Alexander V. Lotov

Visualizing the Pareto Frontier

We describe techniques for visualizing the Pareto optimal set that can be used if the multiobjective optimization problem considered has more than two objective functions. The techniques discussed can be applied in the framework of both MCDM and EMO approaches. First, lessons learned from methods developed for biobjective problems are considered. Then, visualization techniques for convex multiobjective optimization problems based on a polyhedral approximation of the Pareto optimal set are discussed. Finally, some visualization techniques are considered that use a pointwise approximation of the Pareto optimal set.

Multiobjective optimization and marginal pollution abatement cost in the electricity sector - An Israeli case study

Abstract The multiple objective optimization models for capacity expansion problem of power generation system in the long run as a base for setting up the marginal abatement cost were examined. In the optimization model the objective function is considered as the weighted sum of several objective functions. Air pollutants are taken into account in both the objective function and the constraints. Different scenarios of pollutant reduction were analyzed. The periods of the years 2003–2013 were taken into account and the results are based on the real data of the Israel electricity sector. Several environmental policies were considered by using the CAPEX system to evaluate the environmental and economic deficiencies in different abatement cost scenarios. The following are obtained: abatement cost for each pollutant, amount of emissions and additional cost connected with the pollutants. Modern decision tools are implemented, such as data envelopment analysis (DEA) and reasonable goal method/interactive decision maps (RGM/IDM) technique as a base for decision-makers to make decisions on energy and environmental policy.

Visualization-based multi-objective improvement of environmental decision-making using linearization of response surfaces

This study presents a new interactive procedure for supporting Decision Makers (DMs) in environmental planning problems involving large, process-based, dynamic models and many (more than two) conflicting objectives. Because of such features of the model, computationally-onerous simulations are the only feasible way of analysis, while the multi-objective nature of the problem entails the combined use of optimization techniques and appropriate tools for the visualization of the associated Pareto frontier. The procedure proposed is based on the iterative improvement of the current best compromise alternative based on interactions with the DM. At each iteration, the DM is informed about the Pareto frontier of a local multi-objective optimization problem, which is generated by linearizing the response surfaces that describe the objectives and constraints of the original planning problem. Interactive visualization of the multi-dimensional Pareto frontier is used to support the DM in choosing the new best compromise alternative. The procedure terminates when the DM is fully satisfied with the current best compromise alternative. The approach is demonstrated in Googong Reservoir (Australia), which is periodically affected by high concentrations of Manganese and Cyanobacteria. Results indicate that substantial improvements could be observed by simply changing the location of the two mixers installed in 2007 and adding another pair of mixers.

Hybrid adaptive methods for approximating a nonconvex multidimensional Pareto frontier

New hybrid methods for approximating the Pareto frontier of the feasible set of criteria vectors in nonlinear multicriteria optimization problems with nonconvex Pareto frontiers are considered. Since the approximation of the Pareto frontier is an ill-posed problem, the methods are based on approximating the Edgeworth-Pareto hull (EPH), i.e., the maximum set having the same Pareto frontier as the original feasible set of criteria vectors. The EPH approximation also makes it possible to visualize the Pareto frontier and to estimate the quality of the approximation. In the methods proposed, the statistical estimation of the quality of the current EPH approximation is combined with its improvement based on a combination of random search, local optimization, adaptive compression of the search region, and genetic algorithms.

Integration of Two Multiobjective Optimization Methods for Nonlinear Problems

In this paper, we bring together two existing methods for solving multiobjective optimization problems described by nonlinear mathematical models and create methods that benefit from both heir strengths. We use the Feasible Goals Method and the NIMBUS method to form new hybrid approaches. The Feasible Goals Method (FGM) is a graphic decision support tool that combines ideas of goal programming and multiobjective methods. It is based on the transformation of numerical information given by mathematical models into a variety of feasible criterion vectors (that is, feasible goals). Visual interactive display of this variety provides information about the problem that helps the decision maker to detect the limits of what is possible. Then, the decision maker can identify a preferred feasible criterion vector on the graphic display. NIMBUS is an interactive multiobjective optimization method capable of solving nonlinear and even nondifferentiable and nonconvex problems. The decision maker can iteratively evaluate the problem to be solved and express personal preferences in a simple form: the method is based on the classification of the criteria, where the decision maker can indicate what kind of changes to the current solution are desirable. We describe two possible hybrids of the FGM and the NIMBUS method for helping in finding the most preferable decision (using simple questions posed to the decision maker). First, feasible criterion values are explored, and the decision makers preferences are expressed roughly in the form of a preferable feasible goal (FGM stage). Then, the identified goal is refined using the classification of the criteria (NIMBUS stage). Alternatively, the two methods can be used interactively. Both the hybrid approaches are here illustrated with an example.

A framework for participatory decision support using Pareto frontier visualization, goal identification and arbitration

There is a growing interest in promoting participation of lay stakeholders in public decision-making processes, possibly with the aid of Internet-based systems. This implies supporting non-sophisticated users and, consequently, developing user-friendly, yet rigorous, participatory decision support methods. We outline a framework to develop such methods based on interactive Pareto frontier visualization combined with expression of preferences in terms of feasible goals and using feasible goal-based arbitration.

HUMAN BEHAVIOR IN A MULTI-CRITERIA CHOICE PROBLEM WITH INDIVIDUAL TASKS OF DIFFERENT DIFFICULTIES

This paper is devoted to a laboratory study of human behavior in a multi-criteria choice problem. The specific feature of the experimental study is the creation of an individually adjusted instance of a general task for each subject in accordance with his/her preferences over each criterion. Human behavior is studied in a specially constructed choice situation based on the decomposition of the alternatives of a multi-criteria problem. The procedure is based on multiple steps of pair-wise comparisons involving only some (two or three) of the original components of the alternatives. Abilities of subjects to use such comparisons and to answer the questions in a logical way are tested. The experiment was carried out in two countries: Finland and Russia.

Computer-Based Support for Planning and Negotiation on Environmental Rehabilitation of Water Resource Systems

Strategies of the environmental rehabilitation of water resource systems are usually characterised by multiple performance indicators which represent interests of different social groups. To support negotiations aimed at the solution of problems of this kind, we use a computer methodology based on the Feasible Goals Method (FGM) coupled with the Interactive Decision Maps (IDM) technique. The methodology provides the display of objective tradeoffs among performance indicators informing by this negotiators, experts and public opinion on potentialities of choice and on nondominated combinations of indicators. Moreover, it includes the development of efficient environmental rehabilitation strategies which may be displayed using various multimedia and virtual reality tools as well as the Geographical Information Systems. The FGM/IDM technique may be used for supporting both planning as well as negotiations. An example of planning support system based on the FGM/IDM technique is provided. The concept of the INTERNET-based Active Public Information Clearing House devoted to informing the public opinion on the environmental rehabilitation problems is introduced.

Multicriteria DSS for River Water–Quality Planning

A decision support system (DSS) devoted to water–quality planning is described. The DSS is based on a graphic multiple–criteria technique called generalized reachable sets (GRS) method, which provides experts and decision makers with objective tradeoff curves among cost and pollution criteria. The information improves their understanding of the problem and helps to identify wastewater treatment strategies that provide reasonable balance between cost and pollution. These strategies are starting points for further negotiation between governmental agencies, private and state–owned enterprises, and regional and local authorities involved in wastewater treatment. The DSS is implemented on personal computers.

Visualization-Based data mining tool and its web application

The paper is devoted to a visualization-based data mining tool that helps to explore properties of large volumes of data given in the form of relational databases. It is shown how the tool can support the process of exploration of data properties and selecting a small number of preferable items from the database by application a graphic form of goal programming. The graphic Web application server is considered which implements the data mining tool via Internet. Its current and future applications are discussed.