PURPOSES : This study aims to develop an algorithm to solve the user equilibrium traffic assignment problem using soft link capacity constraints. This model is used to relax the hard capacity constraints model. METHODS : In the traffic assignment model that imposes the hard capacity constraints, the well-known solution algorithms used are the augmented Lagrange multiplier method and the inner penalty function method. The major drawback of using the hard-capacity constraint model is the feasible solution issue. If the capacities in the network are not sufficient to absorb the flow from the diverged flows through the hard capacity constraints, it might result in no solution; whereas, using a soft capacity constraint model guarantees a feasible solution because the soft capacity constraint model uses the penalization of constraint violation in the objective function. In this study, the gradient projection (GP) algorithm was adapted. RESULTS : Two numerical experiments were conducted to demonstrate the features of the soft capacity constraint model and the computational performance of the solution algorithm. The results revealed that imposing the soft link capacity constraints can ensure convergence. CONCLUSIONS : The proposed model can be easily extended by considering other traffic assignment models, for e.g., non-additive traffic equilibrium problem, stochastic traffic equilibrium model, and, elastic demand traffic equilibrium problem. Furthermore, the model can exist regardless of the sufficient capacity for each O-D pair to cater to their demands.

We focus on the weapon target assignment and fire scheduling problem (WTAFSP) with the objective of minimizing the makespan, i.e., the latest completion time of a given set of firing operations. In this study, we assume that there are m available weapons to fire at n targets (> m). The artillery attack operation consists of two steps of sequential procedure : assignment of weapons to the targets; and scheduling firing operations against the targets that are assigned to each weapon. This problem is a combination of weapon target assignment problem (WTAP) and fire scheduling problem (FSP). To solve this problem, we define the problem with a mixed integer programming model. Then, we develop exact algorithms based on a dynamic programming technique. Also, we suggest how to find lower bounds and upper bounds to a given problem. To evaluate the performance of developed exact algorithms, computational experiments are performed on randomly generated problems. From the results, we can see suggested exact algorithm solves problems of a medium size within a reasonable amount of computation time. Also, the results show that the computation time required for suggested exact algorithm can be seen to increase rapidly as the problem size grows. We report the result with analysis and give directions for future research for this study. This study is meaningful in that it suggests an exact algorithm for a more realistic problem than existing researches. Also, this study can provide a basis for developing algorithms that can solve larger size problems.

Quantum-inspired Genetic Algorithm (QGA) is a probabilistic search optimization method combined quantum computation and genetic algorithm. In QGA, the chromosomes are encoded by qubits and are updated by quantum rotation gates, which can achieve a genetic search. Asset-based weapon target assignment (WTA) problem can be described as an optimization problem in which the defenders assign the weapons to hostile targets in order to maximize the value of a group of surviving assets threatened by the targets. It has already been proven that the WTA problem is NP-complete. In this study, we propose a QGA and a hybrid-QGA to solve an asset-based WTA problem. In the proposed QGA, a set of probabilistic superposition of qubits are coded and collapsed into a target number. Q-gate updating strategy is also used for search guidance. The hybrid-QGA is generated by incorporating both the random search capability of QGA and the evolution capability of genetic algorithm (GA). To observe the performance of each algorithm, we construct three synthetic WTA problems and check how each algorithm works on them. Simulation results show that all of the algorithm have good quality of solutions. Since the difference among mean resulting value is within 2%, we run the nonparametric pairwise Wilcoxon rank sum test for testing the equality of the means among the results. The Wilcoxon test reveals that GA has better quality than the others. In contrast, the simulation results indicate that hybrid-QGA and QGA is much faster than GA for the production of the same number of generations.

A missile defense system is composed of radars detecting incoming missiles aiming at defense assets, command control units making the decisions on weapon target assignment, and artillery batteries firing of defensive weapons to the incoming missiles. Although, the technology behind the development of radars and weapons is very important, effective assignment of the weapons against missile threats is much more crucial. When incoming missile targets toward valuable assets in the defense area are detected, the asset-based weapon target assignment model addresses the issue of weapon assignment to these missiles so as to maximize the total value of surviving assets threatened by them. In this paper, we present a model for an asset-based weapon assignment problem with shoot-look-shoot engagement policy and fixed set-up time between each anti-missile launch from each defense unit. Then, we show detailed linear approximation process for nonlinear portions of the model and propose final linear approximation model. After that, the proposed model is applied to several ballistic missile defense scenarios. In each defense scenario, the number of incoming missiles, the speed and the position of each missile, the number of defense artillery battery, the number of anti-missile in each artillery battery, single shot kill probability of each weapon to each target, value of assets, the air defense coverage are given. After running lpSolveAPI package of R language with the given data in each scenario in a personal computer, we summarize its weapon target assignment results specified with launch order time for each artillery battery. We also show computer processing time to get the result for each scenario.

In designing and operating cellular networks, it is assumed that the area of coverage is geographically divided into hexagonal cells. Among these cells, a certain number of cells are chosen to install switches that serve as relays for communications between any pair of cells. Then, each cell is assigned to a switch to complete the cellular network. This decision regarding assignment of cells to switches is known as a CSA (Cell-to-Switch Assignment) problem. Since this problem is so-called NP hard problem, many researches have proposed heuristic-based algorithms to provide near-optimal solutions with a reasonable computation time. Considering these characteristics of the CSA problem, this work develops a genetic algorithm and a local search algorithm. Throu호out a number of experiments, the performance of the proposed algorithms are evaluated, and compared with existing heuristic method

Given the plant layout, the number of workers, the maximum number of machines that a worker can handle, and the preferences between each worker and each machine, the problem to minimize the deviations of workloads assigned to workers and to maximize the total preference between each worker and each machine is considered. The number of workers are fixed (no part time workers) because of the high expense of technology education and the increase of current employees. Since the workforce assignment problem in this paper is in NP-class, a heuristic algorithm is presented in multiple-row plant layout during according to two types (slow and peak) of periods. The proposed algorithm is developed based on the combination of a mixed model scheduling, simulated annealing technique and graph theory. The solution generated satisfies the zone constraint (machines assigned to a worker are adjacently located). Computational results show that the presented algorithms can find a good solution quickly.

A berth assignment problem has a direct impact on assessment of charges made to ships and goods. In this paper, we concerned with of fuzzy mathematical programming models for a berth assignment problem to achieved an efficient berth operation in a fuzzy environment. In this paper, we focus on the berth assignment programming with fuzzy parameters which are based on personal opinions or subjective judgement. From the above point of view, assume that a goal and a constraint are given by fuzzy sets, respectively, which are characterized by membership functions. Let a fuzzy decision be defined as the fuzzy set resulting from the intersection of a goal and constraint. This paper deals with fuzziness in all parameters which are expressed by fuzzy numbers. A fuzzy parameter defined by a fuzzy number means a possibility distribution of the parameters. These fuzzy 0-1 integer programming problems are formulated by fuzzy functions whose concept is also called the extension principle. We deal with a berth assignment problem with triangular fuzzy coefficients and propose a branch and bound algorithm for solving the problem. We suggest three models of berth assignment to minimizing the objective functions such as total port time, total berthing time and maximum berthing time by using a revised Maximum Position Shift(MPS) concept. The berth assignment problem is formulated by min-max and fuzzy 0-1 integer programming. Finally, we gave the numerical solutions of the illustrative examples.