Solving k

Coverage problem is a critical issue in wireless sensor networks for security applications. The k-barrier coverage is an effective measure to ensure robustness. In this paper, we formulate the k-barrier coverage problem as a constrained optimization problem and introduce the energy constraint of sensor node to prolong the lifetime of the k-barrier coverage. A novel hybrid particle swarm optimization and gravitational search algorithm (PGSA) is proposed to solve this problem. The proposed PGSA adopts a k-barrier coverage generation strategy based on probability and integrates the exploitation ability in particle swarm optimization to update the velocity and enhance the global search capability and introduce the boundary mutation strategy of an agent to increase the population diversity and search accuracy. Extensive simulations are conducted to demonstrate the effectiveness of our proposed algorithm

A Lagrange Relaxation Method for Solving Weapon-Target Assignment Problem

We study the weapon-target assignment (WTA) problem which has wide applications in the area of defense-related operations research. This problem calls for finding a proper assignment of weapons to targets such that the total expected damaged value of the targets to be maximized. The WTA problem can be formulated as a nonlinear integer programming problem which is known to be NP-complete. There does not exist any exact method for the WTA problem even small size problems, although several heuristic methods have been proposed. In this paper, Lagrange relaxation method is proposed for the WTA problem. The method is an iterative approach which is to decompose the Lagrange relaxation into two subproblems, and each subproblem can be easy to solve to optimality based on its specific features. Then, we use the optimal solutions of the two subproblems to update Lagrange multipliers and solve the Lagrange relaxation problem iteratively. Our computational efforts signify that the proposed method is very effective and can find high quality solutions for the WTA problem in reasonable amount of time

A New Implementable Prediction-Correction Method for Monotone Variational Inequalities with Separable Structure

The monotone variational inequalities capture various concrete applications arising in many areas. In this paper, we develop a new prediction-correction method for monotone variational inequalities with separable structure. The new method can be easily implementable, and the main computational effort in each iteration of the method is to evaluate the proximal mappings of the involved operators. At each iteration, the algorithm also allows the involved subvariational inequalities to be solved in parallel. We establish the global convergence of the proposed method. Preliminary numerical results show that the new method can be competitive with Chen's proximal-based decomposition method in Chen and Teboulle (1994)

Dynamic Route Guidance Using Improved Genetic Algorithms

This paper presents an improved genetic algorithm (IGA) for dynamic route guidance algorithm. The proposed IGA design a vicinity crossover technique and a greedy backward mutation technique to increase the population diversity and strengthen local search ability. The steady-state reproduction is introduced to protect the optimized genetic individuals. Furthermore the junction delay is introduced to the fitness function. The simulation results show the effectiveness of the proposed algorithm

Sensitivity Analysis of the Proximal-Based Parallel Decomposition Methods

The proximal-based parallel decomposition methods were recently proposed to solve structured convex optimization problems. These algorithms are eligible for parallel computation and can be used efficiently for solving large-scale separable problems. In this paper, compared with the previous theoretical results, we show that the range of the involved parameters can be enlarged while the convergence can be still established. Preliminary numerical tests on stable principal component pursuit problem testify to the advantages of the enlargement

An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem