Manuel Laguna

University of Colorado Boulder | CUB · Leeds School of Business

The Cyclic Cutwidth Minimization Problem (CCMP) is a Graph Layout Problem that consists of finding an embedding of the vertices of a candidate graph in a host graph, in order to minimize the maximum cut of a host edge. In this case, the host graph is restricted to be a cycle. In this paper, we identify a new lower bound for the problem, and also a...

The speed by which the COVID-19 pandemic spread throughout the world caught some national and local governments unprepared. Healthcare systems found themselves struggling to increase capacity and procure key supplies, such as personal protective equipment. Protective face shields became essential for healthcare professionals. However, most hospital...

Metaheuristic optimization is at the heart of the intersection between computer science and operations research. The INFORMS Journal of Computing has been fundamental in advancing the ideas behind metaheuristic methodologies. Fred Glover’s “Tabu Search—Part I” was published more than 30 years ago in the first volume of the then ORSA Journal on Comp...

In this paper, a new solution method is implemented to solve a bi‐objective variant of the vehicle routing problem that appears in industry and environmental enterprises. The solution involves designing a set of routes for each day in a period, in which the service frequency is a decision variable. The proposed algorithm, a muti‐start multi‐objecti...

The optimization of a production process is often based on the efficient utilization of the production facility and equipment. In particular, reducing the time to change from producing one product to another is critical to the fulfillment of demand at a minimum cost. We study the production of steel coils in the context of searching for groups of p...

A Muti-Start Multiobjective Local Search algorithm is implemented to solve a bi-objective variant of the Vehicle Routing Problem appearing in industry and environmental enterprises. The problem seeks to design a set of routes for each time on a period and in which the service frequency is a decision variable. The algorithm minimizes total emissions...

Metaheuristics have become a very popular family of solution methods for optimization problems because they are capable of finding “acceptable” solutions in a “reasonable” amount of time. Most optimization problems in practice are too complex to be approached by exact methods that can guarantee finding global optimal solutions. The time required to...

Linear programming is perhaps the best-known tool for optimization. Linear programming is a general-purpose framework that allows a real system to be abstracted as a model with a linear objective function subject to a set of linear constraints.

In this chapter, we describe the process of designing heuristic procedures to solve combinatorial optimization problems.

Models, as a simplified representation of reality, are used daily in an attempt to control or understand some aspects of a real system. Simplification of reality is the accepted view of the modeling process, which assumes that reality represents the absolute truth. Without getting too deep into a philosophical discourse, it is worth mentioning the...

In this chapter we describe one of the most successful methodologies for obtaining high quality solutions to difficult optimization problems. It was proposed by Fred Glover (Decision Sciences 8:371–392, 1997) [3] under the term Tabu Search, which refers to the way in which the method explores the solution region of a given problem. We will use Clus...

This essential metaheuristics tutorial provides descriptions and practical applications in the area of business analytics. It addresses key problems in predictive and prescriptive analysis, while also illustrating how problems that arise in business analytics can be modelled and how metaheuristics can be used to find high-quality solutions. Readers...

Automated graph-drawing systems utilize procedures to place vertices and arcs in order to produce graphs with desired properties. Incremental or dynamic procedures are those that preserve key characteristics when updating an existing drawing. These methods are particularly useful in areas such as planning and logistics, where updates are frequent....

Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edg...

The Maximum Minsum Dispersion Problem (Max-Minsum DP) is a strongly NP-Hard problem that belongs to the family of equitable dispersion problems. When dealing with dispersion, the operations research literature has focused on optimizing efficiency-based objectives while neglecting, for the most part, measures of equity. The most common efficiency-ba...

We tackle a combinatorial problem that consists of finding the optimal configuration of a binary matrix. The configuration is determined by the ordering of the rows in the matrix and the objective function value is associated with a value B, the so-called bandpass number. In the basic version of the problem, the objective is to maximize the number...

Given a set of positive integers S, the minimum generating set problem consists in finding a set of positive integers T with a minimum cardinality such that every element of S can be expressed as the sum of a subset of elements in T. It constitutes a natural problem in combinatorial number theory and is related to some real-world problems, such as...

We address one of the external factors of personnel inventory behavior, deployments. The configuration of persistent unit deployments has the ability to affect everything from individual perceptions of service palatability to operational effectiveness. There is little evidence to suggest any analytical underpinnings to the U.S. Army deployment sche...

While the cross entropy methodology has been applied to a fair number of combinatorial optimization problems with a single objective, its adaptation to multiobjective optimization has been sporadic. We develop a multiobjective optimization cross entropy (MOCE) procedure for combinatorial optimization problems for which there is a linear relaxation...

The capacitated clustering problem (CCP) consists of forming a specified number of clusters or groups from a set of elements in such a way that the sum of the weights of the elements in each cluster is within some capacity limits, and the sum of the benefits between the pairs of elements in the same cluster is maximized. This problem—which has been...

The goal of this work is to develop an improved procedure for the solution of the lexicographic bottleneck variant of the assembly line balancing problem (LB-ALBP). The objective of the LB-ALBP is to minimize the workload of the most heavily loaded workstation, followed by the workload of the second most heavily loaded workstation and so on. This p...

We study the problem of minimizing the profile of a graph and develop a solution method by following the tenets of scatter search. Our procedure exploits the network structure of the problem and includes strategies that produce a computationally efficient and agile search. Among several mechanisms, our search includes path relinking as the basis fo...

A recent study (Yin, et al., 2010) showed that combining Particle Swarm Optimization (PSO) with the strategies of Scatter Search (SS) and Path Relinking (PR) produces a Cyber Swarm Algorithm that creates a more effective form of PSO than methods that do not incorporate such mechanisms. In this chapter, the authors propose a Complementary Cyber Swar...

Production systems with closed-loop facilities must deal with the problem of sequencing batches in consecutive loops. This article studies a problem encountered in a production facility in which plastic parts of several shapes must be painted with different colors to satisfy the demand given by a set of production orders. The shapes and the colors...

Scatter search (SS) is an evolutionary approach for optimization. It has been applied to problems with continuous and discrete variables and with one or multiple objectives. The success of SS as an optimization technique is well documented in a constantly growing number of journal articles, book chapters (Glover et al. 2003a, 2003b, 2004; Laguna 20...

Resumen En este trabajo se propone un algoritmo basado en Scat-ter Search para resolver el problema de la minimización del Profile. Se utiliza la estrategia Path Relinking como método base para la genera-ción de nuevas soluciones mediante combinación. El problema del Profile (PMP) es NP-duro y tiene aplicaciones relevantes en técnicas de análi-sis...

The min-max vehicle routing problem VRP is a variant of the classical VRP in which the objective is to minimize the duration of the longest route. Examination of the VRP literature indicates that the min-max VRP has received less attention than other variants have over the years. However, the problem has important practical applications, such as th...

We propose new heuristic procedures for the maximally diverse grouping problem (MDGP). This NP-hard problem consists of forming maximally diverse groups - of equal or different size - from a given set of elements. The most general formulation, which we address, allows for the size of each group to fall within specified limits. The MDGP has applicat...

The goal of this work is the development of a black-box solver based on the scatter search methodology. In particular, we seek a solver capable of obtaining high quality outcomes to optimization problems for which solutions are represented as a vector of integer values. We refer to these problems as integer optimization problems. We assume that the...

Tabu search, also called adaptive memory programming, is a method for solving challenging problems in the field of optimization. The goal is to identify the best decisions or actions in order to maximize some measure of merit (such as maximizing profit, effectiveness, quality, and social or scientific benefit) or to minimize some measure of demerit...

Though its origins can be traced back to 1977, the development and application of the metaheuristic Scatter Search (SS) has stayed dormant for 20 years. However, in the last 10 years, research interest has positioned SS as one of the recognizable methodologies within the umbrella of evolutionary search. This paper presents an application of SS to t...

A recent study (Yin et al., 2010) showed that combining particle swarm optimization (PSO) with the strategies of scatter search (SS) and path relinking (PR) produces a Cyber Swarm Algorithm that creates a more effective form of PSO than methods that do not incorporate such mechanisms. This paper proposes a Complementary Cyber Swarm Algorithm (C/Cyb...

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting...

Metaheuristic approaches based on the neighborhood search escape local optimality by applying predefined rules and constraints, such as tabu restrictions (in tabu search), acceptance criteria (in simulated annealing), and shaking (in variable neighborhood search). We propose a general approach that attempts to learn (off-line) the guiding constrain...

We propose a hybrid heuristic procedure based on scatter search and tabu search for the problem of clustering objects to optimize multiple criteria. Our goal is to search for good approximations of the efficient frontier for this class of problems and provide a means for improving decision making in multiple application areas. Our procedure can be...

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting...

Drug discovery is the process of designing compounds that have desirable properties, such as activity and non-toxicity. Molecule classification techniques are used along this process to predict the properties of the compounds in order to expedite their testing. Ideally, the classification rules found should be accurate and reveal novel chemical pro...

A recent study Yin et al., 2010 showed that combining particle swarm optimization PSO with the strategies of scatter search SS and path relinking PR produces a Cyber Swarm Algorithm that creates a more effective form of PSO than methods that do not incorporate such mechanisms. This paper proposes a Complementary Cyber Swarm Algorithm C/CyberSA that...

Though its origins can be traced back to 1977, the development and application of the metaheuristic Scatter Search (SS) has stayed dormant for 20 years. However, in the last 10 years, research interest has positioned SS as one of the recognizable methodologies within the umbrella of evolutionary search. This paper presents an application of SS to t...

Given a matrix of weights, the Linear Ordering Problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This well known NP-complete problem can also be formulated on a complete weighted graph, where the objective is to find an acyclic tournament that maximizes the sum...

Scatter search (SS) is an evolutionary approach for optimization. It has been applied to problems with continuous and discrete variables and with a single or multiple objectives. The success of SS as an optimization technique is well documented in a constantly growing number of journal articles and book chapters. This article first focuses on the b...

There is renewed interest in the development of effective and efficient methods for optimizing models of which the optimizer has no structural knowledge. This is what in the literature is referred to as optimization of black boxes. In particular, we address the challenge of optimizing expensive black boxes, that is, those that require a significant...

The purpose of this paper is to apply the scatter search methodology to general classes of binary problems. We focus on optimization problems for which the solutions are represented as binary vectors and that may or may not include constraints. Binary problems arise in a variety of settings, including engineering design and statistical mechanics (e...

The problem of finding a global optimum of a constrained multimodal function has been the subject of intensive study in recent years. Several effective global optimization algorithms for constrained problems have been developed; among them, the multi-start procedures discussed in Ugray et al. [1] are the most effective. We present some new multi-st...

Particle swarm optimization (PSO) has emerged as an acclaimed approach for solving complex optimization problems. The nature metaphors of flocking birds or schooling fish that originally motivated PSO have made the algorithm easy to describe but have also occluded the view of valuable strategies based on other foundations. From a complementary pers...

The maximum diversity problem presents a challenge to solution methods based on heuristic optimization. We undertake the development of hybrid procedures within the scatter search framework with the goal of uncovering the most effective designs to tackle this difficult but important problem. Our research revealed the effectiveness of adding simple...

This presentation explores the evolutionary approach called scatter search, which originated from strategies for creating composite decision rules and surrogate constraints. Recent studies have demonstrated the practical advantages of this approach for solving a diverse collection of optimization problems from both classical and real world settings...

The Max-Cut problem consists of finding a partition of the nodes of a weighted graph into two subsets such that the sum of the weights between both sets is maximized. This is an NP-hard problem that can also be formulated as an integer quadratic program. Several solution methods have been developed since the 1970s and applied to a variety of fields...

Cross-entropy has been recently proposed as a heuristic method for solving combinatorial optimization problems. We briefly review this methodology and then suggest a hybrid version with the goal of improving its performance. In the context of the well-known max-cut problem, we compare an implementation of the original cross-entropy method with our...

RESUMEN El Minmax VRP es una variante del clásico VRP en el que el objetivo es minimizar la duración de la ruta más larga. Este modelo ha aparecido en algunas situaciones reales, especialmente en el contexto de transporte escolar en áreas rurales, como se refleja en diferentes trabajos recientes. En este trabajo se trata una variante del VRP con 2...

Tabu search, also called adaptive memory programming, is a method for solving challenging problems in the field of optimization. The goal is to identify the best decisions or actions in order to maximize some measure of merit (such as maximizing profit, effectiveness, quality, and social or scientific benefit) or to minimize some measure of demerit...

We introduce and test a new approach for the bi-objective routing problem known as the traveling salesman problem with profits. This problem deals with the optimization of two conflicting objectives: the minimization of the tour length and the maximization of the collected profits. This problem has been studied in the form of a single objective pro...

The purpose of this paper is to develop a context-independent method for solving an important class of combinatorial optimization problems. Specifically we tackle problems whose solutions can be represented as binary vectors. We consider both constrained and unconstrained problems. Our general-purpose heuristic is based on a model that treats the o...

Not Available

A fertile complementarity exists between scatter search (SS) and particle swarm optimization (PSO). Shared and contrasting principles underlying these methods provide a fertile basis for combining them to create a hybrid method. We identify a specific hybrid, scatter PSO, giving rise to two variants that prove more effective than the constriction f...

The navigation of autonomous guided vehicles (AGV's) in industrial environments is often controlled by positioning systems based on landmarks or artificial beacons. In these systems, the position of an AGV navigating in an interior space is determined by the calculation of its relative distance to beacons, whose location is known in advance. A fund...

We introduce a simulation optimization approach that is effective in guiding the search for optimal values of input parameters to a simulation model. Our proposed approach, which includes enhanced data mining methodology and state-of-the-art optimization technology, is applicable to settings in which a large amount of data must be analyzed in order...

We describe the development and testing of a metaheuristic procedure, based on the scatter search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-o...

We describe a solution procedure for a special case of the periodic vehicle routing problem (PVRP). Operation managers at an auto parts manufacturer in the north of Spain described the optimization problem to the authors. The manufacturer must pick up parts (raw material) from geographically dispersed locations. The parts are picked up periodically...

We address a project scheduling problem with resource availability cost for which the activity durations are uncertain. The problem is formulated within the robust optimization framework, where uncertainty is modeled via a set of scenarios. The proposed solution method is based on the scatter search methodology and employs advanced strategies, such...

A growing number of business process management software vendors are offering simulation capabilities to extend their modeling functions and enhance their analytical proficiencies. Simulation is promoted to enable examination and testing of decisions prior to actually making them in the "real" environment. In this paper, we illustrate how to optimi...

The purpose of this paper is to describe the implementation and testing of the tabu cycle method and two variants of the conditional probability method. These methods were originally described in Glover and Laguna (1997) but have been largely ignored in the tabu search literature. For the purpose of testing, we employ a single- attribute implementa...

Scatter search (SS) is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effec...

In this chapter we discuss the development and application of a library of functions that is the optimization engine for the OptQuest system. OptQuest is commercial software designed for optimizing complex systems, such as those formulated as simulation models. OptQuest has been integrated with several simulation packages with the goal of adding op...

This paper considers a project scheduling problem with the objective of minimizing resource availability costs, taking into account a deadline for the project and precedence relations among the activities. Exact methods have been proposed for solving this problem, but we are not aware of existing heuristic methods. Scatter search is used to tackle...

Researchers and practitioners frequently spend more time fine-tuning algorithms than designing and implementing them. This is particularly true when developing heuristics and metaheuristics, where the right choice of values for search parameters has a considerable effect on the performance of the procedure. When testing metaheuristics, performance...

Scatter search is an evolutionary method that has been successfully applied to hard optimization problems. The fundamental concepts and principles of the method were first proposed in the 1970s, based on formulations dating back to the 1960s for combining decision rules and problem constraints. In contrast to other evolutionary methods like genetic...

This chapter discusses the principles and foundations behind scatter search and its application to the problem of training neural networks. Scatter search is an evolutionary method that has been successfully applied to a wide array of hard optimization problems. Scatter search constructs new trial solutions by combining so-called reference solution...

We develop a metaheuristic procedure for multiobjective clustering problems. Our goal is to find good approximations of the efficient frontier for this class of problems and provide a means for improving decision making in multiple areas of application and in particular those related to marketing. The procedure is based on the tabu and scatter sear...

In this work, a system to solve the labor scheduling problem in a passengers flow model at an airport is developed. Specifically, the objective consists on rationalizing personnel costs (check and security), at the same time that the minimum level of service required in the passengers transit (measured with the waiting time) is guaranteed. The syst...

In this paper, we address a logistics problem that a manufacturer of auto parts in the north of Spain described to the authors. The manufacturer stores products in its warehouse until customers retrieve them. The customers and the manufacturer agree upon an order pickup frequency. The problem is to find the best pickup schedule, which consists of t...