Balanced dynamic multiple travelling salesmen: algorithms and continuous approximations

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are tested for instances in the Euclidean plane. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean-average-percentage error of two of these models is below 3%.

Conditional probability generation methods for high reliability effects-based decision making

Decision making is often based on Bayesian networks. The building blocks for Bayesian networks are its conditional probability tables (CPTs). These tables are obtained by parameter estimation methods, or they are elicited from subject matter experts (SME). Some of these knowledge representations are insufficient approximations. Using knowledge fusion of cause and effect observations lead to better predictive decisions. We propose three new methods to generate CPTs, which even work when only soft evidence is provided. The first two are novel ways of mapping conditional expectations to the probability space. The third is a column extraction method, which obtains CPTs from nonlinear functions such as the multinomial logistic regression. Case studies on military effects and burnt forest desertification have demonstrated that so derived CPTs have highly reliable predictive power, including superiority over the CPTs obtained from SMEs. In this context, new quality measures for determining the goodness of a CPT and for comparing CPTs with each other have been introduced. The predictive power and enhanced reliability of decision making based on the novel CPT generation methods presented in this paper have been confirmed and validated within the context of the case studies.