Seong In Kim

A genetic algorithm with a mixed region search for the asymmetric traveling salesman problem

Abstract This paper presents a genetic algorithm to solve the asymmetric traveling salesman problem. The genetic algorithm proposed in this study extends search space by purposefully generating and including infeasible solutions in the population. Instead of trying to maintain feasibility with crossover operations, it searches through both feasible and infeasible regions for good quality solutions. It is also shown in the article that the size of the infeasible region defined by solutions with subtours dominates that of a feasible region in the asymmetric traveling salesman problem. A comparative computational study using benchmark problems shows that the proposed genetic algorithm is a viable option for hard asymmetric traveling salesman problems. Scope and purpose The asymmetric traveling salesman problem appears in various applications, such as vehicle routing problems, mixed Chinese postman problems, and scheduling problems with sequence dependent setups. Although there exist several heuristic procedures and branch and bound algorithms for it, the problem is still a difficult combinatorial optimization problem. The main purpose of the paper is to present a new genetic algorithm for the problem and to show its effectiveness. To give a justification for the algorithm, the paper also analyses the sizes of feasible and infeasible regions in the asymmetric traveling salesman problem. This analysis provides a basis for the choice of the solution representation (coding) scheme adopted in the genetic algorithm. The genetic operators that are well suited for this representation scheme are then identified for the problem.

A Branch-and-Cut Algorithm for Solving an Intraring Synchronous Optical Network Design Problem

In this paper, we deal with a network design problem arising from the deployment of synchronous optical networks (SONET), a standard of transmission using optical fiber technology. The problem is to find an optimal clustering of traffic demands in the network such that the total number of node assignments (and, hence, add-drop multiplexer equipment requirements) is minimized, while satisfying the ring capacity and node cardinality constraints. This problem can be conceptualized as an edge-capacitated graph partitioning problem with node cardinality constraints. We formulate the problem as a mixed-integer programming model and develop a new branch-and-cut algorithm along with preprocessing routines for optimally solving the problem. We also prescribe an effective heuristic procedure. Promising computational results are obtained using the proposed method.

A Location-Routing Problem in Designing Optical Internet Access with WDM Systems

In this paper, we deal with a location-routing problem in designing the optical Internet with WDM systems. This problem arises from the design of broadband local access networks that deliver high-speed access service to residential subscribers. The problem is to find an optimal location of the gateway and optimal routing of traffic demands in the optical access network. We develop mixed-integer programming models for solving the location-routing problem to minimize the total cost of network elements used in the network while carrying the offered traffic. By exploiting the inherent structure of the problem, we derive two effective tabu search procedures. We present promising computational results of the proposed solution procedures.

Decomposition based heuristic algorithm for lot-sizing and scheduling problem treating time horizon as a continuum

In this paper, we deal with a new lot-sizing and scheduling problem (LSSP) that minimizes the sum of production cost, setup cost, and inventory cost. Incorporating the constraints of setup carry-over and overlapping as well as demand splitting, we develop a mixed integer programming (MIP) formulation. In the formulation, problem size does not increase as we enhance the precision level of a time period; for example, by dividing a time period into a number of microtime periods. Accordingly, in the proposed model, we treat the time horizon as a continuum not as a collection of discrete time periods. Since the problem is theoretically intractable, we develop a simple but efficient heuristic algorithm by devising a decomposition scheme coupled with a local search procedure. Even if in theory the heuristic may not guarantee finding a feasible solution, computational results demonstrate that the proposed algorithm is a viable choice in practice for finding good quality feasible solutions within acceptable time limit.

An expert system to facilitate the uniform administration of justice in criminal cases

Abstract As an attempt to facilitate uniform sentencing in the criminal justice system of the Korean Judiciary, we have developed an expert system which determines sentences for traffic (vehicular) offenses described in chapter 268 of the Korean Criminal Code. Through interviews and discussions with judges, we have selected the main factors based upon which respective sentence is determined. Next, on that ground we have established key facts of each main factor, and then have embodied the reasoning process in imposing a sentence. In addition to judges, professional knowledge and experience of medical doctors, police officers, and insurance experts are reflected in this system. The expert system developed is a kind of factor comparison model and normative model.

A simple variational problem for a moving vehicle

The problem of determining an optimal path of a moving vehicle, considered in Sherali and Kim (1992), is studied in this paper. We generalize their model by including a general cost structure in the problem and show that a specific, non-trivial cost function in this setting yields an easy solution. This follows from the observation that the variational problem that arises in the model with this particular cost function is the problem of geodesics on the Liouville surface. Through a comparative computational study, we also show that the optimal path for the model with this cost function better approximates the optimal path for the original model in Sherali and Kim than their second-order approximation approach does.

An ATM Switch Capacity Allocation Problem

In this paper, we consider a capacity allocation problem arising in the context of deploying asynchronous transfer mode (ATM) networks. Given types of ATM switches, the problem is to find an optimal allocation of capacity such that the total cost of installed switch modules is minimized, while satisfying all traffic demands. We formulate the problem as an integer programming model, which can be conceptualized as a generalized bin packing problem with capacity constraints. We then develop a surrogate constraint technique of the formulation for enhancing the representation of the model. Guided by the tight lower bound of the surrogate relaxation, we devise an effective tabu search heuristic that provides good quality solutions with guaranteed optimality. We present promising computational results that show the viability of the proposed heuristic and lower bounding methods, and that provide insights into implementation for configuring ATM switch in practice.