This paper presents two new dynamic programming (DP) algorithms to find the exact Pareto frontier for the bi-objective integer knapsack problem. First, a property of the traditional DP algorithm for the multiobjective integer knapsack problem is identified. The first algorithm is developed by directly using the property. The second algorithm is a hybrid DP approach using the concept of the boun...

W describe a new algorithm for computing the efficient frontier of the “bi-objective maximum-flow network-interdiction problem.” In this problem, an “interdictor” seeks to interdict (destroy) a set of arcs in a capacitated network that are Pareto-optimal with respect to two objectives, minimizing total interdiction cost and minimizing maximum flow. The algorithm identifies these solutions throu...

The single objective quadratic multiple knapsack problem (QMKP) is a useful model to formulate a number of practical problems. However, it is not suitable for situations where more than one objective needs to be considered. In this paper, we extend the single objective QMKP to the bi-objective case such that we simultaneously maximize the total profit of the items packed into the knapsacks and ...

We consider constrained biobjective optimization problems. One of the extant issues in this area is that of uniform sampling of the Pareto front. We utilize equispacing constraints on the vector of objective values, as discussed in a previous paper dealing with the unconstrained problem. We present a direct and a dual formulation based on arc-length homotopy continuation and illustrate the dire...

Daniel Guimarans , Silvia Padrón , Juan José Ramos , Salma Fitouri-Trabelsi 3 and Liana Napalkova 2 1 Optimisation Research Group, National ICT Australia (NICTA), 13 Garden Street, Eveleigh NSW 2015, Australia [email protected] 2 Dpt. Telecommunication and Systems Engineering, Universitat Autònoma de Barcelona, Emprius 2, 08202 Sabadell, Barcelona, Spain {silvia.padron, juanjose.ram...

In a multimodal optimization task, the main purpose is to find multiple optimal solutions (global and local), so that the user can have better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable optimum solution. To this end, evolutionary optimization algorithms (EA) stand as viable methodologies mainly...

This paper presents a multicriterion algorithm for dealing with joint facility location and network design problems, formulated as bi-objective problems. The algorithm is composed of two modules: a multiobjective quasi-Newton algorithm, that is used to find the location of the facilities; and a multiobjective genetic algorithm, which is responsible for finding the efficient topologies. These mo...

This paper presents a meta-objective optimization approach, called Bi-Goal Evolution (BiGE), to deal with multi-objective optimization problems with many objectives. In multi-objective optimization, it is generally observed that 1) the conflict between proximity and diversity requirements is aggravated with the increase of the number of objectives and 2) the Pareto dominance loses its effective...

We present a bi-objective model for a green truck scheduling and routing problem at a cross-docking system. This model determines three key decisions at the cross dock: (1) defining a sequence and schedule of inbound trucks at the receiving door, (2) specifying a sequence and a schedule of outbound trucks at the shipping door, and (3) determining the routes of the outbound truck while serving c...

This paper proposes a framework named multiobjective ant colony optimization based on decomposition (MoACO/D) to solve bi-objective traveling salesman problems (bTSPs). In the framework, a bTSP is first decomposed into a number of scalar optimization subproblems using Tchebycheff approach. To suit for decomposition, an ant colony is divided into many subcolonies in an overlapped manner, each of...