Juana López Redondo

Heuristics for the facility location and design (1|1)-centroid problem on the plane

A chain (the leader) wants to set up a single new facility in a planar market where similar facilities of a competitor (the follower), and possibly of its own chain, are already present. The follower will react by locating another single facility after the leader locates its own facility. Fixed demand points split their demand probabilistically over all facilities in the market in proportion to their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational model. Both the location and the quality (design) of the new leader’s facility are to be found. The aim is to maximize the profit obtained by the leader following the follower’s entry. Four heuristics are proposed for this hard-to-solve global optimization problem, namely, a grid search procedure, an alternating method and two evolutionary algorithms. Computational experiments show that the evolutionary algorithm called UEGO_cent.SASS provides the best results.

Parallel algorithms for continuous competitive location problems

A continuous location problem in which a firm wants to set up a single new facility in a competitive environment is considered. Other facilities offering the same product or service already exist in the area. Both the location and the quality of the new facility are to be found so as to maximize the profit obtained by the firm. This is a hard-to-solve global optimization problem. An evolutionary algorithm called Universal Evolutionary Global Optimizer (UEGO) seems to be the best procedure to cope with it, but the algorithm needs several hours of CPU time for solving large instances. In this paper, four parallelizations of UEGO are presented. They all are coarse-grain methods which differ in their migratory policies. A computational study is carried out to compare the performance of the parallel algorithms. The results show that one of the parallelizations always gives the best objective function value and has an almost linear speed-up for up to 16 processing elements for large instances.

GASUB: finding global optima to discrete location problems by a genetic-like algorithm

In many discrete location problems, a given number s of facility locations must be selected from a set of m potential locations, so as to optimize a predetermined fitness function. Most of such problems can be formulated as integer linear optimization problems, but the standard optimizers only are able to find one global optimum. We propose a new genetic-like algorithm, GASUB, which is able to find a predetermined number of global optima, if they exist, for a variety of discrete location problems. In this paper, a performance evaluation of GASUB in terms of its effectiveness (for finding optimal solutions) and efficiency (computational cost) is carried out. GASUB is also compared to MSH, a multi-start substitution method widely used for location problems. Computational experiments with three types of discrete location problems show that GASUB obtains better solutions than MSH. Furthermore, the proposed algorithm finds global optima in all tested problems, which is shown by solving those problems by Xpress-MP, an integer linear programing optimizer (21). Results from testing GASUB with a set of known test problems are also provided.

Parallel evolutionary algorithms based on shared memory programming approaches

In this work, two parallel techniques based on shared memory programming are presented. These models are specially suitable to be applied over evolutionary algorithms. To study their performance, the algorithm UEGO (Universal Evolutionary Global Optimizer) has been chosen.

Solving the facility location and design (1∣1)-centroid problem via parallel algorithms

Several parallel strategies for solving a centroid problem are presented. In the competitive location problem considered in this paper, the aim is to maximize the profit obtained by a chain (the leader) knowing that a competitor (the follower) will react by locating another single facility after the leader locates its own facility. Axa0global optimization memetic algorithm called UEGO_cent.SASS was proposed to cope with this hard-to-solve optimization problem. Now, five parallel implementations of the optimization algorithm have been developed. The use of several processors, and hence more computational resources, allows us to solve bigger problems and to implement new methods which increase the robustness of the algorithm at finding the global optimum. A computational study comparing the new parallel methods in terms of efficiency and effectiveness has been carried out.

Parallel algorithms for continuous multifacility competitive location problems

We consider a continuous location problem in which a firm wants to set up two or more new facilities in a competitive environment. Both the locations and the qualities of the new facilities are to be found so as to maximize the profit obtained by the firm. This hard-to-solve global optimization problem has been addressed in Redondo etxa0al. (Evol. Comput.17(1), 21–53, 2009) using several heuristic approaches. Through a comprehensive computational study, it was shown that the evolutionary algorithm uego is the heuristic which provides the best solutions. In this work, uego is parallelized in order to reduce the computational time of the sequential version, while preserving its capability at finding the optimal solutions. The parallelization follows a coarse-grain model, where each processing element executes the uego algorithm independently of the others during most of the time. Nevertheless, some genetic information can migrate from a processor to another occasionally, according to a migratory policy. Two migration processes, named Ring-Opt and Ring-Fusion2, have been adapted to cope the multiple facilities location problem, and a superlinear speedup has been obtained.

A population global optimization algorithm to solve the image alignment problem in electron crystallography

Knowledge of the structure of biological specimens is critical to understanding their function. Electron crystallography is an electron microscopy (EM) approach that derives the 3D structure of specimens at high-resolution, even at atomic detail. Prior to the tomographic reconstruction, the images taken from the microscope have to be properly aligned. Traditional alignment methods in electron crystallography are based on a phase residual function to be minimized by inefficient exhaustive search procedures. This work addresses this minimization problem from an evolutionary perspective. Universal Evolutionary Global Optimizer (UEGO), an evolutionary multimodal optimization algorithm, has been applied and evaluated for the task of image alignment in this field. UEGO has turned out to be a promising technique alternative to the standard methodology. The alignments found out by UEGO show high levels of accuracy, while reducing the number of function evaluations by a significant factor with respect to the standard method.

Finding multiple global optima for unconstrained discrete location problems

We consider a class of problems where a given number p of facility locations must be selected from a set of s potential locations so as to optimize a pre-determined fitness function. There exist outstanding location problems in this class, such as the p-median, max-covering, MAXCAP, and MAXPROFIT problems. These location problems may contain more than a single global optimal solution. Obtaining multiple global optimal solutions allows us to consider other characteristics in the process of selecting the preferred solution. In [B. Pelegrín, J. Redondo, P. Fernández, I. García, and P. Ortigosa, GASUB: Finding global optima to discrete location problems by a genetic-like algorithm, J. Glob. Optim. 38 (2007), pp. 249–264], a new ‘multimodal’ algorithm (gasub) was presented for solving the previously mentioned location problems. In the paper, the algorithm was fine-tuned to obtain a single global optimum (with 100% success) as fast as possible, and it was compared with two widely used techniques, that is, the standard optimizer Xpress-MP [Xpress-MP, Dashoptimization, 2004.] and the Multi Start Heuristic. In this paper, we propose a new set of parameter values so that gasub can explore the space more deeply and consequently find several alternative global optimal solutions. Moreover, two coarse-grain parallelizations of gasub are presented, cggasub and cggasub_mo. cggasub is able to reduce the computational time of gasub where solutions of the same quality are generated, while cggasub_mo finds more alternative global optima than the sequential version and spending similar computational time in the process. gasub, with the new parameter setting and also the parallel algorithms, will be evaluated using a comprehensive computational set of experiments. Additionally, some criteria can also be used to select one of the known global optimal solutions when several alternatives optimize the corresponding objective function.

A global optimization approach to image translational alignment in electron microscopy

Electron microscope tomography allows determination of the 3D structure of biological specimens, which is critical to understanding their function. Prior to the 3D reconstruction procedure, the images taken from the microscope have to be properly aligned. Traditional alignment methods in this field are based on a phase residual function to be minimized by inefficient exhaustive search procedures. This work addresses this minimization problem from a global optimization perspective. UEGO, an evolutionary multimodal optimization algorithm, has been applied and evaluated for the task of image alignment in this field. UEGO has turned out to be a promising technique alternative to the standard methodology. The alignments found out by UEGO show high levels of accuracy, while reducing the number of function evaluations by a significant factor with respect to the standard method.