Mohammed Said Radjef

Nondifferentiable multiobjective programming under generalized dI-invexity

In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce new concepts of dI-invexity and generalized dI-invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di. New Fritz-John type necessary and Karush-Kuhn-Tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient, efficient or properly efficient. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual under various types of generalized dI-invexity assumptions.

A note on ideal Nash equilibrium in multicriteria games

This paper is a contribution to the problem of existence of ideal Nash equilibrium in noncooperative multicriteria games in strategic form. We give an existence theorem by using the maximal element theorem due to Deguire et al. [P. Deguire, K.K. Tan, G.X.-Z. Yuan, The study of maximal elements, fixed points for Ls-majorized mappings and their applications to minimax and variational inequalities in product topological spaces, Nonlinear Anal. TMA 37 (1999) 933-951] and the characterization provided by Voorneveld et al. [M. Voorneveld, S. Grahn, M. Dufwenberg, Ideal equilibria in non cooperative multicriteria games, Math. Methods Oper. Res. 52 (2000) 65-77].

Automatic multi-objective clustering based on game theory

Novel multi-objective clustering algorithm based-sequential games was proposed.It optimizes simultaneously and efficiently multiple conflicting objectives.Proposed approach can automatically calculate the optimal number of clusters.This algorithm shows good performance of generating high-quality solutions.Experimental study demonstrates the effectiveness of our algorithm over others. Data clustering is a very well studied problem in machine learning, data mining, and related disciplines. Most of the existing clustering methods have focused on optimizing a single clustering objective. Often, several recent disciplines such as robot team deployment, ad hoc networks, multi-agent systems, facility location, etc., need to consider multiple criteria, often conflicting, during clustering. Motivated by this, in this paper, we propose a sequential game theoretic approach for multi-objective clustering, called ClusSMOG-II. It is specially designed to optimize simultaneously intrinsically conflicting objectives, which are inter-cluster/intra-cluster inertia and connectivity. This technique has an advantage of keeping the number of clusters dynamic. The approach consists of three main steps. The first step sets initial clusters with their representatives, whereas the second step calculates the correct number of clusters by resolving a sequence of multi-objective multi-act sequential two-player games for conflict-clusters. Finally, the third step constructs homogenous clusters by resolving sequential two-player game between each cluster representative and the representative of its nearest neighbor. For each game, we define payoff functions that correspond to the model objectives. We use a methodology based on backward induction to calculate a pure Nash equilibrium for each game. Experimental results confirm the effectiveness of the proposed approach over state-of-the-art clustering algorithms.

Properly efficient Nash equilibrium in multicriteria noncooperative games

The aim of this paper is to study the concept of properly efficient equilibrium for a multicriteria noncooperative strategic game. Using results of multicriteria optimization programming, we give some characterizations and existence results of this concept in the considered game.

Evolutionary Game-Based Defense Mechanism in the MANETs

Providing a long term security of a computer system requires an efficient management of the resources consumption. This is particularly true for the Mobile Ad-hoc NETworks (MANETs) where nodes are characterized by limited resources. In this paper, we propose a game theoretic framework to predict malicious behaviors within a MANET and to analyze the best security alternatives that preserve the resources consumption of network entities. We model the interactions between an attacker and a defender evolving in the same environment as an evolutionary game. In these games, each entity can learn about the behavior of its opponent over time allowing the adjustment of its strategy. The main results of our game model are the elaboration of the Evolutionary Stable Strategies (ESSs) which is a stronger concept of equilibria and the illustration of the evolution process, based on the replicator dynamic. Numerical experiments verify the correctness of our theoretical analysis and show the feasibility and effectiveness of our model.

Customers’ strategic behavior in batch arrivals M2/M/1 queue

The investigated problem is the analysis of customers’ strategic behavior in a single server Markovian M2/M/1 queue with batch arrivals of two customers with a reward-cost structure. At their arrival time, customers can decide to join the queue or to balk. The utility of each one depends on his decision, on his partner’s decision and on the system state. Two cases are considered: when the system provides the information about its state (observable case), and when this information is not provided (unobservable case). Both problems are modeled as games in extensive form with complete and imperfect information. We give the Nash equilibria for each corresponding game and we compare between both cases in order to determine the policy which arranges the system’s manager.

A Game Approach for an Efficient Intrusion Detection System in Mobile Ad Hoc Networks

Intrusion Detection Systems (IDS) have become a necessary complement to any security infrastructure and are widely deployed as an additional line of defense to conventional security techniques. Intrusion detection techniques have been widely studied in the literature for the conventional networks. However, due to the specific characteristics of the mobile ad hoc networks (MANET), such as the lack of a fixed infrastructure and a centralized management, the implementation of an IDS presents several new challenges that must be addressed. In this paper, we present a game-based approach to implement an intrusion detection system in MANETs. We consider the selfish node behavior and discuss mechanisms that stimulate cooperation between nodes while reducing the consumption of energy due to deployment of the IDS. We also address the problem of increasing the effectiveness of security mechanism by developing a network packet sampling strategy, to effectively detect network intrusions with respect to a given total sampling budget, and find the right moment for notifying specific nodes to launch countermeasures. Finally, we evaluate the proposed approach via simulations where the results show the effectiveness of the proposed intrusion detection model.

Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity

In this paper, we use a generalized Fritz John condition to derive optimality conditions and duality results for a nonlinear programming with inequality constraints, under weak invexity with respect to different (η i )i assumption. The equivalence between saddle points and optima, and a characterization of optimal solutions are established under suitable generalized invexity requirements. Moreover, we prove weak, strong, converse and strict duality results for a Mond-Weir type dual. It is shown in this study, with examples, that the introduced generalized Fritz John condition combining with the invexity with respect to different (η i )i are especially easy in application and useful in the sense of sufficient optimality conditions and of characterization of solutions.

Efficient algorithms for the offline variable sized bin-packing problem

We addresses a variant of the classical one dimensional bin-packing problem where several types of bins with unequal sizes and costs are presented. Each bin-type includes limited and/or unlimited identical bins. The goal is to minimize the total cost of bins needed to store a given set of items, each item with some space requirements. Four new heuristics to solve this problem are proposed, developed and compared. The experiments results show that higher quality solutions can be obtained using the proposed algorithms.

Security modeling of an ad hoc network under the constraint of energy by an approach in two steps: Clustering-Evolutionary game

Ad hoc networks are subject to multiple challenges, particularly the problem of limited resources such as energy and vulnerability in terms of security. Indeed, the nodes are subject to various attacks and malicious actions. Thus, each mobile is confronted with a dilemma: cooperate to ensure security, in this case the node spend a part of its energy, or not cooperate which allows it to save energy but making the security of the network more vulnerable. In this work, we develop an approach which takes into account two conflicting objectives: contribute to network security while reducing energy consumption. The approach is based on alternating two steps: Clustering-Evolutionary game. The clustering step is performed by an algorithm that takes into account the energy constraint in election of cluster-heads. The interactions between each pair of cluster-heads, when exchanging data, in their contribution to the security of the network, are modeled as an evolutionary game which is the second step of the proposed approach.