Vassil Vassilev

An interactive algorithm for solving multiple objective integer linear programming problems

Abstract We propose a reference direction based interactive algorithm to solve multiple objective integer linear programming (MOILP) problems. At each iteration of the solution procedure, the algorithm finds (weak) nondominated solutions to the relaxed MOILP problem. Only at certain iterations, if the DM so desires, an additional mixed integer programming problem is solved to find an integer (weak) nondominated solution which is close to the current continuous (weak) nondominated solution to the relaxed MOILP problem. In the proposed algorithm, DM has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.

A reference direction approach to multiple objective integer linear programming

Abstract We propose the use of a reference direction/reference point approach to solving multiple objective integer linear programming problems. The reference direction/reference point is determined by the aspiration levels for the criteria that the decision-maker wants to improve. Within this framework, two methods are developed, viz., a pure integer method that operates entirely with integer solutions and a continuous/integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function. Obviously, the pure integer method is time consuming. We therefore propose a decision support system that combines the two methods. This way the adBANtages of each method can be used to their fullest extent. We illustrate the proposed decision support system with a numerical example.

Reference direction approach for solving multiple objective nonlinear programming problems

Proposes an interactive algorithm based on the reference direction approach to solve multiple objective nonlinear programming problems. The decision maker gives his/her aspiration levels in terms of the reference point in the objective function space. A number of efficient solutions are generated along the projection of the reference direction onto the efficient frontier. Each solution is an (weak) efficient solution. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example. >

An Interactive Reference Direction Algorithm For Solving Multi‐Objective Convex Nonlinear Integer Programming Problems

We present a learning-oriented interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. At each iteration the decision-maker (DM) sets his/her preferences as aspiration levels of the objective functions. The modified aspiration point and the solution found at the previous iteration define the reference direction. Based on the reference direction, we formulate a mixed-integer scalarizing problem with specific properties. By solving this problem approximately, we find one or more integer solutions located close to the efficient surface. At some iteration (usually at the last iteration), the DM may want to solve the scalarizing problem to obtain an exact (weak) efficient solution. Based on the proposed algorithm, we have developed a research-decision support system that includes one exact and one heuristic algorithm. Using this system, we illustrate the proposed algorithm with an example, and report some computational results.

A multicriteria analysis decision support system

The paper presents a multicriteria analysis decision support system called MultiChoice, designed to support decision makers in solving different multicriteria analysis problems. Various well-known methods and software systems are discussed. The basic features of the solving modules, the interface modules and the system modules are described.

TRASY -- An automated system for real-time control of the industrial truck haulage in open-pit mines

Abstract The control of truck haulage in open-pit mines is an essential problem in the production process of the mines. We describe an automated system for real-time control of the haulage vehicles in terms of the underlying models and solution procedures and we report on the experiences with the system in a real industrial environment.

A Method for Solving Multiple Objective Linear Programming Problems

An interactive method is presented for solving multiple objective linear programming problems. The method develops an idea for successive reduction of the set of normalized weighting coefficients. A set of Pareto efficient solutions is generated at each iteration. The dialog is in terms of aspiration levels in the objective space. A theoretical comparison with other related methods is done.

A Reference Neighbourhood Interactive Method for Solving a Class of Multiple Criteria Decision Analysis Problem

Abstract An interactive method intended to solve multiple criteria decision analysis problems with a large number of discrete alternatives and a few criteria is proposed in the paper. The decision-maker (DM) sets his/her local preferences in terms of desired or acceptable changes in the criteria values for some criteria and the desired or acceptable change of directions for a few of the remaining criteria. A small ordered set of relatively “close” alternatives is defined with the help of a scalarizing problem. If required by the DM, this set is ranked by a formal procedure on the basis of the local intra- and intercriteria information provided by him/her. The ranked set is presented to the DM who selects the most preferred alternative or enters his/her new preferences for improving the current alternative. The software realization of the interactive method proposed is included in an experimental decision support system called MultiChoice for solving multicriteria analysis problems.

Linear multicriteria decision support system

The paper presents a multicriteria decision support system, designed to model and solve linear problems of multicriteria optimization. The system is developed on the basis of an interactive classification-based algorithm, which allows the decision makers describe their local preferences with the help of desired and acceptable levels, directions and intervals of change in the values of a part or of all the criteria.The structure and the users interface of the system are described.

Software Tools for Multi-Criteria Programming

In the last few decades researchers’ efforts have concentrated particularly on the theory and methodology of Multiple Objective Programming. A considerable amount of theoretical properties and extensions of traditional mathematical programming to the case of multiple objective optimization, methodological approaches, methods, algorithms and procedures have been developed (Benayoun et al., 1971; Fishburn et al., 1990; Korhonen and Laakso, 1986; Lewandowski and Wierzbicki, 1989; Nakayama and Sawaragi, 1984; Sawaragi et al., 1985; Shin and Ravindran, 1991; Steuer, 1986; Wierzbicki, 1982; Zionts, 1988). Quite a lot real-life Multiple Objective Linear Programming (MOLP) problems have been solved by specific implementations of the developed methodology. Generally, many multiple objective interdisciplinary problems relevant in practice have multiple nonlinear objectives and nonlinear constraints. Within the past two decades research interest grows to involve Multiple Objective Nonlinear Programming (MONP). The progress has been mainly theoretically and methodologically oriented. Only few real-life applications were reported in literature (Nakayama and Furukawa, 1985; Nakayama and Sawaragi, 1984; Roy and Wallenius, 1992). Still, effective computer codes for MONP models are insufficiently available. Even if the MONP problem is well-structured as to settle itself to algorithmic procedures, there are inherent restraints to the practical achievement of optimal solutions. MONP problems need algorithms that are known to require exponentially much computer time — such problems are said to be NP-hard.