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 solutions with no guarantee of optimality. Exact methods (like Gurobi) and metaheuristic solvers have greatly improved in recent years, enabling high-quality and often optimal solutions to be found to a growing set of MSCPs. Alternative model forms can have a significant impact on the success of exact and heuristic methods in such settings, often providing enhanced performance compared with traditional model forms. In this paper, we introduce several alternative models for MSCP, including the quadratic unconstrained binary problem plus (QUBO-Plus) model for solving problems with constraints that are not folded into the objective function of the basic quadratic unconstrained binary problem (QUBO) model. We provide a computational study using a standard set of test problems from the literature that compares the general purpose exact solver from Gurobi with the leading QUBO metaheuristic solver NGQ and a special solver called Q-Card that belongs to the QUBO-Plus class. Our results highlight the effectiveness of the QUBO and QUBO-Plus models when solved with these metaheuristic solvers on this test bed, showing that the QUBO-Plus solver Q-Card provides the best performance for finding high-quality solutions to these important problems. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0334 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0334 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In the last years, many areas in science, business, and engineering have experienced an enormous growth in the amount of data that they are required to analyze. In many cases, this analysis relies intimately on data visualization and, as a result, graph drawing has emerged as a new field of research. This paper addresses the challenge of drawing hierarchical graphs, which is one of the most widely used drawing standards. We introduce a new mathematical model to automatically represent a graph based on the alignment of long arcs, which we combine with the classic arc crossing minimization objective in hierarchical drawings. We complement our proposal with a heuristic algorithm that can obtain high-quality results in the short computational time required by graph drawing systems. Our algorithm joins two methodologies, tabu search and strategic oscillation (SOS), to perform a fast and effective exploration of the search space. We conduct extensive experimentation that integrates our new mathematical programming formulation and the SOS tabu search that targets large instances. Our statistical analysis confirms the effectiveness of this proposal.

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 emission monitoring, network security, and drug design. To solve the problem, we present a “reduce-solve-combine” memetic search approach that integrates a problem reduction mechanism into the popular population-based memetic algorithm framework. At each generation, a common pattern mined from two parent solutions is first used to reduce the given problem instance, then the reduced instance is solved by a component-based hybrid neighborhood search that effectively combines an articulation point impact strategy and a node weighting strategy, and finally an offspring solution is produced by combining the mined common pattern and the solution of the reduced instance. Extensive evaluations on 42 real-world and synthetic benchmark instances show the efficacy of the proposed method, which discovers nine new upper bounds and significantly outperforms the current state-of-the-art algorithms. Investigation of key algorithmic modules additionally discloses the importance of the proposed ideas and strategies. Finally, we demonstrate the generality of the proposed method via its adaptation to solve the node-weighted critical node problem. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72371157, 61903144, 72031007]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0130 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0130 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

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 unconstrained optimization subproblems with fixed containers. The proposed algorithm relies on a two-phase search strategy that combines a thresholding search method reinforced by two general-purpose perturbation operators and a container adjustment method. The performance of the algorithm is assessed relative to a large number of benchmark instances widely studied in the literature. Computational results show a high performance of the algorithm on both problems compared with the state-of-the-art results. For circle packing, the algorithm improves 156 best-known results (new upper bounds) in the range of [Formula: see text] and matches 242 other best-known results. For sphere packing, the algorithm improves 66 best-known results in the range of [Formula: see text], whereas matching the best-known results for 124 other instances. Experimental analyses are conducted to shed light on the main search ingredients of the proposed algorithm consisting of the two-phase search strategy, the mixed perturbation and the parameters. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 61703213 and 61933005]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1290 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0004 ) at ( http://dx.doi.org/10.5281/zenodo.7579558 ).

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 MCDS problem, which integrates several distinguishing features, such as a vertex weighting-based local search with tabu and perturbation strategies to help the search to jump out of the local optima, as well as a search space reduction strategy to improve the search efficiency. Computational experiments on four sets of 112 commonly used public benchmark instances, as well as 15 newly introduced sparse instances, show that FVW is highly competitive compared with the state-of-the-art algorithms in the literature despite its simplicity. FVW improves the previous best-known results for 20 large public benchmark instances while matching the best-known results for all but 2 of the remaining ones. Several ingredients of FVW are investigated to demonstrate the importance of the proposed ideas and techniques. Summary of Contribution: As a challenging classical NP-hard problem, the minimum connected dominating set (MCDS) problem has been studied for decades in the areas of both operations research and computer science, although there does not exist an exact polynomial algorithm for solving it. Thus, the new breakthrough on this classical NP-hard problem in terms of the computational results on classical benchmark instances is significant. This paper presents a new fast vertex weighting local search for solving the MCDS problem. Computational experiments on four sets of 112 commonly used public benchmark instances show that fast vertex weighting (FVW) is able to improve the previous best-known results for 20 large instances while matching the best-known results for all but 2 of the remaining instances. Several ingredients of FVW are also investigated to demonstrate the importance of the proposed ideas and techniques.

Abstract 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 performed with a primal network flow algorithm operating on the parametric GI. Computational testing is carried out on well‐known problems from the literature plus a new set of large‐scale fixed‐charge transportation and transshipment network instances. We also provide comparisons against CPLEX 12.8 and demonstrate that the new GI algorithm with tabu search (TS) is effective on large problem instances, finding solutions with statistically equivalent objective values at least 700 times faster. The attractive outcomes produced by the current GI/TS implementation provide a significant advance in our ability to solve fixed‐cost network problems efficiently and invites its use for larger instances from a variety of application domains.

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, and maximum cut problems on bipartite graphs. This paper introduces three main algorithms for solving the BBQP, based on three variants of tabu search, the first two consisting of strategic oscillation–tabu search (SO-TS) algorithms, which use destructive and constructive procedures to guide the search into unexplored and promising areas. The third algorithm, whichDoes also incorporates the SO-TS algorithms as solution improvement methods, uses a path relinking (PR) algorithm that is capable of further enhancing search performance. Experimental results demonstrate that all three algorithms perform very effectively compared with the best methods in the literature, and the PR algorithm joined with tabu search is able to discover new best solutions for two-thirds of the large problem instances and match the previous best known solutions for the other instances. Additional analysis discloses the contributions of the key ingredients of each of the proposed algorithms.

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 problem (FJSP). To ensure the diversity and the quality of the evolution, MAE integrates a tabu search procedure, a recombination operator based on path relinking using a novel distance definition, and an effective individual updating strategy, taking into account the multiple complex constraints of FJSP. Experiments on 313 widely-used public instances show that MAE improves the previous best known results for 47 instances and matches the best known results on all except 3 of the remaining instances while consuming the same computational time as current state-of-the-art metaheuristics. MAE additionally establishes solution quality records for 10 hard instances whose previous best values were established by a well-known industrial solver and a state-of-the-art exact method.

Critical node problems (CNPs) involve finding a set of critical nodes from a graph whose removal results in optimizing a predefined measure over the residual graph. As useful models for a variety of practical applications, these problems are computationally challenging. In this paper, we study the classic CNP and introduce an effective memetic algorithm for solving CNP. The proposed algorithm combines a double backbone-based crossover operator (to generate promising offspring solutions), a component-based neighborhood search procedure (to find high-quality local optima), and a rank-based pool updating strategy (to guarantee a healthy population). Extensive evaluations on 42 synthetic and real-world benchmark instances show that the proposed algorithm discovers 24 new upper bounds and matches 15 previous best-known bounds. We also demonstrate the relevance of our algorithm for effectively solving a variant of the classic CNP, called the cardinality-constrained CNP. Finally, we investigate the usefulness of each key algorithmic component.

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 that underlying the most general assignment‐based neighborhoods proposed in the past, giving rise to new tour constructions that encompass and go beyond previous proposals. The resulting neighborhoods provide greater flexibility for generating new tours while simultaneously accounting for sparse traveling salesman graphs that were previously omitted from consideration. Finally, our approaches are applicable for improving the solution of some versions of the vehicle routing problem.

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 edge density restrictions is generating a growing interest in ways to transform the underlying QUBO structure into an equivalent graph having fewer nodes and edges. In this article, we present rules for reducing the size of the QUBO matrix by identifying variables whose value at optimality can be predetermined. We verify that the reductions improve both solution quality and time to solution and, in the case of metaheuristic methods where optimal solutions cannot be guaranteed, the quality of solutions obtained within reasonable time limits. We discuss the general QUBO structural characteristics that can take advantage of these reduction techniques and perform careful experimental design and analysis to identify and quantify the specific characteristics most affecting reduction. The rules make it possible to dramatically improve solution times on a new set of problems using both the exact Cplex solver and a tabu search metaheuristic. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(2), 79–97 2017

Ejection chain methods, which include the classical Lin–Kernighan (LK) procedure and the Stem‐and‐Cycle (S&C) reference structure, have been the source of the currently leading algorithms for large scale symmetric traveling salesman problems (STSP). Although these methods proved highly effective in generating large neighborhoods for symmetric instances, their potential application to the asymmetric setting of the problem (ATSP) introduces new challenges that require special consideration. This article extends our studies on the single‐rooted S&C to examine the more advanced doubly‐rooted (DR) reference structure. The DR structure, which is allied both to metaheuristics and network optimization, allows more complex network‐related (alternating) paths to transition from one tour to another, and offers special advantages for the ATSP. Computational experiments on an extensive testbed exhibits superior performance for the DR neighborhood over its LK counterpart for the ATSP. We additionally show that a straightforward implementation of a DR ejection chain algorithm outperforms the best local search algorithms and obtains solutions comparable to those obtained by the currently most advanced special‐purpose algorithms for the ATSP, while requiring dramatically reduced computation time. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(1), 23–33 2016

Abstract In this study, we present a new tabu search algorithm for the quadratic assignment problem (QAP) that utilizes an embedded neighborhood construction called an ejection chain. Our ejection chain approach provides a combinatorial leverage effect, where the size of the neighborhood grows multiplicatively while the effort of finding a best move in the neighborhood grows only additively. Our results illustrate that significant improvement in solution quality is obtained in comparison to the traditional swap neighborhood. We also develop two multistart tabu search algorithms utilizing the ejection chain approach in order to demonstrate the power of embedding this neighborhood construction within a more sophisticated heuristic framework. Comparisons to the best large neighborhood approaches from the literature are presented. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010

In this paper we consider the problem of finding a global optimum of an unconstrained multimodal function within the framework of adaptive memory programming, focusing on an integration of the Scatter Search and Tabu Search methodologies. Computational comparisons are performed on a test-bed of 11 types of problems. For each type, four problems are considered, each one with dimension 50, 100, 200 and 500 respectively; thus totalling 44 instances. Our results show that the Scatter Tabu Search procedure is competitive with the state-of-the-art methods in terms of the average optimality gap achieved.

This paper presents a performance study of two versions of a unidimensional search algorithm aimed at solving high-dimensional optimization problems. The algorithms were tested on 11 scalable benchmark problems. The aim is to observe how metaheuristics for continuous optimization problems respond with increasing dimension. To this end, we report the algorithms' performance on the 50, 100, 200 and 500-dimension versions of each function. Computational results are given along with convergence graphs to provide comparisons with other algorithms during the conference and afterwards.

The quadratic assignment problem (QAP) is a well-known combinatorial optimization problem with a wide variety of applications, prominently including the facility location problem. The acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this paper, we show the benefit of utilizing strategic diversification within the tabu search (TS) framework for the QAP, by incorporating several diversification and multistart TS variants. Computational results for an extensive and challenging set of QAP benchmark test problems demonstrate the ability of our TS variants to improve on a classic TS approach that is one of the principal and most extensively used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate the classic TS method as a subroutine.

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 factor model of PSO. Applied to finding global minima for continuous nonlinear functions, Scatter PSO not only is able to obtain better solutions to a widely used set of benchmark functions, but also proves more robust under a variety of experimental conditions.

The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for any gradient-based local solver for nonlinear programming (NLP) problems. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to Floudas et al. (1999), most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.

In this paper, a tabu-search algorithm enhanced by scatter search is presented. The algorithm solves the DNA sequencing problem with negative and positive errors, yielding outcomes of high quality. We compare the new method with two other metaheuristic approaches: a previous tabu-search method and a hybrid genetic algorithm, and also with an old branch-and-bound approach.

We propose a tabu search algorithm for the generalized assignment problem, which is one of the representative combinatorial optimization problems known to be NP-hard. The algorithm features an ejection chain approach, which is embedded in a neighborhood construction to create more complex and powerful moves. We also incorporate an adaptive mechanism for adjusting search parameters, to maintain a balance between visits to feasible and infeasible regions. Computational results on benchmark instances of small sizes show that the method obtains solutions that are optimal or that deviate by at most 0.16% from the best known solutions. Comparisons with other approaches from the literature show that, for instances of larger sizes, our method obtains the best solutions among all heuristics tested.

The objectives in this paper are twofold: design an approach for the netlist partitioning problem using the cooperative multilevel search paradigm introduced by Toulouse et al. and study the effectiveness of this paradigm for solving combinatorial optimization problems, in particular, those arising in the very large scale integration (VLSI) computer-aided design (CAD) area. The authors present a cooperative multilevel search algorithm CoMHP and describe a parallel implementation on the SGI O2000 system. Experiments on ISPD98 benchmark suite of circuits show, for four-way and eight-way partitioning, a reduction of 3% to 15% in the size of hyperedge cuts compared to those obtained by hMETIS. Bisections of hypergraphs based on the algorithm also outperform hMETIS, although more modestly. The authors present experimental results to demonstrate that the cooperation scheme plays a key role in the performance of CoMHP. In fact, the improvement in the quality of the solutions produced by CoMHP is to a large extent independent of the partitioners used in the implementation of CoMHP. The experimental results also demonstrate the effectiveness of the cooperative multilevel search paradigm for solving the netlist partitioning problem.

Article Free Access Share on Multilevel cooperative search: application to the circuit/hypergraph partitioning problem Authors: Min Ouyang U. Nebraska-Lincoln Dept CS&E U. Nebraska-Lincoln Dept CS&EView Profile , Michel Toulouse U. Manitabo Dept CS U. Manitabo Dept CSView Profile , Krishnaiyan Thulasiraman U. Oklahoma School of CS U. Oklahoma School of CSView Profile , Fred Glover U. Colorado Graduate School of Business U. Colorado Graduate School of BusinessView Profile , Jitender S. Deogun U. Nebraska-Lincoln Dept CS&E U. Nebraska-Lincoln Dept CS&EView Profile Authors Info & Claims ISPD '00: Proceedings of the 2000 international symposium on Physical designMay 2000 Pages 192–198https://doi.org/10.1145/332357.332399Online:01 May 2000Publication History 6citation255DownloadsMetricsTotal Citations6Total Downloads255Last 12 Months4Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Multistart constructive approaches operate by applying a local search procedure to start from different initial solutions produced by a repeated (variable) constructive process. The classical Random Restart procedure and the more recent GRASP procedure are prominent examples of such approaches. Adaptive memory strategies that are the heart of tabu search methods give a foundation for alternative, enhanced, multistart approaches. We demonstrate this by showing that a simple implementation of adaptive memory search principles, even when restricted to the constructive phases, can provide more effective multistart methods. Computational experiments for the quadratic assignment problem disclose that these methods improve significantly over previous multistart methods that do not incorporate such memory based strategies.

We present a new and highly efficient algorithm for the integer knapsack problem based on a special strategy for aggregating integer-valued equations. Employing a new theorem for creating a single equation with the same nonnegative integer solution set as a system of original equations, we transform the integer knapsack problem into an equivalent problem of determining the consistency of an aggregated equation for a parameterized right hand side. This last problem is solved by a newly developed algorithm with complexity O(min(n α1, n + α12)), where n is the number of variables and α1 is the smallest coefficient in the aggregated equation. Empirical outcomes show our procedure is significantly superior to advanced branch-and-bound methods (previously established to be the most efficient knapsack solution procedures), obtaining solutions several orders of magnitude faster for hard problems.

There is an appeal to methods like simulated annealing and threshold acceptance that operate by imposing a monotonically declining ceiling on objective function levels or degrees of disimprovement (treated probabilistically or deterministically). An alternative framework, embodied in tabu search, instead advocates a nonmonotonic form of control, keyed not only to the objective function but to other elements such as values of variables, direction of search, and levels of feasibility and infeasibility. This creates a more flexible search behavior and joins naturally with the use of memory-based strategies that are the hallmark of tabu search approaches. Embodied particularly in the strategic oscillation component of tabu search, this nonmonotonic control has been shown in a variety of studies to yield outcomes superior to those of simulated annealing and threshold acceptance. The question arises whether such an approach offers a sufficiently rich source of search trajectories to be relied upon as a primary guidance mechanism, with greatly reduced reliance on forms of memory customarily used in tabu search. To provide an easily implemented method of this type we propose a tabu thresholding approach, which joins prescriptions of strategic oscillation with a candidate list procedure derived from network optimization studies. The candidate list and tabu search philosophies are mutually reinforcing, and the computational advantages contributed by these elements, documented by studies cited in this paper, motivate a closer look at combining them. The result yields a method with a significant potential for variation and an ability to take advantage of special structure. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

This is the second half of a two part series devoted to the tabu search metastrategy for optimization problems. Part I introduced the fundamental ideas of tabu search as an approach for guiding other heuristics to overcome the limitations of local optimality, both in a deterministic and a probabilistic framework. Part I also reported successful applications from a wide range of settings, in which tabu search frequently made it possible to obtain higher quality solutions than previously obtained with competing strategies, generally with less computational effort. Part II, in this issue, examines refinements and more advanced aspects of tabu search. Following a brief review of notation, Part II introduces new dynamic strategies for managing tabu lists, allowing fuller exploitation of underlying evaluation functions. In turn, the elements of staged search and structured move sets are characterized, which bear on the issue of finiteness. Three ways of applying tabu search to the solution of integer programming problems are then described, providing connections also to certain nonlinear programming applications. Finally, the paper concludes with a brief survey of new applications of tabu search that have occurred since the developments reported in Part I. Together with additional comparisons with other methods on a wide body of problems, these include results of parallel processing implementations and the use of tabu search in settings ranging from telecommunications to neural networks. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range of problems for which it is best suited. This paper undertakes to present the major ideas and findings to date, and to indicate challenges for future research. Part I of this study indicates the basic principles, ranging from the short-term memory process at the core of the search to the intermediate and long term memory processes for intensifying and diversifying the search. Included are illustrative data structures for implementing the tabu conditions (and associated aspiration criteria) that underlie these processes. Part I concludes with a discussion of probabilistic tabu search and a summary of computational experience for a variety of applications. Part II of this study (to appear in a subsequent issue) examines more advanced considerations, applying the basic ideas to special settings and outlining a dynamic move structure to insure finiteness. Part II also describes tabu search methods for solving mixed integer programming problems and gives a brief summary of additional practical experience, including the use of tabu search to guide other types of processes, such as those of neural networks. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Abstract Shortest and/or longest path analysis is a major analytical component of quantitative models used by transportation planners. The importance of shortest path analysis in all phases of transportation planning has given rise to intensive research and software development over the last three decades for solving shortest path problems. This paper presents a new hybrid solution algorithm called THRESH, which integrates the features of label setting and label correcting algorithms, yet appears to have performance characteristics that transcend both. Preliminary computational results indicate that it is substantially more efficient than the methods determined to be best by previous studies.

Abstract This paper examines different algorithms for calculating the shortest path from one node to all other nodes in a network. More specifically, we seek to advance the state‐of‐the‐art of computer implementation technology for such algorithms and the problems they solve by exmining the effect of innovative computer science list structures and labeling techniques on algorithmic performance. The study shows that the procedures examined indeed exert a powerful influence on solution efficiency, with the identity of the best dependent upon the topology of the network and the range of the arc distance coefficients. The study further discloses, for the problems tested, that the lable‐setting shortest path algorithm previously documented as the most efficient is dominated for all problem structures examined by the new methods.

Networks and network related problems occur with remarkable frequency in practical mathematical programming applications. This paper presents a variety of applications from industry and government that illustrate the scope and usefulness of network related formulations. In addition, recent breakthroughs in specialized methods and mathematical programming software systems that are capable of solving in only a few minutes problems that require many hours of computing time with commercial LP packages are reported. Finally, the latest developments in large scale applications are reported. These developments have made it possible to solve a manpower planning problem involving 450,000 variables in 26 minutes of central processing time on the IBM 360-65. Key Words and Phrases: network applications, transshipment algorithms, machine independent software, computational testing, network problem formulations, fixed charge mathematical programming CR Categorms: 3.25, 3.57, 5.25, 5.32 ~ 5.41

Abstract This paper presents extensive computational experience with a special purpose primal simplex algorithm. The performance is compared to that of several “state of the art” out‐of‐kilter computer codes. The computational characteristics of several different primal feasible start procedures and pivot selection strategies are also examined. The study discloses the advantages, in both computation time and memory requirements, of the primal approach over the out‐of‐kilter method. The test environment has the following distinguishing properties: (1) all of the codes are tested on the same machine and the same problems, (2) the test set includes capacitated and uncapacitated transhipment networks, transportation problems, and assignment problems, and (3) problem sizes ranging from 200 to 8,000 nodes with up to 35,000 arcs are examined.