multi-objective optimization

Establishing security in the different borders of the country is one of the most important priorities of the military forces, especially the ground forces. In this article, the security games between a defender and several attackers are investigated and the players' preferences and how to calculate them are described. To solve the problem of the uncertainty of the defender to face the unknown type of attacker, the Bayesian game approach is used. and in order to solve the problem of uncertainty caused by the ambiguity in the understanding of experts and their imprecise judgment, the phase theory has been used as a practical example of this type of games in creating security at land borders, and the model of this problem is expressed as a game. multi-objective security has been investigated, for this purpose we have investigated the movements and actions of the Republic of Azerbaijan in the region and to prevent this country from attacking the common land borders of Iran and Azerbaijan, the appropriate allocation and coverage of four bordering provinces (Gilan, Ardabil) , West Azerbaijan and East Azerbaijan) by the ground units in the operational area. Finally, it can be concluded that many complex military issues can be investigated using security games and the model of its optimal solution can be designed.

Security is one of the key parameters in any society that will have a direct impact on the process of that society. In most areas of security, security resources are limited for protection and full security. One way to solve this problem is to use game theory. Game theory provides a logical way to allocate security resources to enemy targets. The aim of this article is to examine security games, their importance, modeling, solving and application in defense decision making and decision making in an uncertain environment. In this article, security games between a defender and several attackers are examined and the utilities of the players and how they are calculated are described. Due to the uncertainty in the presentation of payoffs by experts, the utilities are considered as interval. The game is modeled as a multi-objective optimization problem with interval-valued objective functions. There are several ways to solve this problem. A practical example of this type of game is the creation of security at the air border, and the model of this issue has been studied as a multi-objective security game. Finally, it can be concluded that many complex military problems can be explored using security games and an optimal solution model can be designed.

Security is one of the most important concerns around the world. In most fields of security, accessibility to security resources for protection is limited. Some important issues, including universal threats of terrorism, drug-smuggling, has increased our requirement of settling limited security resources in order to maximize the efficiency of resources. Game theory provides a logical method in order for allocating security resources to prevent enemies’ targets. In addition, it helps us to analyze a competitive situation using a mathematical approach. The aim of this paper is to study Stackleberg games model and its applications in allocating limited security resources. In this model, first, the defender chooses its strategy and then the attacker, with information of what the defender chose, chooses its strategy. Now, the defender has to make its decision. In most security problems, the defender maybe confronts two or more different attackers which they have their own targets. These games are called multi-objective Stackelberg Games which is formulated as multi-objective optimization problem. For determining the payoffs of each player, the experts’ opinions are employed and also for modelling the uncertainty due to the experts’ opinions, the theory of uncertainty is used. Then the method of weighted summation for this type of games has been used. Finally, an application of this model for providing security in borders is expressed.