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Lagrangian relaxation has been a powerful methodology to solve discrete and mixed integer optimization problems such as planning, scheduling, coordination, and unit commitment. The subgradient method is frequently used within Lagrangian relaxation to update multipliers, where a subgradient direction is obtained by fully minimizing the relaxed problem. A dual value is a lower bound to the optimal feasible...
Combinatorial optimization problems arise in many applications such as task assignment, facility location, and elevator scheduling. A wide variety of population-based solution methods have been developed, either instance-based (e.g., genetic algorithm (GA) and particle swarm optimization (PSO)) or model-based (e.g., ant colony optimization(ACO) and estimation of distribution algorithms (EDAs)). Their...
Building emergency evacuation has long been recognized as an important issue, and crowd guidance is a key to improve egress efficiency and occupant survivability. Most existing methods assume that crowd behaviors are independent of emergency situations and are fully controllable under guidance. This assumption makes it difficult to capture important features such as stampeding or blocking. In this...
Combinatorial optimization problems arise in many applications such as task assignment, facility location, and elevator scheduling. One powerful method to address those difficult problems is the nested partitions method (NP). This method, however, cannot use historical information because it is required that the sampling of different iterations should be independent in order to guarantee global convergence...
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