The dynamic programming method in the generalized traveling salesman problem

A procedure of the dynamic programming (DP) for the discrete-continuous problem of a route optimization is considered. It is possible to consider this procedure as a dynamic method of optimization of the towns choice in the well-known traveling salesman problem. In the considered version of DP, elements of a dynamic optimization are used. Two variants of the function of the aggregations of losses are investigated:

• 1.(1) the additive functions;
• 2.(2) the function characterizing the aggregation of losses in the bottle-neck problem.

     

Common knowledge revisited

We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two solutions to this paradox:

• 1.(1) modeling the world with a coarser granularity, and
• 2.(2) relaxing the requirements for coordination.

     

An optimal time to sleep for an auto-sleep system considering multi-usage states

An auto-sleep system is defined by the following two properties:

• 1.(i) a call for the system occurs randomly and intermittently
• 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.

It considers four states:

• 1.(a) sleep
• 2.(b) warm-up
• 3.(c) nonusage
• 4.(d) usage.

For such a system, the time to sleep has been discussed based on suitable criteria. This study extends the model for an auto-sleep system so that the model can deal with multi-usage states. With a view to determining an optimal time to sleep under the extended model, the expected energy consumed per unit time is formulated as a criterion to be minimized. The existence of an optimal time to sleep is examined under a general call distribution. Numerical examples are also provided for a Weibull as well as a log-normal call distribution.     

System dynamics and feedback control problem formulations for real time dynamic traffic routing

This paper formulates the Dynamic Traffic Routing (DTR) problem as a real-time feedback control problem. Three different forms of the formulation are presented:

• 1.(1) distributed parameter system form derived from the conservation law;
• 2.(2) space discretized continuous lumped parameter form;
• 3.(3) space and time discretized lumped parameter form.

These formulations can be considered as the starting points for development of feedback control laws for the different control problems stated in this paper. This paper presents the feedback control problems, and does not discuss in detail the methodology of solution techniques which could be used to solve these problems. However, for the sake of completeness a brief treatment of the three forms are included in this paper to show possible ways to design the controllers.     

Determining the optimal place and capacity of spare parts warehouses in the construction industry

In the construction industry, places, capacities and levels of demand in basic spare parts are changing in relatively short periods of time. This creates an optimization problem of the following form.We are given the following:o

1. (i)The location and the level of demand for each basic spare part in each work site for a specific time period.
2. (ii)The places and the levels of demand can be altered.
3. (iii)There are more than one supplier of each part geografically distributed.
4. (iv)The number of basic equipment spare parts.
5. (v)The transportation cost per load of spare parts.
6. (vi)The purchasing and functioning cost of the various air houses used as warehouses of spare parts.

In this paper we present an algorithm which determines the place, capacity and number of supply points to minimize the total cost of the supply system under the constraints (i) to (vi) above.     

Single machine scheduling with common due date assignment in a group technology environment

We consider a scheduling problem in which n jobs are grouped into F groups and are to be processed on a single machine. A machine setup time is required when the machine switches from one group of jobs to the other. All jobs have a common due date that needs to be determined. The objective is to find an optimal common due date and an optimal sequence of jobs to minimize the sum of the cost of tardy jobs and the cost related to the common due date. We consider two cases:

• 1.(i) the jobs have to be processed in groups; and
• 2.(ii) the jobs do not have to be processed in groups.

Analytical results are presented and computational algorithms are developed.     

A model for an age-structured population with two time scales

In the modelisation of the dynamics of a sole population, an interesting issue is the influence of daily vertical migrations of the larvae on the whole dynamical process. As a first step towards getting some insight on that issue, we propose a model that describes the dynamics of an age-structured population living in an environment divided into N different spatial patches. We distinguish two time scales: at the fast time scale, we have migration dynamics and at the slow time scale, the demographic dynamics. The demographic process is described using the classical McKendrick model for each patch, and a simple matrix model including the transfer rates between patches depicts the migration process. Assuming that the migration process is conservative with respect to the total population and some additional technical assumptions, we proved in a previous work that the semigroup associated to our problem has the property of positive asynchronous exponential growth and that the characteristic elements of that asymptotic behaviour can be approximated by those of a scalar classical McKendrick model. In the present work, we develop the study of the nature of the convergence of the solutions of our problem to the solutions of the associated scalar one when the ratio between the time scales is ε (0 < ε ⪡ 1). The main result decomposes the action of the semigroup associated to our problem into three parts:

• 1.(1) the semigroup associated to a demographic scalar problem times the vector of the equilibrium distribution of the migration process;
• 2.(2) the semigroup associated to the transitory process which leads to the first part; and
• 3.(3) an operator, bounded in norm, of order ε.

     

An Integrated Framework for Generating and Revising Factory Schedules

Practical solutions to the production scheduling problem must provide two broad capabilities:

1. i)
   an ability to efficiently generate schedules that reflect the actual constraints and objectives of the manufacturing environment, and
    
2. ii)
   an ability to incrementally revise these schedules over time in response to unexpected executional circumstances. In this paper, we advocate a common view of predictive and reactive scheduling as an incremental problem solving process that is opportunistically focused by characteristics of the current solution constraints.
    

We describe the architecture of OPIS (opportunistic intelligent scheduler), which defines a general framework for configuring scheduling systems according to this view. We then examine the scheduling knowledge (e.g. analysis and scheduling methods, schedule generation or revision strategies) that is exploited within this architecture by the current OPIS scheduler. Experimental studies with the OPIS scheduler have demonstrated the potential of this constraint-directed scheduling methodology in both predictive and reactive scheduling contexts.     

Solving a vehicle routing problem by balancing the vehicles time utilization

Various vehicle routing problems (VRP) appear in the literature due to their important applications in the area of transportation and distribution.A VRP is characterized by the constraints that the involved factors must satisfy and by an optimality goal.In this paper, we develop a heuristic algorithm that

• (i)partitions suitably a distribution network into subnetworks. A single depot complies with every subnetwork, where a fleet of identical vehicles will start their itinerary. The nodes of the corresponding subnetwork are demand nodes that require a onetime visit by one only vehicle.
• (ii)Determine the routes of k vehicles, k=2,3,…, for every subnetwork so to minimize the visiting time of the corresponding demand nodes. Consequently the method computes the necessary vehicle number for each subnetwork so as to complete promptly the visiting requirement of all the demand nodes of the whole network. The main strategy of the algorithm for designing the vehicle routes consists of balancing the time utilization of the used vehicles. The paper is integrated by an application of the presented algorithm to the center of the city of Thessaloniki.

     

A dynamic network loading model for mesosimulation in transportation systems

Flow propagation models can be divided into static and dynamic network loading models. Different approaches to dynamic network loading problem formulated in the literature point out models that can be classified as disaggregate or aggregate.Applying aggregate models, it is possible to trace implicitly or explicitly vehicles movements. The second case concerns mesoscopic models. These models consider the traffic as a sequence of “packets” of vehicles. Two approaches can be followed:

• (a)continuous packets, where vehicles are distributed inside each packet, defined by the head and the tail points;
• (b)discrete packets, where all users belonging to a packet are grouped and represented by a single point, for instance the head.

In this paper, a mesoscopic model based on discrete packets has been developed, taking into account the vehicles acceleration. The proposed model, assuming discrete packets and uniformly accelerated movement, appears lifelike in the representation of outflow dynamics and quite easy to calculate.     

Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)

This paper is devoted to the characterization of external electrostatic potentials for which the Vlasov-Poisson-Fokker-Planck system satisfies one of the following properties:

• (i) the system admits stationary solutions,
• (ii) any solution to the evolution problem converges to a stationary solution, or, equivalently, no mass vanishes for large times,
• (iii) the free energy is bounded from below, We give conditions under which these different notions of confinement are equivalent.

     

Warranty cost analysis for second-hand products

For second-hand products sold with warranty, the expected warranty cost for an item to the manufacturer, depends on

• 1.(i) the age and/or usage as well as the maintenance history for the item
• 2.(ii) the terms of the warranty policy.

The paper develops probabilistic models to compute the expected warranty cost to the manufacturer when the items are sold with free replacement or pro rata warranties.     

Analysis of performance of an iron-bath reactor using computational fluid dynamics

The performance of an iron-bath reactor has been studied using a comprehensive numerical model that combines a computational fluid dynamics approach for the gas phase and a heat and mass balance model for the bath. The model calculates:

• •coal, ore, flux and oxygen consumption;
• •post-combustion ratio (PCR);
• •heat-transfer efficiency (HTE);
• •off-gas temperature and composition;
• •heat transfer and chemical reactions between gas and iron and slag droplets; and
• •heat transfer between gas and bath, refractories and lance.

The model was validated with data reported by the Nippon Steel Corporation for a 100 t pilot plant, and the calculated and measured data are in good agreement. Modelling results showed that the dominant mechanisms of heat transfer from the gas to the bath are radiation to the slag surface and convection heat transfer to droplets.     

An Algorithm for the Vehicle-dispatching Problem

The vehicle-scheduling problem involves the design of several vehicle tours to meet a given set of requirements for customers with known locations, subject to a capacity constraint for the vehicles and a distance (or time) constraint for vehicle tours. Three methods of solution are considered in this paper:

1. a
   A branch-and-bound approach.
    
2. b
   The "savings" approach.
    
3. c
   The 3-optimal tour method.
    

The excessive computation time and computer storage required for the first method renders it impracticable for large problems. Ten problems are examined and the results suggest that method C is superior to the other two methods.     

Dynamic graph models

Research in graph theory has focused on studying the structure of graphs with the assumption that they are static. However, in many applications, the graphs that arise change with time, i.e., they are dynamic in nature. This is especially true of applications involving graph models in computer science. We present an expository study of dynamic graphs with the main driving force being practical applications. We first develop a formal classification of dynamic graphs. This taxonomy in the form of generalizations and extensions will in turn suggest new areas of application. Next, we discuss areas where dynamic graphs arise in computer science such as compilers, databases, fault-tolerance, artificial intelligence, and computer networks. Finally, we propose approaches that can be used for studying dynamic graphs. The main objective in any study of dynamic graphs should be to

• 1.(i) extend results developed for static graph theory to dynamic graphs,
• 2.(ii) study the properties that describe how a dynamic graph changes,
• 3.(iii) investigate problems and issues in dynamic graph theory that are raised by practical applications of dynamic graphs in computer science.

     

On the computational complexity of the theory of Abelian groups

We develop a series of Ehrenfeucht games and prove the following results:

• 1.(i) The first order theory of the divisible and indecomposable p-group, the first order theory of the group of rational numbers with denominators prime to p and the first order theory of a cyclic group of prime power order can be decided in 2^{2cn log n} Turing time.
• 2.(ii) The first order theory of the direct sum of countably many infinite cyclic groups, the first order theory of finite Abelian groups and the first order theory of all Abelian groups can be decided in 2^2dn Turing space.

     

Mathematical modelling of the flotation deinking process

The overall flotation deinking process can be divided into four basic microprocesses:

• 1.(1) collision or capture of an (ink) particle by an air bubble
• 2.(2) adhesion of an (ink) particle to the air bubble by sliding
• 3.(3) development of a three-phase contact at the air bubble/water/particle interface, and
• 4.(4) bubble/particle stability or instability after an aggregate is formed each of these microprocesses have an associated probability that they will occur successfully in a flotation cell.

In this paper, the associated probabilities of each microprocess are employed in the development of a kinetic- or population balance-type model of the overall flotation process. The overall model contains two kinetic constants: the first, k₁ governs the overall probability of a free ink particle successfully intercepting and adhering to an air bubble; the second, k₂ is a measure of the probability that a bubble/particle aggregate pair will become unstable and split to yield a “new” free ink particle.The solution to the kinetic model is presented in terms of k₁ and k₂, which are themselves functions of system parameters such as bubble and particle physical properties (e.g., diameter, density), fluid properties (e.g., viscosity, surface tension), etc. From this solution, a definition of a theoretical flotation efficiency, as well as other system performance parameters are presented.