Semu Mitiku Kassa

Epidemiological models with prevalence dependent endogenous self-protection measure.

A simple mathematical model for human disease epidemics that takes the human learning behaviour and self-protective measures into account is proposed and investigated. We have analysed the effect of endogenous self-protective measures with respect to the prevalence level of the disease and conversely. In the model it is assumed that people start reacting against contracting a disease with self-protective measures whenever they are informed about the disease and when the burden of the disease is in a recognizable stage. It is shown that increasing the average effectiveness of self-protective measures is more important in decreasing the prevalence of a disease than increasing the proportion of individuals in a population into which awareness is created.

The impact of self-protective measures in the optimal interventions for controlling infectious diseases of human population.

A mathematical model for infectious disease epidemics with behaviour change and treatment is formulated and analysed. It is indicated that behaviour modification by the population has a significant impact on the dynamics of the disease. Moreover, an optimal control theory is applied to propose the best possible combination of efforts in controlling a disease. It is shown that it may not be necessary to continuously apply treatment at a full rate to eradicate the disease, if the effort is supported by effective behaviour modification strategies.

A new algorithm for multilevel optimization problems using evolutionary strategy, inspired by natural adaptation

Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leaders level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular levels optimization problem is solved the solution will be adapted the levels variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.

A branch-and-bound multi-parametric programming approach for non-convex multilevel optimization with polyhedral constraints

In this paper we develop a general but smooth global optimization strategy for nonlinear multilevel programming problems with polyhedral constraints. At each decision level successive convex relaxations are applied over the non-convex terms in combination with a multi-parametric programming approach. The proposed algorithm reaches the approximate global optimum in a finite number of steps through the successive subdivision of the optimization variables that contribute to the non-convexity of the problem and partitioning of the parameter space. The method is implemented and tested for a variety of bilevel, trilevel and fifth level problems which have non-convexity formulation at their inner levels.

Systematic evolutionary algorithm for general multilevel Stackelberg problems with bounded decision variables (SEAMSP)

Multilevel Stackelberg problems are nested optimization problems which reply optimally to hierarchical decisions of subproblems. These kind of problems are common in hierarchical decision making systems and are known to be NP-hard. In this paper, a systematic evolutionary algorithm has been proposed for such types of problems. A unique feature of the algorithm is that it is not affected by the nature of the objective and constraint functions involved in the problem as long as the problem has a solution. The convergence proof of the proposed algorithm is given for special problems containing non-convex and non-differentiable functions. Moreover, a new concept of

Impacts of Vaccination and Behavior Change in the Optimal Intervention Strategy for Controlling the Transmission of Tuberculosis

(\varepsilon ,\delta )

Approximate solution algorithm for multi-parametric non-convex programming problems with polyhedral constraints

(ε,δ)-approximation for Stackelberg solutions is defined. Using this definition comparison of approximate Stackelberg solutions has been studied in this work. The numerical results on various problems demonstrated that the proposed algorithm is very much promising to multilevel Stackelberg problems with bounded constraints, and it can be used as a benchmark for a comparison of approximate results by other algorithms.

Traffic flow optimization on roundabouts

In this paper we investigate multilevel programming problems with multiple followers in each hierarchical decision level. It is known that such type of problems are highly non-convex and hard to solve. A solution algorithm have been proposed by reformulating the given multilevel program with multiple followers at each level that share common resources into its equivalent multilevel program having single follower at each decision level. Even though, the reformulated multilevel optimization problem may contain non-convex terms at the objective functions at each level of the decision hierarchy, we applied multi-parametric branch-and-bound algorithm to solve the resulting problem that has polyhedral constraints. The solution procedure is implemented and tested for a variety of illustrative examples.