Some computationally relevant group theoretic structures of fixed charge problems

The vehicle routing problem is one of the most studied combinatorial optimization problems in operations research. The problem deals with a homogenous fleet of capacitated vehicles that operates from a central depot serving a set of customers with known demands. The objective of the problem is to design a set of routes serving customers with minimum cost. The vehicle routing problem is classified as NP-hard problem. Exact and approximate algorithms have been developed in the literature to solve the Capacitated Vehicle Routing Problem (CVRP). However, exact methods can only solve relatively small-size problems while approximate algorithms have been able to reach near-optimum solutions of large problems. The purpose of this paper is to develop a new hybrid search algorithm that combines the evolutionary genetic search with a new local search heuristic to solve the CVRP. The proposed heuristic calculates a resultant objective function based on both the distance travelled and the demand associated with the given customer. A new set of genetic operators suited for the problem was employed. Several computational experiments were conducted. The algorithm was validated and was capable of converging to the optimum solution of the tested benchmark instance.KeywordsVehicle routing problemTransportationOptimizationEvolutionary search

Graph theory was founded by Euler [78] in 1736 as a generalization to the solution of the famous problem of the Konisberg bridges. From 1736 to 1936, the same concept as graph, but under different names, was used in various scientific fields as models of real world problems, see the historic book by Biggs, Lloyd and Wilson [19]. This chapter intents to survey the domination problem in graph theory, which is a natural model for many location problems in operations research, from an algorithmic point of view.

A hybrid particle swarm optimization algorithm for the vehicle routing problem

Nowadays, getting substantial results for problems in operations research is crucial. The transportation problem can be solved very effectively with Vogel's Approximation Method (VAM) and discover a workable solution that is closer to the ideal solution. The basic principle of VAM is to allocate as many resources as possible to the cell with the smallest cost in the column or row with the greatest penalty. This cell will receive the maximum number of resources. A problem arises when the magnitudes of the least cost and the next-least cost are identical. Then, we devised a new method called the "New Vogel's Approximation Method (NVAM)" to provide a workable solution to the transportation problem that may then be used to determine the optimal solution. Transporting capacity to the required location is done by three distinct companies. The supply chain's participants seek to move their goods from warehouse to distribution centre, from plant to warehouse, and from distribution centre to retail store. In this study, the VAM method and the NVAM approach are used to determine the optimal transportation cost. These techniques are examined to provide potential supply chain management techniques.

Contributors

A sequential irrigation scheduling problem is the problem of preparing a schedule to sequentially service a set of water users. This problem has an analogy with the classical single machine earliness/tardiness scheduling problem in operations research. In previously published work, integer program and heuristics were used to solve sequential irrigation scheduling problems; however, such scheduling problems belong to a class of combinatorial optimization problems known to be computationally demanding (NP-hard). This is widely reported in operations research. Hence, integer program can only be used to solve relatively small problems usually in a research environment where considerable computational resources and time can be allocated to solve a single schedule. For practical applications, metaheuristics such as genetic algorithms (GA), simulated annealing, or tabu search methods need to be used. These need to be formulated carefully and tested thoroughly. The current research is to explore the potential of GA to solve the sequential irrigation scheduling problems. Four GA models are presented that model four different sequential irrigation scenarios. The GA models are tested extensively for a range of problem sizes, and the solution quality is compared against solutions from integer programs and heuristics. The GA is applied to the practical engineering problem of scheduling water scheduling to 94 water users.

In recent years there has been a growth of interest in the development of systematic search methods for solving problems in operational research and artificial intelligence. This chapter introduces a new idea for the integration of approaches for hard combinatorial optimisation problems. The proposed methodology evaluates objects in a way that combines fuzzy reasoning with a greedy mechanism. In other words, a fuzzy solution space is exploited using greedy methods. This seems to be superior to the standard greedy version. The chapter consists of two main parts. The first part focuses on description of the theory and mathematics of the so-called fuzzy greedy evaluation concept. The second part demonstrates through computational experiments the effectiveness and efficiency of the proposed method for a number of complex problems in engineering management and beyond.

The multidimensional knapsack problem (MKP), which is a generalization of the 0-1 simple Knapsack problem, is one of the classical NP-hard problems in operations research having a number of engineering applications. Several exact as well as heuristic algorithms are available in literature for its solution. In this paper, we propose a new particle swarm optimization (PSO) algorithm namely socio-cognitive particle swarm optimization (SCPSO) for solving the MKP. Comparing with the basic binary particle swarm optimization (BPSO), this improved algorithm introduces the distance between gbest and pbest as a new velocity update equation which maintains the diversity in the swarm and makes it more effective and efficient in solving MKP. We present computational experiments with various data instances for fine tuning of parameters of SCPSO and to validate our ideas and demonstrate the efficiency of the proposed algorithm.

Observational or nonrandomized studies of treatment effects are often constructed with the aid of polynomial-time algorithms that optimally form matched treatment-control pairs or matched sets. Because each observational comparison may potentially be affected by bias, investigators often reinforce a single comparison with an additional comparison that is unlikely to be affected by the same biases, for instance using multiple control groups or evidence factors or control + instrument designs. Use of two comparisons affected by different biases may detect bias if the two comparisons disagree, or may show that two comparisons with different weakness concur in their conclusions. Even this simplest addition—a second comparison—creates design problems without polynomial-time solutions. Faced with a problem that no polynomial-time algorithm can solve, a so-called approximation algorithm is a type of compromise: it provides a solution in polynomial time that is provably not much worse than the unattainable optimal solution. Building upon existing techniques for related problems in operations research, we develop an approximation algorithm for minimum distance matching with near-fine balance for three comparison groups. This algorithm is a practical approach to most observational designs that add a second comparison. The method is applied to an observational study of the effects of side airbags on injury severity in the U.S. Fatality Analysis Reporting System. For many car makes and models, side airbags were initially unavailable, then later available as optional equipment for an additional fee, then still later provided as standard equipment. Within sets matched for make and model of car, for safety belt use, for direction of impact, and other covariates, we compare crashes in these three periods, where each comparison has different limitations. The method is implemented in the R package approxmatch, whose example reproduces some of the calculations. Supplementary materials for this article are available online.

A alocação de recursos é um dos problemas clássicos abordados pela Pesquisa Operacional. A inserção de modelos de Análise de Envoltória de Dados (DEA) nesse contexto traz novas possibilidades de estudo, em especial quando combinada com o uso de algoritmos de programação inteira. Este artigo apresenta um algoritmo para distribuição de recursos discretos usando modelos DEA de forma seqüencial. O método proposto é aplicado no estudo de caso da alocação de vagas docentes na Universidade Federal Fluminense. Os resultados são comparados com aqueles obtidos pela comissão encarregada da distribuição das vagas.

Quantum multi-programming has become a key method for improving qubit utilization and computational throughput on noisy intermediate-scale quantum (NISQ) devices. Due to inherent hardware limitations and quantum noise, only a limited number of available qubits can be effectively used in practical quantum computing scenarios, leading to severe resource waste and task queuing delays.The parallel execution of multiple programs can effectively address this issue. In this paper, we propose abstracting multi-program layout as a combinatorial optimization problem in operations research, and we use a prediction-based algorithm to solve this combinatorial optimization problem.The core idea of the method is as follows: first, the quantum circuit is modeled as a fixed geometric shape, and then a geometry-aware evaluation function is applied for a comprehensive assessment in order to identify placement locations that maximize qubit utilization.Under this evaluation function, we adopt a multi-step lookahead based on breadth-first beam search, which accumulates scores and selects placements by explicitly evaluating feasible placements over a limited number of future steps. This modeling and method can better improve hardware throughput. It provides valuable insight for alleviating the shortage of quantum resources and reducing user waiting time, thereby promoting the practical application of quantum multi-programming.

Multi-stage production planning on the IBM PC — an application

Some Queueing Problems in Operational Research

Biological Applications for Online Methods of Resource Allocation

Computations involving sparse and structured matrices arise frequently in problems in operations research, science and engineering. Exploiting this structure has been a major contributor to the efficient application of past and current computing platforms, and will continue to play an important role for next-generation systems.