs! to solving layout problems is relatively recent. GAs work with a family of solutions, known as the ‘‘current population,’’ from which we obtain the ‘‘next generation’’ of solutions. When the algorithm is designed properly, we obtain progressively better solutions from one generation to the next. The main advantage of using GAs is in the fact that it only needs an objective function with no specific knowledge about the problem space. The challenge, however, remains in finding an appropriate problem representation that results in an efficient and successful implementation of the algorithm. GAs ~Goldberg 1989! have been applied to solving the facility layout problem ~FLP! in the area of production facilities ~Tanaka and Yoshimoto 1993; Tate and Smith 1993, 1995; Hamamoto et al. 1999! and to solving the ‘‘construction site-level facility layout’’ ~Li and Love 1998!. In both applications, the layout problem was modeled as a location-allocation problem, which consists of allocating a set of predetermined facilities into a set of predetermined sites where the smallest site can accommodate the largest facility. GAs have not been used, however, to solve the site layout problem as defined in this paper. URNAL OF COMPUTING IN CIVIL ENGINEERING / APRIL 2002 / 143 This paper presents an evolutionary algorithm for optimally solving the site layout problem as characterized by affinity weights and 2D geometric constraints between facilities. The algorithm is tested on a variety of layout problems to illustrate its performance in the cases of ~1! loosely versus tightly constrained layouts with equal levels of interaction between facilities; ~2! loosely versus tightly packed layouts with variable levels of interaction between facilities; and ~3! loosely versus tightly constrained layouts. The paper concludes with a discussion of the capabilities and limitations of the proposed approach. Geometrically Constrained Site Layout Problem The layout problem as modeled in this paper is characterized by rectangular layout objects with fixed dimensions representing the facilities to be positioned on site. Facilities can be positioned in one of two orientations only: a 0 or 90° orientation. In addition, facilities can have 2D constraints on their relative positions: namely, minimum and maximum distance, orientation, and nonoverlap constraints. Minimum and maximum distance constraints limit the distance between the facing sides of two facilities in the xor y-direction to be greater than or less than a predefined value, respectively. Distance constraints can be used to model equipment reach or general clearance requirements. Orientation constraints limit a facility’s position to be to the north, south, east, or west of another reference facility. These constraints can be used to locate access roads or gates with respect to the main facility. Nonoverlap constraints are default constraints that restrict the positions of any two facilities from overlapping. The geometric constraints are considered hard constraints that should be satisfied for the layout to be feasible. The objective is to find a feasible arrangement for all layout objects within the site space that minimizes the sum of the weighted distances separating the layout objects ~Z!: Z5SS j,i~wi j3di j! (1) where wi j is the affinity weight between objects i and j that could be used to represent the flow or the unit transportation cost between i and j, and di j is the rectilinear distance separating objects i and j. A feasible arrangement is obtained by finding positions for all layout objects that satisfy the 2D constraints between them.