Interactive procedure for multiobjective dynamic programming with the mixed ordered structure

The paper presents a multiobjective dynamic programming problem with the values of the criteria function in ordered structures. The first problem is a model with deterministic values; the second, one with triangular fuzzy numbers; and the third, one with discrete random variables with the k-th absolute moment finite. The fourth model is a product of the three models listed above. The aim of the paper is to present an interactive procedure which uses trade-offs and which allows to determine the final solution in the mixed ordered structure. The ordered structures and the proposed procedure are illustrated by numerical examples

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

River Basin Water Quality Management Models: A State-of-the-Art Review

With the increasing human activities within river basins, the problem of water quality management is becoming increasingly important. Quality management can be achieved through control/prevention measures that have various economic and water quality implications. To facilitate the analysis of available management options, decision models are needed which represent the many facets of the problem. Such models must be capable of adequately depicting the hydrological, chemical and biological processes occurring in the river; while incorporating social, economic and political considerations within the decision framework. Management analyses can be performed using simulation, optimization, or both, depending on the management goal and the size and type of the problem. The critical issues in a management model are the nonlinearities, uncertainties, multiple pollutant nature of waste discharges, multiple objectives, and the spatial and temporal distribution of management actions. Literature on various management models were reviewed under the headings of linear, nonlinear and dynamic programming approaches; their stochastic counterparts, and combined or miscellaneous approaches. Dynamic programming was found to be an attractive methodology which can exploit the sequential decision problem pertaining to river basin water quality problems (downstream control actions do not influence water quality upstream). DP handles discrete decision variables which represent discrete management alternatives, and it is generic in the sense that both linear and non-linear water quality models expressing the relation between emissions and ambient quality levels can be incorporated. An example problem is presented which demonstrates the application of a DP-based management model to formulate least-cost strategies for the Nitra River basin in Slovakia. However, it is hardly possible for a single model to represent all the aspects of a complex decision problem. Different types of management models (e.g. deterministic vs stochastic models) have different capabilities and limitations. The only way to compensate for the deficiencies is to perform the analysis in a sensitivity style. The necessity for sensitivity analyses is further implied due to the fact that water quality problems are rather loosely formulated with respect to the quality and economic goals

Aspiration Based Decision Analysis and Support Part I: Theoretical and Methodological Backgrounds

In the interdisciplinary and intercultural systems analysis that constitutes the main theme of research in IIASA, a basic question is how to analyze and support decisions with help of mathematical models and logical procedures. This question -- particularly in its multi-criteria and multi-cultural dimensions -- has been investigated in System and Decision Sciences Program (SDS) since the beginning of IIASA. Researchers working both at IIASA and in a large international network of cooperating institutions contributed to a deeper understanding of this question. Around 1980, the concept of reference point multiobjective optimization was developed in SDS. This concept determined an international trend of research pursued in many countries cooperating with IIASA as well as in many research programs at IIASA -- such as energy, agricultural, environmental research. SDS organized since this time numerous international workshops, summer schools, seminar days and cooperative research agreements in the field of decision analysis and support. By this international and interdisciplinary cooperation, the concept of reference point multiobjective optimization has matured and was generalized into a framework of aspiration based decision analysis and support that can be understood as a synthesis of several known, antithetical approaches to this subject -- such as utility maximization approach, or satisficing approach, or goal -- program -- oriented planning approach. Jointly, the name of quasisatisficing approach can be also used, since the concept of aspirations comes from the satisficing approach. Both authors of the Working Paper contributed actively to this research: Andrzej Wierzbicki originated the concept of reference point multiobjective optimization and quasisatisficing approach, while Andrzej Lewandowski, working from the beginning in the numerous applications and extensions of this concept, has had the main contribution to its generalization into the framework of aspiration based decision analysis and support systems. This paper constitutes a draft of the first part of a book being prepared by these two authors. Part I, devoted to theoretical foundations and methodological background, written mostly by Andrzej Wierzbicki, will be followed by Part II, devoted to computer implementations and applications of decision support systems based on mathematical programming models, written mostly by Andrzej Lewandowski. Part III, devoted to decision support systems for the case of subjective evaluations of discrete decision alternatives, will be written by both authors

Multiobjective Simulation Optimization Using Enhanced Evolutionary Algorithm Approaches

In today\u27s competitive business environment, a firm\u27s ability to make the correct, critical decisions can be translated into a great competitive advantage. Most of these critical real-world decisions involve the optimization not only of multiple objectives simultaneously, but also conflicting objectives, where improving one objective may degrade the performance of one or more of the other objectives. Traditional approaches for solving multiobjective optimization problems typically try to scalarize the multiple objectives into a single objective. This transforms the original multiple optimization problem formulation into a single objective optimization problem with a single solution. However, the drawbacks to these traditional approaches have motivated researchers and practitioners to seek alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated in stochastic environments when the objectives take on uncertain (or noisy ) values due to random influences within the system being optimized, which is the case in real-world environments. Moreover, in stochastic environments, a solution approach should be sufficiently robust and/or capable of handling the uncertainty of the objective values. This makes the development of effective solution techniques that generate Pareto optimal solutions within these problem environments even more challenging than in their deterministic counterparts. Furthermore, many real-world problems involve complicated, black-box objective functions making a large number of solution evaluations computationally- and/or financially-prohibitive. This is often the case when complex computer simulation models are used to repeatedly evaluate possible solutions in search of the best solution (or set of solutions). Therefore, multiobjective optimization approaches capable of rapidly finding a diverse set of Pareto optimal solutions would be greatly beneficial. This research proposes two new multiobjective evolutionary algorithms (MOEAs), called fast Pareto genetic algorithm (FPGA) and stochastic Pareto genetic algorithm (SPGA), for optimization problems with multiple deterministic objectives and stochastic objectives, respectively. New search operators are introduced and employed to enhance the algorithms\u27 performance in terms of converging fast to the true Pareto optimal frontier while maintaining a diverse set of nondominated solutions along the Pareto optimal front. New concepts of solution dominance are defined for better discrimination among competing solutions in stochastic environments. SPGA uses a solution ranking strategy based on these new concepts. Computational results for a suite of published test problems indicate that both FPGA and SPGA are promising approaches. The results show that both FPGA and SPGA outperform the improved nondominated sorting genetic algorithm (NSGA-II), widely-considered benchmark in the MOEA research community, in terms of fast convergence to the true Pareto optimal frontier and diversity among the solutions along the front. The results also show that FPGA and SPGA require far fewer solution evaluations than NSGA-II, which is crucial in computationally-expensive simulation modeling applications

Multiobjective metaheuristic approaches for mean-risk combinatorial optimisation with applications to capacity expansion

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 200

Trade-off Between Cost and Effectiveness of Control of Nutrient Loading into a Water Body

A system consisting of a watershed and a water body is considered, and a methodology is presented for selecting the alternative scheme offering the best compromise between economic activity in the watershed and quality of the water body. The general problem is specified for the system of a watershed and a lake endangered by eutrophication. Both economic activity and eutrophication can be characterized by several criteria. The method is applied to actual data from a subwatershed of Lake Balaton, Hungary, where the economic objective is to minimize the sum of costs and losses for the various control measures and the environmental objective is to minimize the amount of P available for algal growth. Both of these objectives are decomposed into several criteria. The action space consists of six pure strategies, namely, the control of (1) point-source pollution, (2) fertilizer, (3) erosion, (4) land use, (5) runoff control, and (6) sediment yield. These six pure actions lead to the definition of eight mixed alternatives. The phosphorus-loading portion of the model is run repeatedly with different stochastic input sequences to account for hydrologic uncertainty and the corresponding environmental objective is expressed as the probability "uj" that alternative "j" results in the largest decrease of P-loading. Model parameters are estimated using available data or published tables and graphs. Compromise programming is used to find a trade-off (or satisfactum solution) that balances the two conflicting objectives. In order to facilitate further application of the methodology, several points are discussed such as the relationship between the lake and its catchment, the error in stochastic simulation, the consideration of various uncertainties, the effect of snowmelt, and possible coupling with detailed lake eutrophication models. Finally, a step-by-step summary of the methodology is given to facilitate application of the model to other cases. Multicriterion decision-making techniques are briefly reviewed in the appendix so that cases with more than two objectives may also be approached