In the present paper a bi-objective integer linear programming problem (BILP) is discussed. The main effort in this work to effectively implement ?-constraint method produce complete set of non dominated points. convergence algorithm has been established theoretically. Further comparative study some existing also made.

Objectives optimization and constraints satisfaction are two equally important goals to solve constrained many-objective problems (CMaOPs). However, most existing studies for CMaOPs can be classified as feasibility-driven-constrained evolutionary algorithms (CMaOEAs), they always give priority satisfy constraints, while ignoring the maintenance of population diversity dealing with conflicting o...

Scheduling for job shop is very important in both fields of production management and combinatorial op-timization. However, it is quite difficult to achieve an optimal solution to this problem with traditional opti-mization approaches owing to the high computational complexity. The combination of several optimization criteria induces additional complexity and new problems. In this paper, we pro...

1 Graduate Student, Department of Knowledge Engineering and Computer Sciences, Doshisha University ,1-3 Tatara Miyakodani,Kyo-tanabe, Kyoto, 610-0321, JAPAN [email protected] http://mikilab.doshisha.ac.jp/~sin/ 2 Department of Knowledge Engineering and Computer Sciences, Doshisha University ,1-3 Tatara Miyakodani,Kyo-tanabe, Kyoto, 610-0321, JAPAN [email protected],[email protected]...

In this paper, we introduce the COmbinatorial Multi-Objective Multi-Armed Bandit (COMOMAB) problem that captures the challenges of combinatorial and multi-objective online learning simultaneously. In this setting, the goal of the learner is to choose an action at each time, whose reward vector is a linear combination of the reward vectors of the arms in the action, to learn the set of super Par...

We study a 0-1 knapsack problem, in which the objective value is forbidden to take some values. We call gaps related forbidden intervals. The problem is NP-hard and pseudopolynomially solvable independently on the measure of gaps. If the gaps are large, then the problem is polynomially non-approximable. A non-trivial special case with respect to the approximate solution appears when the gaps ar...

In this paper, we approach a multi-objectiveH problem with several H constraints from the Banach duality point of view. The problem is reduced to an abstract norm minimization problem, and the dual problem is derived using the classical Banach result. It completes the primal-dual pair which can be used to solve the problem numerically by finitedimensional approximations. While the approximation...

In this paper, a new approach to risk minimizing vehicle routing and scheduling problem is presented. Forwarding agents or companies have two main concerns for the collection of high-risk commodities like cash or valuable commodities between the central depot and the customers: one; because of the high value of the commodities transported, the risk of ambush and robbery are very high. Two; the ...

1 Sub-Problems and Objectives Divide and conquer techniques in problem solving are familiar and intuitive; first find the solution to sub-problems and then re-use these to find solutions to the whole problem. For example, we may decompose the problem of designing a vehicle into designing the engine and designing the body. It is acknowledged that most real-world problems (vehicles included) do n...