Combined resource allocation and route optimization in multiagent networks: A scalable approach

Inequality Constraints in Facility Location and Other Similar Optimization Problems: An Entropy Based Approach

“…In this paper we expound on the optimization problems that fall into the above category and develop a framework to incorporate several inequality constraints on the underlying decision variable. In particular, we consider the (a) Facility Location Problem (FLP) [10], (b) Facility Location with Path Optimization (FLPO) [8], [11] and the (b) Last Mile Delivery Problem (LMDP) [12], where the underlying objectives are to (a) allocate facilities to a network of spatially scattered nodes, (b) overlay a network of facilities on an existing network of nodes and design path from each node to a given destination via the network of facilities, and (c) schedule the package delivery from a transportation hub to its final destination, respectively. In several application areas, that pose the above optimization problems, the facilities, paths and the vehicles, based on their size, endurance and design capabilities, have an inherent upper bound on the number of nodes or packages they handle.…”

“…In fact, in addition to combinatorially large possible partitioning of the nodes, the FLPO problem comprises of exponentially (2 M ) large number of possible paths from each node to the destination via the network of facilities. The work done in [8], [11] develop heurisitcs to solve the FLPO problem while addressing its inherent issues of non-convexity [8] and exponentially large number of decision variables [11]. In the constrained setting, the equality or inequality constraints on the decision variables involved in the above optimization problems, render additional complexity to them.…”