Fred Glover

University of Colorado Boulder | CUB · School of Engineering & Leeds School of Business

In recent years the quadratic unconstrained binary optimization (QUBO) problem has e merged as a unified framework for modeling and solving a wide variety of combinatorial optimization problems. The unexpected versatility of the QUBO model is opening door to the solution of a diverse array of important and challenging applications. Developments in...

In recent years the quadratic unconstrained binary optimization (QUBO) problem has e merged as a unified framework for modeling and solving a wide variety of combinatorial optimization problems. The unexpected versatility of the QUBO model is opening door to the solution of a diverse array of important and challenging applications. Developments in...

The minimum sum coloring problem (MSCP), a well-known NP-hard (nondeterministic polynomial time) problem with important practical applications, has been the subject of several papers in recent years. Because of the computational challenge posed by these problems, most solution methods employed are metaheuristics designed to find high-quality soluti...

This repository provides data for the problem and scripts for the models. The main folders are 'data', 'scripts', and 'results'. 'data': This folder includes minimum sum graph coloring data sets. 'src': Our metaheuristic solver Q-Card can be found in this folder. 'scripts': This folder provides a running script. 'results': This folder provides the...

Rank aggregation combines the preference rankings of multiple alternatives from different voters into a single consensus ranking, providing a useful model for a variety of practical applications but posing a computationally challenging problem. In this paper, we provide an effective hybrid evolutionary ranking algorithm to solve the rank aggregatio...

This study considers a well-known critical node detection problem that aims to minimize a pairwise connectivity measure of an undirected graph via the removal of a subset of nodes (referred to as critical nodes) subject to a cardinality constraint. Potential applications include epidemic control, emergency response, vulnerability assessment, carbon...

Advances in quantum computing with applications in combinatorial optimization have evolved at an increasing rate in recent years. The quadratic unconstrained binary optimization (QUBO) model is at the center of these developments and has become recognized as an effective alternative method for representing a wide variety of combinatorial optimizati...

Tabu search is a meta-heuristic that guides a local heuristic search procedure to explore the solution space beyond local optimality. One of the main components of tabu search is its use of adaptive memory, which creates an intelligent search pattern based on strategic choices, as opposed to random selections that are widely applied in other method...

This study considers a well-known critical node detection problem that aims to minimize a pairwise connectivity measure of an undirected graph via the removal of a sub-set of nodes (referred to as critical nodes) subject to a cardinality constraint. Potential appli-cations include epidemic control, emergency response, vulnerability assessment, carb...

This paper presents an effective perturbation-based thresholding search for two popular and challenging packing problems with minimal containers: packing N identical circles in a square and packing N identical spheres in a cube. Following the penalty function approach, we handle these constrained optimization problems by solving a series of unconst...

Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the fi...

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutorial...

Rank aggregation aims to combine the preference rankings of a number of alternatives from different voters into a single consensus ranking. As a useful model for a variety of practical applications, however, it is a computationally challenging problem. In this paper, we propose an effective hybrid evolutionary ranking algorithm to solve the rank ag...

QUBO models have proven to be remarkable for their ability to function as an alternative modeling framework for a wide variety of combinatorial optimization problems. Many studies have underscored the usefulness of the QUBO model to serve as an effective approach for modeling and solving important combinatorial problems. The significance of this un...

The minimum connected dominating set (MCDS) problem consists of selecting a minimum set of vertices from an undirected graph, such that each vertex not in this set is adjacent to at least one of the vertices in it, and the subgraph induced by this vertex set is connected. This paper presents a fast vertex weighting (FVW) algorithm for solving the M...

Finding good solutions to clique partitioning problems remains a computational challenge. With rare exceptions, finding optimal solutions for all but small instances is not practically possible. However, choosing the most appropriate modeling structure can have a huge impact on what is practical to obtain from exact solvers within a reasonable amou...

Tabu search is an optimization methodology that guides a local heuristic search procedure to explore the solution space beyond local optimality. It is substantiated by the hypothesis that an intelligent solving algorithm must incorporate memory to base its decisions on information collected during the search. The method creates in this way a learni...

Focal distance tabu search modifies a standard tabu search algorithm for binary optimization by augmenting a periodic diversification step that drives the search away from a current best (or elite) solution until the objective function deteriorates beyond a specified threshold or until attaining a lower bound on the distance from the originating so...

We propose a new algorithm for fixed‐charge network flow problems based on ghost image (GI) processes as proposed in Glover (1994) and adapted to fixed‐charge transportation problems in Glover et al. (2005). Our GI algorithm iteratively modifies an idealized representation of the problem embodied in a parametric GI, enabling all steps to be perform...

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future.This is the second of a two-part tutorial t...

A variety of strategies have been proposed for overcoming local optimality in metaheuristic search. This paper examines characteristics of moves that can be exploited to make good decisions about steps that lead away from a local optimum and then lead toward a new local optimum. We introduce strategies to identify and take advantage of useful featu...

We propose a new self-organizing algorithm for fixed-charge network flow problems based on ghost image (GI) processes as proposed in Glover (1994) and adapted to fixed-charge transportation problems in Glover, Amini and Kochenberger (2005). Our self-organizing GI algorithm iteratively modifies an idealized representation of the problem embodied in...

Scatter Search is an evolutionary metaheuristic introduced by Glover (1977) as a heuristic for integer programming and was joined with a directional rounding strategy for 0–1 Mixed Integer Programming (MIP) problems based on Star Paths in Glover (1995). In this paper, we address directional rounding both independently and together with these other...

The optimum satisfiability problem involves determining values for Boolean variables to satisfy a Boolean expression, while maximizing the sum of coefficients associated with the variables chosen to be true. Existing literature has identified a tabu search heuristic as the best method to deal with hard instances of the problem. This paper combines...

Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a structure for generating overlapping clusters, where data objects can belong to more than one subset, which we join with bi-objective optimization and link to biclustering for problems with binary data. Biclust...

Pareto optimality is the fundamental construct employed to determine whether a given solution to a multi-criteria mathematical optimization model is preferred to another solution. In this paper we describe an approach (Pattern Efficient Set Algorithm – PESA) to generating a pattern-efficient set of non-dominated vectors to a multi-objective optimiz...

Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a generalization called quasi-clustering that allows overlapping of clusters, and which we link to biclustering. Biclustering simultaneously groups the objects and features so that a specific group of objects has...

The multiple vehicle pickup and delivery problem is a generalization of the traveling salesman problem that has many important applications in supply chain logistics. One of the most prominent variants requires the route durations and the capacity of each vehicle to lie within given limits, while performing the loading and unloading operations by a...

Quantum Bridge Analytics relates generally to methods and systems for hybrid classical-quantum computing, and more particularly is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the fi...

Quantum Bridge Analytics relates to methods and systems for hybrid classical-quantum computing, and is devoted to developing tools for bridging classical and quantum computing to gain the benefits of their alliance in the present and enable enhanced practical application of quantum computing in the future. This is the second of a two-part tutoria...

Critical node problems involve identifying a subset of critical nodes from an undirected graph whose removal results in optimizing a pre-defined measure over the residual graph. As useful models for a variety of practical applications, these problems are computational challenging. In this paper, we study the classic critical node problem (CNP) and...

Diversification-Based Learning (DBL) derives from a collection of principles and methods introduced in the field of metaheuristics that have broad applications in computing and optimization. We show that the DBL framework goes significantly beyond that of the more recent Opposition-based learning (OBL) framework introduced in Tizhoosh (2005), which...

We introduce new diversification methods for zero-one optimization that significantly extend strategies previously introduced in the setting of metaheuristic search. Our methods incorporate easily implemented strategies for partitioning assignments of values to variables, accompanied by processes called augmentation and shifting which create greate...

A long-standing challenge in the metaheuristic literature is to devise a way to select parent solutions in evolutionary population-based algorithms to yield better offspring, and thus provide improved solutions to populate successive generations. We identify a way to achieve this goal that simultaneously improves the efficiency of the evolutionary...

Evolutionary computing is a general and powerful framework for solving difficult optimization problems, including those arising in expert and intelligent systems. In this work, we investigate for the first time two hybrid evolutionary algorithms incorporating tabu search for solving the generalized max-mean dispersion problem (GMaxMeanDP) which has...

The bipartite Boolean quadratic programming problem (BBQP) is a generalization of the well-studied NP-hard Boolean quadratic programming problem and can be regarded as a unified model for many graph theoretic optimization problems, including maximum weight-induced subgraph problems, maximum weight biclique problems, matrix factorization problems, a...

Population-based evolutionary algorithms usually manage a large number of individuals to maintain the diversity of the search, which is complex and time-consuming. In this paper, we propose an evolutionary algorithm using only two individuals, called master-apprentice evolutionary algorithm (MAE), for solving the flexible job shop scheduling proble...

Recent years have witnessed the remarkable discovery that the Quadratic Unconstrained Binary Optimization (QUBO) model unifies a wide variety of combinatorial optimization problems, and moreover is the foundation of adiabatic quantum computing and a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart...

Meta-analytics represents the unification of metaheuristics and analytics, two fields of the foremost interest and practical importance. While metaheuristics provide a modern framework and an arsenal of cutting-edge techniques to handle complex, real-world problems, Analytics embodies the use of prediction and optimization techniques in practical c...

We present a new clustering algorithm for handling complexities encountered in analysing data sets of hotel ratings and analyse its performance in a clustering case study. In the setting we address, business constraints and coordinates (among other individual attributes of objects) are unknown and only distances between objects are available to the...

The minimum differential dispersion problem is a NP-hard combinatorial optimization problem with numerous relevant applications. In this paper, we propose an intensification-driven tabu search algorithm for solving this computationally challenging problem by integrating a constrained neighborhood, a solution-based tabu strategy, and an intensified...

The Cross-Docking Assignment Problem (CDAP) is a challenging optimization problem in supply chain management with important practical applications in the trucking industry. The goal is to assign incoming trucks (outgoing trucks) to inbound (outbound) doors to minimize the material handling cost within a cross-docking platform while respecting the c...

This chapter describes the history of metaheuristics in five distinct periods, starting long before the first use of the term and ending a long time in the future. The field of metaheuristics has undergone several paradigm shifts that have changed the way researchers look upon the development of heuristic methods. Most notably, there has been a shi...

The 0–1 multidimensional knapsack problem is a well-known NP-hard combinatorial optimization problem with numerous applications. In this work, we present an effective two-phase tabu-evolutionary algorithm for solving this computationally challenging problem. The proposed algorithm integrates two solution-based tabu search methods into the evolution...

The bipartite boolean quadratic programming problem with partitioned variables (BQP-PV) is an NP-hard combinatorial optimization problem that accommodates a variety of real-life applications. We propose an adaptive tabu search with strategic oscillation (ATS-SO) approach for BQP-PV, which employs a multi-pass search framework where each pass consis...

Integer programming models for clustering have applications in diverse fields addressing many problems such as market segmentation and location of facilities. Integer programming models are flexible in expressing objectives subject to some special constraints of the clustering problem. They are also important for guiding clustering algorithms that...

The maximum min-sum dispersion problem (Max-Minsum DP) is an important representative of a large class of dispersion problems. Having numerous applications in practice, the NP-hard Max-Minsum DP is however computationally challenging. This paper introduces an effective solution-based tabu search (SBTS) algorithm for solving the Max-Minsum DP approx...

We introduce a new class of assignment-based neighborhoods for symmetric and asymmetric traveling salesman problems that exhibits a combinatorial leverage property, by which a tour can be generated in polynomial time that dominates an exponential number of other tours. The ejection chain perspective motivating the new neighborhoods differs from tha...

A cross docking facility is a type of warehouse in supply chain management that allows orders to be prepared with or without going through the phase of storing products in the warehouse and subsequently selecting them for delivery. The goods are unloaded from incoming trucks called origins on inbound doors of a cross-docking facility platform and,...

A cross docking facility is a type of warehouse in supply chain management that allows orders to be prepared with or without going through the phase of storing products in the warehouse and subsequently selecting them for delivery. The goods are unloaded from incoming trucks called origins on inbound doors of a cross-docking facility platform and,...

Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where points do not have numerical coordinates (or categorical coordinates that are translated into numerical form)...

We develop a series of theorems about the graph structure of the classical Minimum Linear Arrangement (MinLA) problem which disclose properties that can be exploited by Multi-Neighborhood Search (MNS) algorithms. As a foundation, we differentiate between swaps of labels attached to adjacent and non-adjacent nodes to create two new neighborhood clas...

This is the latest version of our paper though the type of the file was mislabeled.

The emergence of high-dimensional data requires the design of new optimization methods. Indeed, conventional optimization methods require improvements, hybridization, or parameter tuning in order to operate in spaces of high dimensions. In this paper, we present a new adaptive variant of a pattern search algorithm to solve global optimization probl...

The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class of quantum annealing computer that maps QUBO onto a physical qubit network structure with specific size and ed...

The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving s...

The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving s...

Critical node problems involve identifying a subset of critical nodes from an undirected graph whose removal results in optimizing a pre-defined measure over the residual graph. As useful models for a variety of practical applications, these problems are computational challenging. In this paper, we study the classic critical node problem (CNP) and...

The well-known K-means clustering algorithm has been employed widely in different application domains ranging from data analytics to logistics applications. However, the K-means algorithm can be affected by factors such as the initial choice of centroids and can readily become trapped in a local optimum. In this paper, we propose an improved K-mean...

The well-known K-means clustering algorithm has been employed widely in different application domains ranging from data analytics to logistics applications. However, the K-means algorithm can be affected by factors such as the initial choice of centroids and can readily become trapped in a local optimum. In this paper, we propose an improved K-mean...

We introduce new diversification methods for zero-one optimization that significantly extend strategies previously introduced in the setting of metaheuristic search. Our methods incorporate easily implemented strategies for partitioning assignments of values to variables, accompanied by processes called augmentation and shifting which create greate...

This chapter describes the history of metaheuristics in five distinct periods, starting long before the first use of the term and ending a long time in the future.

We present a new clustering algorithm for handling complexities encountered in modeling hotel ratings data sets and analyze its performance in a clustering case study. In the setting we address, business constraints and coordinates (among other individual attributes of objects) are unknown and only distances between objects are available to the clu...

This paper presents tabu search and memetic search algorithms for solving the minimum differential dispersion problem. The tabu search algorithm employs a neighborhood decomposition candidate list strategy and a rarely used solution-based tabu memory. Unlike the typical attribute-based tabu list, the solution-based tabu strategy leads to a more hig...

In recent years, the general binary quadratic programming (BQP) model has been widely applied to solve a number of combinatorial optimization problems. In this paper, we recast the maximum vertex weight clique problem (MVWCP) into this model which is then solved by a probabilistic tabu search algorithm designed for the BQP. Experimental results on...

Supply chains often experience significant economic losses from disruptions such as facility breakdowns, transportation mishaps, natural calamities, and intentional attacks. To help respond and recover from a disruption, we investigate adjustments in order activity across four echelons including assembly. Simulation experiments reveal that the impa...

Pseudo-Centroid Clustering replaces the traditional concept of a centroid expressed as a center of gravity with the notion of a pseudo-centroid (or a coordinate free centroid) which has the advantage of applying to clustering problems where points do not have numerical coordinates (or categorical coordinates that are translated into numerical form)...