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In many statistical learning problems, it is desired that the optimal solution conform to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires nonsmooth penalty functions that exploit group overlapping. Our study focuses on evaluating the proximal operator of the latent overlapping group lasso developed by Jacob et al. in 2009. We implemented an alternating direction method of multiplier with a sharing scheme to solve large-scale instances of the underlying optimization problem efficiently. In the absence of strong convexity, global linear convergence of the algorithm is established using the error bound theory. More specifically, the paper contributes to establishing primal and dual error bounds when the nonsmooth component in the objective function does not have a polyhedral epigraph. We also investigate the effect of the graph structure on the speed of convergence of the algorithm. Detailed numerical simulation studies over different graph structures supporting the proposed algorithm and two applications in learning are provided. Summary of Contribution: The paper proposes a computationally efficient optimization algorithm to evaluate the proximal operator of a nonsmooth hierarchical sparsity-inducing regularizer and establishes its convergence properties. The computationally intensive subproblem of the proposed algorithm can be fully parallelized, which allows solving large-scale instances of the underlying problem. Comprehensive numerical simulation studies benchmarking the proposed algorithm against five other methods on the speed of convergence to optimality are provided. Furthermore, performance of the algorithm is demonstrated on two statistical learning applications related to topic modeling and breast cancer classification. The code along with the simulation studies and benchmarks are available on the corresponding author's GitHub website for evaluation and future use. [ABSTRACT FROM AUTHOR]

Algorithms for approximating the nondominated set of multiobjective optimization problems are reviewed. The approaches are categorized into general methods that are applicable under mild assumptions and, thus, to a wide range of problems, and into algorithms that are specifically tailored to structured problems. All in all, this survey covers 52 articles published within the last 41 years, that is, between 1979 and 2020. Summary of Contribution: In many problems in operations research, several conflicting objective functions have to be optimized simultaneously, and one is interested in finding Pareto optimal solutions. Because of the high complexity of finding Pareto optimal solutions and their usually very large number, however, the exact solution of such multiobjective problems is often very difficult, which motivates the study of approximation algorithms for multiobjective optimization problems. This research area uses techniques and methods from algorithmics and computing in order to efficiently determine approximate solutions to many well-known multiobjective problems from operations research. Even though approximation algorithms for multiobjective optimization problems have been investigated for more than 40 years and more than 50 research articles have been published on this topic, this paper provides the first survey of this important area at the intersection of computing and operations research. [ABSTRACT FROM AUTHOR]

In this paper, we consider the so-called worst-case linear optimization (WCLO) with uncertainties on the right-hand side of the constraints. Such a problem often arises in applications such as in systemic risk estimation in finance and stochastic optimization. We first show that the WCLO problem with the uncertainty set corresponding to the l p-norm ((WCLOp)) is NP-hard for p ɛ (1,∞). Second, we combine several simple optimization techniques, such as the successive convex optimization method, quadratic convex relaxation, initialization, and branch-and-bound (B&B), to develop an algorithm for (WCLO2) that can find a globally optimal solution to (WCLO2) within a prespecified ε-tolerance. We establish the global convergence of the algorithm and estimate its complexity. We also develop a finite B&B algorithm for (WCLO∞) to identify a global optimal solution to the underlying problem, and establish the finite convergence of the algorithm. Numerical experiments are reported to illustrate the effectiveness of our proposed algorithms in finding globally optimal solutions to medium and large-scale WCLO instances. [ABSTRACT FROM AUTHOR]

Unmanned aircraft systems (UASs) are a promising new mode of transportation for cargo delivery. Although control, navigation, and communication technologies are becoming available on individual flight units, system-level motion management for dense UAS traffic remains an open question. This paper presents a motion-planning model based on nonlinear optimization techniques to centrally coordinate paths for all vehicles traversing a shared two-dimensional (2D) space. An exact bound is derived to characterize the discrete-time separation constraints, and a set of new metrics is proposed to measure 2D traffic flow efficiency. The grand goal is to make all vehicles that come under dispatch reach their respective destinations quickly and efficiently while maintaining a safe intervehicle separation at all times. This infinite-horizon operational problem is formulated as a nonlinear nonconvex optimization model that must be solved in a progressive, receding-horizon fashion. To ensure feasibility and overcome path deadlocks attributed to local optima, a series of heuristic measures are developed. By pivoting on artfully coined intermediate feasibility, the algorithm is able to circumvent imminent deadlocks in a predictive manner and progressively construct the solution with guaranteed feasibility. Simulation experiments are performed at various traffic density levels to generate useful insights for airspace regulators and traffic managers. [ABSTRACT FROM AUTHOR]

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of branch-and-cut solvers for mixed-integer linear programs. Given a basis of the linear programming (LP) relaxation and a split disjunction, the corresponding split cut can be computed with a closed-form expression. In this paper, we use the lift-and-project framework introduced by Balas and Perregaard to provide the basis, and the reduce-and-split algorithm as described by Cornuéjols and Nannicini to compute the split disjunction. We propose a cut generation algorithm that starts from a Gomory mixed-integer cut and alternates between lift-and-project and reduce-and-split in order to strengthen it. This paper has two main contributions. First, we extend the Balas and Perregaard procedure for strengthening cuts arising from split disjunctions involving one variable to split disjunctions on multiple variables. Second, we apply the reduce-and-split algorithm to nonoptimal bases of the LP relaxation. We provide detailed computational testing of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper focuses on a generic model for service network design, which includes asset positioning and utilization through constraints on asset availability at terminals. We denote these relations as "design-balance constraints" and focus on the design-balanced capacitated multicommodity network design model, a generalization of the capacitated multicommodity network design model generally used in service network design applications. Both arc- and cycle-based formulations for the new model are presented. The paper also proposes a tabu search metaheuristic framework for the arc-based formulation. Results on a wide range of network design problem instances from the literature indicate the proposed method behaves very well in terms of computational efficiency and solution quality. [ABSTRACT FROM AUTHOR]

We present a new computational approach to the problem of placing n identical nonoverlapping disks in the unit square in such a way that their radii are maximized. The problem has been studied in a large number of papers, from both a theoretical and a computational point of view. In this paper, we conjecture that the problem possesses a so-called funneling landscape, a feature that is commonly found in molecular conformation problems. Based on this conjecture, we develop a stochastic search algorithm that displays excellent numerical performance. Thanks to this algorithm, we could improve over previously known putative optima in the range n ≤ 130 in as many as 32 instances, the smallest of which is n=53. [ABSTRACT FROM AUTHOR]

The introduction of edge-finding techniques was a significant development in constraint-based scheduling. Today, edge finders are still the state of the art in the disjunctive case and a technique of interest in cumulative scheduling. This paper reconsiders edge-finding algorithms for cumulative scheduling and shows that Nuijten's edge finder, and its derivatives, are incomplete because they use an invalid dominance rule. We then present a correct cumulative edge finder running in time O(n²k), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edge-finder specification. The paper also proposes the first extended edge-finding algorithms that run in time O(n²k), improving the running time of available algorithms. Finally, the paper discusses how to speed up the algorithm in practice and how the first phase can be used to improve algorithms based on energetic reasoning. [ABSTRACT FROM AUTHOR]

This paper presents a theory of traffic equilibrium which involves responsive signal control policies; in this theory drivers' route choices and the control policy's choice of green times are treated in a symmetrical manner. The central theme of the paper is the iterative optimization assignment algorithm. This algorithm may be considered as a means of calculating equilibria which are consistent with a given responsive control policy. But it may also be regarded as a highly idealized model of the day to day dynamics of drivers' route choices when a responsive signal setting policy is employed; on "day" 1 the signals are held fixed and drivers settle down to an equilibrium flow pattern, on "day 2" the flow pattern is held fixed and the signals are updated according to the control policy for the fixed flow pattern, on "day" 3 the signals are held fixed and drivers settle down to an equilibrium flow pattern.... We state natural but strong conditions on the responsive control policy which guarantee that this algorithm is bound to converge to a convex set of (flow, control) pairs such that (i) the flow is a user equilibrium and (ii) the control parameters satisfy the responsive control policy; and we give a proof of convergence under these conditions--we do not seek to minimize total travel cost. Our conditions involve the delay or cost formula used; with the BPR cost formula, modified in a natural way to allow for green times, the traditional policy of choosing control parameters which minimize delay for the observed traffic pattern does satisfy these conditions in full. However, with Webster's delay formula traditional control policies are a long way... [ABSTRACT FROM AUTHOR]

For applications of realistic size, both the discrete and continuous versions of the equilibrium network design problem are too computationally intensive to be solved exactly with the algorithms proposed to date. This intractibility owes to Braess' paradox which makes it necessary to constrain the flow pattern to be a noncooperative Nash or user equilibrium. This paper suggests a new heuristic for finding an approximate solution to the continuous equilibrium network design problem. Numerical tests are reported which indicate that, for networks with significant congestion, the heuristic is markedly more efficient than the Hooke-Jeeves algorithm which has been employed previously. The efficiency of the heuristic results from decomposition of the original problem into a set of interacting optimization subproblems. This decomposition is such that, at each iteration of the algorithm, only one user equilibrium needs to be calculated in order to update the improvement variables of all arcs of the network. This contrasts sharply with the Hooke-Jeeves algorithm which can require that a new user equilibrium be calculated each time an individual arc improvement variable is updated. For applications of realistic size, both the discrete and continuous versions of the equilibrium network design problem are too computationally intensive to be solved exactly with the algorithms proposed to date. This intractibility owes to Braess' paradox which makes it necessary to constrain the flow pattern to be a noncooperative Nash or user equilibrium. This paper suggests a new heuristic for finding an approximate solution to the continuous equilibrium network design problem. Numerical tests are reported which indicate that, for networks with significant congestion, the heuristic is markedly more efficient than the Hooke-Jeeves algorithm which has been employed previously. The efficiency of the heuristic results from decomposition of the original problem into a set of interacting optimization subproblems. This decomposition is such that, at each iteration of the algorithm, only one user equilibrium needs to be calculated in order to update the improvement variables of all arcs of the network. This contrasts sharply with the Hooke-Jeeves algorithm which can require that a new user equilibrium be calculated each time an individual arc improvement variable is updated. [ABSTRACT FROM AUTHOR]

Modeling of transportation systems must invariably balance behavioral richness and computational tractability. In this paper, we develop a transportation equilibrium model and an algorithm for the simultaneous prediction of trip generation, trip distribution, modal split, and trip assignment on large-scale networks. The model achieves a practical compromise between behavioral and computational aspects of modeling the problem. It is formulated as an equivalent convex optimization problem, yet it is behaviorally richer than other models that can be cast as equivalent convex programs. Although the model is not as behaviorally rich as the most general equilibrium models, it has computational advantages. The applications reported in this paper of the model to real systems, i.e., the intercity transport network of Egypt and the urban transportation network of Austin, Texas, illustrate the computational attractiveness of the approach. These results indicate that equivalent optimization formulations are not as restrictive as previously thought, and hence, the equivalent convex programming approach for modeling and predicting equilibrium on transportation systems remains a viable and fruitful avenue for future consideration. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of finding the optimal travel path of a single service unit to nonemergency destinations. Such destinations result from events other than service calls, e.g., repositioning or relocation operations, returning from the scene of the service call to the "home location," preventive patrol, etc. The analysis is performed on a network model of the urban environment. The time period of interest begins when the service unit starts its travel to a nonemergency destination and ends when the new call for service arrives. The paper contains two models each of which is suitable for a different application. For the two models two different algorithms are presented; one of which is a dynamic programming. These algorithms take into considerations the probabilistic nature of the demand for service. Illustrative examples are also included. [ABSTRACT FROM AUTHOR]

This study reviews, in two parts, the formulation, interpretation, and solution methodology of the traffic assignment pro blem with elastic demands, originally described by Beckmann, McGuire and Winsten. This paper (Part I) defines the different possible modes of traffic assignment in a network and identifies the economic rationales of the associated extremism formulations. The accompanying paper (Part II) examines algorithmic approaches for calculating the resulting flow patterns. The assignment pro blem is characterized as an interaction between users and operators of the transportation system, analogous to the interaction between consumers and producers in the marketplace. The notions of "user-optimization" and "system-optimization" thus acquire congruent interpretations, expressed by a systemwide maximization objective. [ABSTRACT FROM AUTHOR]

Some existing simulation optimization algorithms (e.g., adaptive random search) become pure random search methods and thus are ineffective for the zero-one optimization via simulation problem. In this paper, we present highly efficient rapid screening procedures for solving the zero-one optimization via simulation problem. Three approaches adopting different sampling rules and providing different statistical guarantees are described. We also propose efficient neighborhood search methods and a simple algorithm for generation of initial solutions, all of which can be incorporated into our rapid screening procedures. The proposed procedures are more adaptive than ordinary ranking and selection procedures because in each iteration they can eliminate inferior solutions and intelligently sample promising solutions from the neighborhood of the survivors. Empirical studies are performed to compare the efficiency of the proposed procedures with other existing ones. [ABSTRACT FROM AUTHOR]

This paper presents a simple branch-and-bound method based on Lagrangean relaxation and subgradient optimization for solving large instances of the capacitated facility location problem (CFLP) to optimality. To guess a primal solution to the Lagrangean dual, we average solutions to the Lagrangean subproblem. Branching decisions are then based on this estimated (fractional) primal solution. Extensive numerical results reveal that the method is much faster and more robust than other state-of-the-art methods for solving the CFLP exactly. [ABSTRACT FROM AUTHOR]

This paper describes a generic branch-and-cut algorithm applicable to the solution of multiobjective optimization problems for which a lower bound can be defined as a polynomially solvable multiobjective problem. The algorithm closely follows standard branch and cut except for the definition of the lower and upper bounds and some optional speed-up mechanisms. It is applied to a routing problem called the multilabel traveling salesman problem, a variant of the traveling salesman problem in which labels are attributed to the edges. The goal is to find a Hamiltonian cycle that minimizes the tour length and the number of labels in the tour. Implementations of the generic multiobjective branch-and-cut algorithm and speed-up mechanisms are described. Computational experiments are conducted, and the method is compared to the classical ∈-constraint method. [ABSTRACT FROM AUTHOR]

In many branch-and-price algorithms, the column generation pricing problem consists of computing feasible paths in a network. In this paper, we show how, in this context, path-reduced costs can be used to remove some arcs from the underlying network without compromising optimality, and we introduce a bidirectional search technique to compute these reduced costs. This arc elimination method can lead to a substantial speedup of the pricing process and the overall branch-and-price algorithm. Special attention is given to variants of shortestpath problems with resource constraints. Computational results obtained for the vehicle routing problem with time windows show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

With improved tools for collecting genetic data from natural and experimental populations, new opportunities arise to study fundamental biological processes, including behavior, mating systems, adaptive trait evolution, and dispersal patterns. Full use of the newly available genetic data often depends upon reconstructing genealogical relationships of individual organisms, such as sibling reconstruction. This paper presents a new optimization framework for sibling reconstruction from single generation microsatellite genetic data. Our framework is based on assumptions of parsimony and combinatorial concepts of Mendel's inheritance rules. Here, we develop a novel optimization model for sibling reconstruction as a large-scale mixed-integer program (MIP), shown to be a generalization of the set covering problem. We propose a new heuristic approach to efficiently solve this large-scale optimization problem. We test our approach on real biological data as presented in other studies as well as simulated data, and compare our results with other state-of-the-art sibling reconstruction methods. The empirical results show that our approaches are very efficient and outperform other methods while providing the most accurate solutions for two benchmark data sets. The results suggest that our framework can be used as an analytical and computational tool for biologists to better study ecological and evolutionary processes involving knowledge of familial relationships in a wide variety of biological systems. [ABSTRACT FROM AUTHOR]

The computation of a sparse Hessian matrix H using automatic differentiation (AD) can be made efficient using the following four-step procedure: (1) Determine the sparsity structure of H, (2) obtain a seed matrix S that defines a column partition of H using a specialized coloring on the adjacency graph of H, (3) compute the compressed Hessian matrix B =HS, and (4) recover the numerical values of the entries of H from B. The coloring variant used in the second step depends on whether the recovery in the fourth step is direct or indirect: a direct method uses star coloring and an indirect method uses acyclic coloring. In an earlier work, we had designed and implemented effective heuristic algorithms for these two NP-hard coloring problems. Recently, we integrated part of the developed software with the AD tool ADOL-C, which has recently acquired a sparsity detection capability. In this paper, we provide a detailed description and analysis of the recovery algorithms and experimentally demonstrate the efficacy of the coloring techniques in the overall process of computing the Hessian of a given function using ADOL-C as an example of an AD tool. We also present new analytical results on star and acyclic coloring of chordal graphs. The experimental results show that sparsity exploitation via coloring yields enormous savings in runtime and makes the computation of Hessians of very large size feasible. The results also show that evaluating a Hessian via an indirect method is often faster than a direct evaluation. This speedup is achieved without compromising numerical accuracy. [ABSTRACT FROM AUTHOR]

Assembly line balancing problems are concerned with the optimization of manufacturing processes. In this paper we consider the so-called simple assembly line balancing problem with the objective of minimizing the number of used workstations. This problem is denoted by SALB-1 in the literature. For tackling this problem, we present a so-called Beam-ACO approach. This technique results from hybridizing the metaheuristic ant colony optimization with beam search. The experimental results show that our algorithm is a state-of-the-art method for this problem. It can solve 263 of 269 existing benchmark instances to optimality. [ABSTRACT FROM AUTHOR]

Given an undirected graph G = (V,E), the vertex coloring problem (VCP) requires to assign a color to each vertex in such a way that colors on adjacent vertices are different and the number of colors used is minimized. In this paper, we propose a metaheuristic approach for VCP that performs two phases: the first phase is based on an evolutionary algorithm, whereas the second one is a postoptimization phase based on the set covering formulation of the problem. Computational results on a set of DIMACS instances show that the overall algorithm is able to produce high-quality solutions in a reasonable amount of time. For four instances, the proposed algorithm is able to improve the best-known solution while for almost all the remaining instances, it finds the best-known solution in the literature. [ABSTRACT FROM AUTHOR]

This paper solves FC_2TDC, the two-staged fixed-orientation two-dimensional cutting stock problem. FC_2TDC is a variant of the constrained two-dimensional cutting problem where each piece is produced, in the final cutting pattern, by at most two cuts, and each piece has a fixed orientation. It is solved by an algorithm that combines a strip-generation procedure with beam search (BS). BS, which is a truncated branch-andbound, investigates a subset of elite nodes and permanently fathoms the others. It chooses the elite nodes based on an evaluation operator. The importance of the evaluation operator on the performance of BS is highlighted by comparing a local beam search (LBS) that uses a priority cost-evaluation operator to a global beam search (GBS) that adopts a global cost-evaluation operator. Computational results, based on several medium and large instances, further show that LBS provides good solutions, whereas GBS gives (near) optimal solutions within reasonable computational time. [ABSTRACT FROM AUTHOR]

Roughly speaking, the no-free-lunch (NFL) theorems state that any blackbox algorithm has the same average performance as random search. These results have largely been ignored by algorithm researchers. This paper looks more closely at the NFL results and focuses on their implications for combinatorial problems typically faced by many researchers and practitioners. We derive necessary conditions for the NFL results to hold based on common problem structures. Often it is simple to verify that these conditions are not present in the class of problems under investigation, thus providing a theoretical basis for ignoring the doleful implications of NFL giving justification for believing there might be a dominant algorithm for the problem class under study. We apply our results to three common classes of problems. We find that only trivial subclasses of these problems fall under the NFL implications. [ABSTRACT FROM AUTHOR]

The need to validate large amounts of data with the help of the domain expert arises naturally in many dataintensive applications, including data mining, data stream, and database-related applications. This paper presents a general validation approach that generalizes different expert-driven validation methods developed for specialized validation problems. In particular, we model the validation process as a sequence of validation operators, explore various properties of such sequences, and present theoretical results that provide for better understanding of the validation process. We also address the problem of selecting the best validation sequence among the class of equivalent sequence permutations. We demonstrate that this optimization problem is NP-hard and present two heuristic algorithms for improving validation sequences. [ABSTRACT FROM AUTHOR]

In the last two decades, a number of algorithms for the linear single-commodity min-cost flow (MCF) problem have been proposed, and several efficient codes are available that implement different variants of the algorithms. The practical significance of the algorithms has been tested by comparing the time required by their implementations for solving "from-scratch" instances of MCF, of different classes, as the size of the problem (number of nodes and arcs) increases. However, in many applications several closely related instances of MCF have to be sequentially solved, so that reoptimization techniques can be used to speed up computations, and the most attractive algorithm is the one that minimizes the total time required to solve all the instances in the sequence. In this paper we compare the performances of four different efficient implementations of algorithms for MCF under cost reoptimization in the context of decomposition algorithms for the multicommodity min-cost flow (MMCF) problem, showing that for some classes of instances the relative performances of the codes doing "from-scratch" optimization do not accurately predict the relative performances when reoptimization is used. Because the best solver depends both on the class and on the size of the instance, this work also shows the usefulness of a standard interface for MCF problem solvers that we have proposed and implemented. [ABSTRACT FROM AUTHOR]

Many transportation applications, including applications in intelligent transportation systems, require the solution of a series of shortest path problems in which only the travel time along a set of arcs of the network change from one problem instance to the next. One could use an existing path algorithm to solve each problem instance independently as it arises. However, significant savings in computation time can often be achieved through the use of a reoptimization algorithm that would begin from the prior solution in determining the updated optimal solution for the given arc travel-time changes. Such quick solution is critical for providing routing instructions to travelers in real time as travel-time information is retrieved from the traffic network. Numerous works have presented reoptimization techniques for use in updating shortest path trees in deterministic and static networks; however, it appears that no reoptimization technique exists in the literature for updating paths where future travel times in time-varying networks change. In this paper, such procedures are proposed. The proposed techniques can provide updated solutions given simultaneous and arbitrary changes (increasing and decreasing in value) in any number of network arcs. Further, this technique can be extended for use in stochastic networks. [ABSTRACT FROM AUTHOR]

Many real-world vehicle routing problems are dynamic optimization problems, with customer requests arriving over time, requiring a repeated reoptimization. In this paper, we consider a dynamic vehicle routing problem where one additional customer arrives at a beforehand unknown location when the vehicles are already under way. Our objective is to maximize the probability that the additional customer can be integrated into one of the otherwise fixed tours without violating time constraints. This is achieved by letting the vehicles wait at suitable locations during their tours, thus influencing the position of the vehicles at the time when the new customer arrives. For the cases of one and two vehicles, we derive theoretical results about the best waiting strategies. The general problem is shown to be NP-complete. Several deterministic waiting strategies and an evolutionary algorithm to optimize the waiting strategy are proposed and compared empirically. I is demonstrated that a proper waiting strategy can significantly increase the probability of being able to service the additional customer, at the same time reducing the average detour to serve that customer. [ABSTRACT FROM AUTHOR]

This paper develops a new optimization-based feature-selection framework for knowledge discovery in databases. Algorithms following this new framework have attractive theoretical properties such as proven convergence to an optimal set of relevant features and the ability for deriving rigorous statements regarding the quality of the set that is found. Within this framework both wrapper and filter algorithms are derived, and numerical experiments show the new methodology to perform well with respect to accuracy and simplicity of the set of features found to be relevant. [ABSTRACT FROM AUTHOR]

This paper introduces and studies an optimization problem related to the alias method for discrete random-variate generation. The alias method is an efficient method to generate random variates from a discrete probability distribution. The efficiency of the alias method can be improved by designing the alias table such that the expected number of computations that must be performed per value generated is minimized. The problem of optimizing the construction of the alias table is proven to be strongly NP-hard, even if either of two variations of the alias method relaxing the alias-table-generation restrictions are used. Integer-programming formulations describing these three optimization problems are presented, and insights regarding necessary optimality criteria and relationships among their optimal solutions are discussed. [ABSTRACT FROM AUTHOR]

The vehicle routing problem with time windows is a hard combinatorial optimization problem that has received considerable attention in the last decades. This paper proposes a two-stage hybrid algorithm for this transportation problem. The algorithm first minimizes the number of vehicles, using simulated annealing. It then minimizes travel cost by using a large neighborhood search that may relocate a large number of customers. Experimental results demonstrate the effectiveness of the algorithm, which has improved 10 (17%) of the 56 best published solutions to the Solomon benchmarks, while matching or improving the best solutions in 46 problems (82%). More important perhaps,the algorithm is shown to be very robust. With a fixed configuration of its parameters, it returns either the best published solutions (or improvements thereof) or solutions very close in quality on all Solomon benchmarks. Very preliminary results on the extended Solomon benchmarks are also given. [ABSTRACT FROM AUTHOR]

This paper develops a method for moving quickly and cheaply from an arbitrary initial point at an extreme distance from the feasible region to a point that is relatively near the feasible region of a nonlinearly constrained model. The method is a variant of a projection algorithm that is shown to be robust, even in the presence of nonconvex constraints and infeasibility. Empirical results are presented. [ABSTRACT FROM AUTHOR]

This paper considers the shortest path problem with waiting costs (SPWC) as an extension to the shortest path problem with time windows. The problem consists of finding the minimum cost path in a network, where cost and time are two independent quantities associated with a path. Path feasibility is constrained by time windows at each node and a linear cost penalty is imposed for each unit of time spent waiting along the path. Starting from a known, nonlinear, integer programming formulation, we propose two alternative formulations for which algorithms already exist. First, we indicate how to transform the SPWC into a shortest path problem with time windows and linear node costs. Second, we prove that the SPWC can also be formulated as a two-resource generalized shortest path problem with resource constraints. Computational results used to compare these alternative formulations are presented. [ABSTRACT FROM AUTHOR]

This paper introduces a strong valid inequality, the 2-path cut, to produce better lower bounds for the vehicle routing problem with time windows. It also develops an effective separation algorithm to find such inequalities. We next incorporate them as needed in the master problem of a Dantzig-Wolfe decomposition approach. In this enhanced optimization algorithm, the coupling constraints require that each customer be serviced. The subproblem is a shortest path problem with time window and capacity constraints. We apply branch and bound to obtain integer solutions. We first branch on the number of vehicles if this is fractional, and then on the flow variables. The algorithm has been implemented and tested on problems of up to 100 customers from the Solomon datasets. It has succeeded in solving to optimality several previously unsolved problems and a new 150-customer problem. In addition, the algorithm proved faster than algorithms previously considered in the literature. These computational results indicate the effectiveness of the valid inequalities we have developed. [ABSTRACT FROM AUTHOR]

Research in optimization has developed faster and faster algorithms that have analyzed very complicated problems, thereby saving billions of dollars. Solving problems using optimization techniques involves more than just developing clever algorithms, however. Building, debugging, validating, and understanding models, algorithms, data, and solutions require appropriate representations of the models, the algorithms, the data, and the solutions. This paper explores current practice and ongoing research in different representations or visualizations useful for representing optimization models, understanding optimization algorithms, validating and exploring optimal solutions, and summarizing the results. [ABSTRACT FROM AUTHOR]

Accompanying the increasing availability of parallel computing technology is a corresponding growth of research into the development, implementation, and testing of parallel algorithms. This paper examines issues involved in reporting on the empirical testing of parallel mathematical programming algorithms, both optimizing and heuristic. We examine the appropriateness of various performance metrics and explore the effects of testing variability, machine influences, testing biases, and the effects of tuning parameters. Some of these difficulties were explored further in a survey sent to leading computational mathematical programming researchers for their reactions and suggestions. A summary of the survey and proposals for conscientious reporting are presented. [ABSTRACT FROM AUTHOR]

Designing the link topology and selecting capacities in a backbone network of a communication system involve complex tradeoffs between investment and operating costs and service considerations such as network reliability and vulnerability, delays, and blocking. Incorporating all these design criteria simultaneously in a comprehensive model results in a large-scale, nonlinear, discrete optimization problem that is intractable. This paper proposes an alternate optimization-based methodology to generate several cost-effective backbone network designs with varying cost and performance characteristics. Network planners can use this method together with detailed performance evaluation techniques to select a design that achieves the proper balance between conflicting objectives. To generate different configurations, the method parametrically varies a set of hop constraints that restrict the number of links over which messages can be transmitted. Reducing the maximum number of hops increases the number of alternate routes but incurs higher total cost for the communication system. For a given set of hop constraints, we develop a Lagrangian-based algorithm to identify a cost-minimizing network design that satisfies all internode traffic requirements. Our extensive computational tests using randomly generated networks demonstrate that, even for relatively large problems, the method identifies good heuristic solutions and fight lower bounds that confirm the near-optimality of the... [ABSTRACT FROM AUTHOR]

This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branch-and-bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such space-complexity issues. The data-driven mechanism at its core more fully exploits pruning rules developed in operations research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomon's well-known test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2. [ABSTRACT FROM AUTHOR]

This paper examines whether there is a substantial additional payoff to be derived from using mathematical optimization techniques to globally define a set of mini-clusters. Specifically, we present a new approximate method to mini-clustering that involves solving a multi-vehicle pick-up and delivery problem with time windows by column generation. To solve this problem we have enhanced an existing optimal algorithm in several ways. First, we present an original network design based on lists of neighboring transportation requests. Second, we have developed a specialized initialization procedure which reduces the processing time by nearly 40%. Third, the algorithm was easily generalized to multi-dimensional capacity. Finally, we have also developed a heuristic to reduce the size of the network, while incurring only small losses in solution quality. This allows the application of our approach to much larger problems. To be able to compare the results of optimization-based and local heuristic mini-clustering, we also present a parallel insertion approach to mini-clustering. Our computational results highlight the success of our approach. On test problems with up to 250 requests, our optimization-based method reduced the travel time within the mini-clusters by an average of 10% over the parallel insertion approach. Furthermore, for an actual problem with 2545 requests, a substantial 5.9% improvement in total traveling time was achieved over the heuristic. [ABSTRACT FROM AUTHOR]

State-of-the-art decision-making models in the area of infrastructure maintenance and rehabilitation (which are based on the Markov Decision Process) do not take into account the uncertainty in the measurement of facility condition. This paper presents a methodology, the Latent Markov Decision Process (LMDP), which explicitly recognizes the presence of random errors in the measurement of the condition of infrastructure facilities. Two versions of the LMDP are presented. In the first version, the inspection schedule is fixed, which is the usual assumption made in state-of-the-art models. The second version of the LMDP minimizes the sum of inspection and M & R costs. An empirical comparison of the two versions of the LMDP and the traditional MDP illustrates the importance of incorporating measurement uncertainty in decision-making and of optimizing the inspection schedule. [ABSTRACT FROM AUTHOR]

This paper is concerned with some variational calculus/optimization problems involving the determination of constrained optimal path functions or routes of a single moving facility, which traverses a region encompassing a set of existing facilities. Situations of this type may involve a reconnaisance plane maintaining a surveillance of certain locations, a patrol car traveling in radio contact with several stations with the possibility of being dispatched to answer service calls originating over several designated regions, or an aircraft determining a flight plan over a region containing enemy missile sites. We formulate the general problem of maximizing total benefits, or maximizing the benefits per unit travel time, subject to constraints on the travel path function. The specific problems analyzed involve a direct distance related benefit (or cost) function, employing rectilinear or squared-Euclidean distance measures, and they constrain the paths to be straight lines between parallel boundaries or across rectangular regions, with both ends free or with one end fixed, or to be general paths between fixed end-points. In each case, the problem is reduced to a finite dimensional optimization problem. Illustrative examples and computational results on a personal computer are provided, and several extensions are proposed for future research. [ABSTRACT FROM AUTHOR]

The paper describes a model for the optimal management of periodic deliveries of a given commodity. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling and routing policies of the vehicles in order to minimize over the planning horizon the maximum number of vehicles simultaneously employed, i.e., the fleet size. Heuristic algorithms are proposed and computational experience is reported. [ABSTRACT FROM AUTHOR]

The equilibrium network design problem can be formulated as a mathematical program with variational inequality constraints. We know this problem is nonconvex; hence, it is difficult to solve for a globally optimal solution. In this paper we propose a simulated annealing algorithm for the equilibrium network design problem. We demonstrate the ability of this algorithm to determine a globally optimal solution for two different networks. One of these describes an actual city in the midwestern United States. [ABSTRACT FROM AUTHOR]

In this paper we develop a new heuristic for the hierarchical network design problem. The heuristic is based upon Lagrangian relaxation of a reformulation of the problem. In addition, we develop a branch and bound algorithm to identify the optimal solution for the 5% of the test problems for which the new heuristic failed to do so. This algorithm proved to be very efficient due to the tight bounds generated by the heuristic. [ABSTRACT FROM AUTHOR]

This paper deals with the location of service facilities on a transportation network where the closest (in distance, time or cost) facility is known not to service some significant portion of demand. The concept of vector assignment of demand nodes to facilities is introduced to account for non closest facility service. A generalized formulation of the p-median problem incorporating vector assignment is presented. It is shown that an optimal solution to this vector assignment p-median problem exists which consists entirely of nodes of the graph; however, there may be more than one facility per node. Three different solution procedures are discussed for the vector assignment p-median problem. Computational experiments for three different moderately sized data sets give encouraging results. A locational example is included which gives a comparison of an optimal p-median solution and an optimal p-median solution with vector assignment. [ABSTRACT FROM AUTHOR]

This paper discusses a model for the problem of locating garages in an urban mass transit system and the associated assignment of vehicles to garages for background and peak services of transit lines. The objective of this model is to minimize the sum of fixed site-related costs, variable vehicle costs, and crew relief costs. The model is solved by an iterative procedure involving a location interchange heuristic and a network flow-based algorithm. The implementation of the model is discussed through its various stages, from data preparation to the final policy recommendations. [ABSTRACT FROM AUTHOR]

This paper examines the problems of routing freight traffic, scheduling train services and allocating classification work between yards on a rail network. It describes a general optimization model which takes into account the interactions between these activities and develops global strategies for their management over a medium term planning horizon. A heuristic algorithm developed to solve this nonlinear, mixed-integer multicommodity flow problem is also presented with some computational results based on an example at the Canadian National Railroads. [ABSTRACT FROM AUTHOR]

In this paper we consider two network optimization problems which have the following characteristics: control parameters vary continuously and network users behave according to War-drop's first principle of traffic equilibrium ("user-optimization"). For each problem, we study an exact algorithm based on constraint accumulation and a heuristic algorithm previously proposed in the literature. [ABSTRACT FROM AUTHOR]

The combined distribution and assignment problem has been studied by many authors. The problems examined have been of different types. Some authors focus their attention on the user optimized combined distribution and assignment problem whereas others study a system optimized version. Apart from this difference there is also a difference in the way the distribution part and the assignment part are incorporated into the models. In this paper we study a combined distribution and assignment problem with entropy objective and cost constraints and give an algorithm based on Benders decomposition for its solution. The resulting solution method will be a "dual" method. [ABSTRACT FROM AUTHOR]

The maximum concurrent flow problem (MCFP) is the optimization version of the feasibility problem in multicommodity flows. The objective is to maximize the percentage of the demands which is realizable for all commodities, subject to the capacity constraints. A fully polynomial epsilon-approximate algorithm was developed by Shahrokhi and Matula to solve the MCFP when the edge capacities are the same (the MCFP with uniform capacity). In this paper, we present an epsilon-approximate algorithm for the MCFP with uniform demand (when all demands are equal). Our epsilon-approximate algorithm employs a linear size reduction from the MCFP with uniform demand to the MCFP with uniform capacity and the fully polynomial epsilon-approximate algorithm for the MCFP with uniform capacity. The computational results indicate that the algorithm is efficient. We also present an efficient combinatorial algorithm for the MCFP in planar graphs. [ABSTRACT FROM AUTHOR]

This paper presents a method for developing efficient timetables for the operation of fixed schedule common-carrier passenger transportation systems. The ability to compute such timetables is needed in the consideration of planning alternatives for future transportation systems and/or the efficient operation of existing systems. Here, time- table optimization is accomplished by maximizing an objective function consisting of three basic components: operating costs, revenues, and traveler benefits. Traveler benefits are computed using a consumer preference model that specifies a traveler's willingness to pay for alternative trips, based on the scheduling of those trips. The optimization is based on successive iterations of a dynamic programming algorithm that develops timetables for each vehicle in the system. Solutions are termed optimal to within a 'first-order passenger exchange! Examples are presented to illustrate the utilization of the methodology for computing information relevant to the development of system operating policies and to the consideration of planning alternatives. [ABSTRACT FROM AUTHOR]