Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Contemporary Methods for Graph Coloring as an Example of Discrete Optimization

This paper provides an insight into graph coloringapplication of the contemporary heuristic methods. It discusses avariety of algorithmic solutions for The Graph Coloring Problem(GCP) and makes recommendations for implementation. TheGCP is the NP-hard problem, which aims at finding the minimumnumber of colors for vertices in such a way, that none of twoadjacent vertices are marked with the same color.With the adventof multicore processing technology, the metaheuristic approachto solving GCP reemerged as means of discrete optimization. Toexplain the phenomenon of these methods, the author makes athorough survey of AI-based algorithms for GCP, while pointingout the main differences between all these techniques

Meta-heuristic combining prior online and offline information for the quadratic assignment problem

The construction of promising solutions for NP-hard combinatorial optimization problems (COPs) in meta-heuristics is usually based on three types of information, namely a priori information, a posteriori information learned from visited solutions during the search procedure, and online information collected in the solution construction process. Prior information reflects our domain knowledge about the COPs. Extensive domain knowledge can surely make the search effective, yet it is not always available. Posterior information could guide the meta-heuristics to globally explore promising search areas, but it lacks local guidance capability. On the contrary, online information can capture local structures, and its application can help exploit the search space. In this paper, we studied the effects of using this information on metaheuristic's algorithmic performances for the COPs. The study was illustrated by a set of heuristic algorithms developed for the quadratic assignment problem. We first proposed an improved scheme to extract online local information, then developed a unified framework under which all types of information can be combined readily. Finally, we studied the benefits of the three types of information to meta-heuristics. Conclusions were drawn from the comprehensive study, which can be used as principles to guide the design of effective meta-heuristic in the future