Parallel Universes: Multi-Criteria Optimization

In this paper parallel universes are defined by their relation to multi-criteria optimization combined with an explicit or implicit link for the unambiguous identification of an optimum. As an explicit link function the desirability index is introduced. Desirabilities are also used for restricting the Pareto set to desired parts

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

A GPU-based multi-criteria optimization algorithm for HDR brachytherapy

Currently in HDR brachytherapy planning, a manual fine-tuning of an objective function is necessary to obtain case-specific valid plans. This study intends to facilitate this process by proposing a patient-specific inverse planning algorithm for HDR prostate brachytherapy: GPU-based multi-criteria optimization (gMCO). Two GPU-based optimization engines including simulated annealing (gSA) and a quasi-Newton optimizer (gL-BFGS) were implemented to compute multiple plans in parallel. After evaluating the equivalence and the computation performance of these two optimization engines, one preferred optimization engine was selected for the gMCO algorithm. Five hundred sixty-two previously treated prostate HDR cases were divided into validation set (100) and test set (462). In the validation set, the number of Pareto optimal plans to achieve the best plan quality was determined for the gMCO algorithm. In the test set, gMCO plans were compared with the physician-approved clinical plans. Over 462 cases, the number of clinically valid plans was 428 (92.6%) for clinical plans and 461 (99.8%) for gMCO plans. The number of valid plans with target V100 coverage greater than 95% was 288 (62.3%) for clinical plans and 414 (89.6%) for gMCO plans. The mean planning time was 9.4 s for the gMCO algorithm to generate 1000 Pareto optimal plans. In conclusion, gL-BFGS is able to compute thousands of SA equivalent treatment plans within a short time frame. Powered by gL-BFGS, an ultra-fast and robust multi-criteria optimization algorithm was implemented for HDR prostate brachytherapy. A large-scale comparison against physician approved clinical plans showed that treatment plan quality could be improved and planning time could be significantly reduced with the proposed gMCO algorithm.Comment: 18 pages, 7 figure

Multi-Criteria Optimization Manipulator Trajectory Planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions

Multi-Criteria Optimization in Answer Set Programming

We elaborate upon new strategies and heuristics for solving multi-criteria optimization problems via Answer Set Programming (ASP). In particular, we conceive a new solving algorithm, based on conflictdriven learning, allowing for non-uniform descents during optimization. We apply these techniques to solve realistic Linux package configuration problems. To this end, we describe the Linux package configuration tool aspcud and compare its performance with systems pursuing alternative approaches

System Architecture Design Using Multi-Criteria Optimization

System architecture is defined as the description of a complex system in terms of its functional requirements, physical elements and their interrelationships. Designing a complex system architecture can be a difficult task involving multi-faceted trade-off decisions. The system architecture designs often have many project-specific goals involving mix of quantitative and qualitative criteria and a large design trade space. Several tools and methods have been developed to support the system architecture design process in the last few decades. However, many conventional problem solving techniques face difficulties in dealing with complex system design problems having many goals. In this research work, an interactive multi-criteria design optimization framework is proposed for solving many-objective system architecture design problems and generating a well distributed set of Pareto optimal solutions for these problems. System architecture design using multi-criteria optimization is demonstrated using a real-world application of an aero engine health management (EHM) system. A design process is presented for the optimal deployment of the EHM system functional operations over physical architecture subsystems. The EHM system architecture design problem is formulated as a multi-criteria optimization problem. The proposed methodology successfully generates a well distributed family of Pareto optimal architecture solutions for the EHM system, which provides valuable insights into the design trade-offs. Uncertainty analysis is implemented using an efficient polynomial chaos approach and robust architecture solutions are obtained for the EHM system architecture design. Performance assessment through evaluation of benchmark test metrics demonstrates the superior performance of the proposed methodology

Stochastic Approaches to Interactive Multi-Criteria Optimization Problems

A stochastic approach to the development of interactive algorithms for multicriteria optimization is discussed in this paper. These algorithms are based on the idea of a random search and the use of a decision-maker who can compare any two decisions. The questions of both theoretical analysis (proof of convergence, investigation of stability) and practical implementation of these algorithms are discussed