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The term problem solving is used in many disciplines, sometimes with different perspectives.
As one of the important topics in artiï¬cial intelligence (AI) research, it is a computerized
process of human problem-solving behaviors. So the aim of problem solving is to develop
techniques that program computers to ï¬nd solutions to problems that can properly be
described.
In the early stage of AI, symbolists play a dominant role. They believe that all human cognitive
behaviors, including problem solving, can be modeled by symbolic representation and
reasoning and do not advocate the use of strict mathematical models. The most general
approach to tackle problem-solving processes is “generation and test”. Applying an action to
an initial state, a new state is generated. Whether the state is the goal state is tested; if it is not,
repeat the procedure, otherwise stop and the goal is reached. This principle imitates human
trial-and-error behaviors in problem solving sufï¬ciently. The principle has widely been used to
build AI systems such as planning, scheduling, diagnosis, etc. and to solve a certain kind of real
problems. Therefore, the heuristic and scratch method is misunderstood as a unique one in
AI for many people. We believe that more and more modern sciences such as mathematics,
economics, operational research, game theory and cybernetics would inï¬ltrate into AI when it
becomes mature gradually. Over the years, we devoted ourselves to introducing mathematics to
AI. Since 1979 we have introduced statistical inference methods to heuristic search,
topological dimension reduction approach to motion planning, and relational matrix to
temporal planning. Due to the introduction of these mathematical tools, the efï¬ciency and
performance of AI algorithms have been improved signiï¬cantly. There are two main trends in
AI research recently. One is attaching importance to the usage of modern scientiï¬c methods,
especially mathematics; the other is paying attention to real-world problem solving.
Fortunately, our efforts above are consistent with these new trends. |