Research Of Lanchester Equation And Effierential Game Problem Based On Artificial Fish Swarm Algorithm

Differential games theory has been applied to economics, engineering, biology and allother fields. Especially in the world today, high technology in military affairs iswidespread usage, making the research of differential games problem more important. Thispaper directs at theoretical researches on the numerical calculation methods of differentialgame; also made researches on some problem of its application in attack, command andcontrol. Main contents include:1,Numerical calculation methods to differential game are researched. Development ofartificial intelligence provides an effective method and technological approach fordifferential game theoretical research. Principle, implementation steps and characteristicsof the chaos optimization and artificial fish-swarm algorithm are researched deeply. Due tolow speed and inadequate optimal efficiency of AFSA and chaotic variables with therandomness, regularity, an efficiency optimal hybrid algorithm (SCAFSA) whichcombines chaos optimization and artificial fish-swarm is proposed. The simulatingexperiment of test function verifies that this hybrid algorithm is stronger than AFSA inglobal optimization and the search efficiency is higher. Theoretically, this paper provesthat under certain circumstances the hybrid algorithm is convergent in probability to globaloptimum.2,Applications of differential game on operational commanding are researched.Based on Lanchester equation, the optimal fire allocation problem is focused on. Becausethe diversity and complexity of war, the article mainly discusses at straight war weaponsthe typical differential game model of one to many. Using the maximum and minimumprinciple in differential game, optimum allocation strategy is obtained. So the side withmore arms should attack the only arm with full power. The attack policy of single arm sidedepends on the descending order of battle intensity. And then the question of bad situationarm winning in military confront is solved. 3,In consideration of Battle of Trafalgar historical case, on the basis of the MilitaryScenario base appropriate mathematical model is set up, using SCAFSA which is proposedin the article. Then the results are analysed and researched properly, getting both sides inmilitary affairs optimizing decision of power distribution.