The Markowitz mean return-standard deviation portfolio selection model refers to single-period investing. A common practice is using this model for multi-period investing with portfolio rebalancing at specified times. Such investing is suboptimal compared to dynamic multi-period investing but is much simpler, which matters in practice. Usually, the investor controls the risk implicitly by selecting the desired mean return within the range of possible mean returns. Next, depending on the location of the selected value in the range, the investor assesses the risk according to his/her mean return-risk profile. However, this setup does not apply to multi-period investing because the ranges of possible mean returns and the relation between mean return and risk vary from period to period. As a result, the mean return selected in one period can correspond to a different level of risk in the next one. To address this issue, we propose to use a flexible approach, where the investor's risk is assessed relative to the possible mean return range and thus can be kept relatively consistent throughout the entire investment horizon. We experimentally examine the adequacy and predictive power of the proposed relative risk assessment in multi-period investments with rebalancing versus single-period over-the-whole-horizon investing.

We investigate a class of polyhedral convex cones, with R^k_+ (the nonegative orthant in ℝ^k ) as a special case. We start with the observation that for convex cones contained in R^k_+ , the respective cone efficiency is inconsistent with Pareto efficiency, the latter being deeply rooted in economics, decision theory, and multiobjective optimization theory. Despite that, we argue that convex cones contained in R^k_+ and the respective cone efficiency are also relevant to these domains. To demonstrate this, we interpret polyhedral convex cones of the investigated class in terms of assessment functions, i.e., functions that aggregate multiple numerical attributes into single numbers. Further, we observe that all assessment functions in the current use share the same limitation; that is, they do not take explicitly into account attribute proportionality. In consequence, the issue of attribute balance (meaning balance of attribute values) escapes them. In contrast, assessment functions defined by polyhedral convex cones of the investigated class, contained in R^k_+ , enforce attribute balance in a more dominant manner. However, enforcing attribute balance is, in general, inconsistent with the well-established paradigm of Pareto efficiency. We give a practical example where such inconsistency is meaningful.

Compared to deciding under a single criterion, in Multicriteria Decision Aiding the role of the decision-maker is much more predominant. This is because in the former case, once the decision model is formulated, the notion of optimal decision is well defined, whereas in the latter, it is not. The behavioral biases influencing the model construction can be in both cases the same; however, in Multicriteria Decision Aiding decisions are selected from a range of incomparable Pareto optimal candidates. Thus, in Multicriteria Decision Aiding there is more space where behavioral biases can emerge. In this study we identify, within the Multicriteria Decision Aiding setting, the most important decision process drivers that cause the decisions to be satisficing but rarely the best possible. To tame the impact of those drivers on the decision aiding process, we propose a generic Multicriteria Decision Aiding tool, a sort of {\it what-if analysis}, and show how to make it operational.

Intensity Modulated Radiation Therapy is an effective cancer treatment. Models based on the Generalized Equivalent Uniform Dose (gEUD) provide radiation plans with excellent planning target volume coverage and low radiation for organs at risk. However, manual adjustment of the parameters involved in gEUD is required to ensure that the plans meet patient-specific physical restrictions. This paper proposes a radiotherapy planning methodology based on bi-level optimization. We evaluated the proposed scheme in a real patient and compared the resulting irradiation plans with those prepared by clinical planners in hospital devices. The results in terms of efficiency and effectiveness are promising.

In this paper, we address the aspect of knapsack balancing in the classic knapsack problem. Recognizing that excessive dispersion in the objective function or constraint coefficients of the optimal solution can be undesirable, we propose, when appropriate, to control this effect through problem multiobjectivization. By multiobjectivization, we mean the addition of one or more objective functions that aim to shift the original problem’s optimal solutions towards Pareto optimal solutions of the multiobjectivized problem, reducing the dispersion of the respective coefficients. We detail how the knapsack balance aspect can be incorporated into the standard knapsack problem model and demonstrate the functionality of this enriched model through illustrative examples.

The method BISSA, proposed by Bednarczuk, Miroforidis, and Pyzel, provides approximate solutions to the multiple-choice knapsack problem. To fathom the optimality gap that is left by BISSA, we present a method that starts from the BISSA solution and it is able to provide a better approximation and in consequence a tighter optimality gap. Like BISSA, the new method is based on the multiobjectivization of the multiple-choice knapsack but instead of the linear scalarization used in BISSA, it makes use of the Chebyshev scalarization. We validate the new method on the same set of problems used to validate BISSA.

We investigate assessment functions, i.e., functions that aggregate numerical attribute values into single numbers. All assessment functions in the current use share the same limitation: they do not explicitly account for the attribute values balance. Here, we present assessment functions that provide for that. However, those functions are at odds with the well-established paradigm of Pareto efficiency. As an example, the relevance of assessment functions to rankings is discussed.

Radiotherapy treatments apply high doses of radiation to tumorous cells to break the structure of cancer DNA, trying at the same time to minimize radiation doses absorbed by healthy cells. The personalized design of radiotherapy plans has been a relevant challenge since the beginning of these therapies. A wide set of models have been defined to translate complex clinical prescriptions into optimization problems. The model based on the generalized equivalent uniform dose, gEUD, is very relevant for IMRT radiotherapy planning in clinical practice. This way, the expert physicists can tune plans near the prescriptions, solving the optimization problem based on gEUD in a trial-and-error process. The gradient descent methods can be applied for solving these models personalized for every patient. However, their computational requirements are huge. So, to facilitate their use in clinical practice it is necessary to apply HPC techniques to implement such models. In this work, we have developed two parallel implementations of an gEUD model for IMRT planning on multi-core and GPU architectures, as they are increasingly available in clinical settings. Both implementations are evaluated with two Head &Neck clinical tumor cases on modern GPU and multi-core CPU platforms. Our implementations are very useful since they help expert physicists obtain fast plans that can satisfy all the prescriptions.

In the expected mean return, standard deviation portfolio selection problem, the first step is usually to derive the set of efficient portfolios, which in the space of objective function values is represented by the efficient frontier. With modern methods and software, it is an easy task even for thousands of assets provided that the problem is continuous. However, investors often introduce the requirement to limit the number of assets in portfolios (portfolio cardinality). The resulting mixed-integer quadratic formulations are computationally much more complex. In this work, we assume that besides risky assets, the risk-free asset is available to the investor, and short selling is not allowed. Since in this case the efficient frontier cannot be directly derived by a quadratic solver, we propose a naive but intuitive heuristic to approximate the efficient frontier in the presence of the risk-free asset. In contrast to the general-purpose evolutionary heuristics, we exploit the underlying mechanism of portfolio composition. We show by numerical experiments that in large-scale instances it works well, even compared to a state-of-the-art evolutionary multiobjective optimization algorithm. Moreover, the heuristic produces portfolios of remarkably limited cardinalities.

The rapid growth of computing power and the development of highly effective optimization solvers build the appetite for solving increasingly extensive problems. However, despite all these efforts, resource constraints (time, memory) often strike back. The ”curse of dimensionality” haunts primarily combinatorial problems, but not only. The issue is even more acute in multiobjective optimization, where several Pareto optimal solutions have to be derived. In our earlier works, we developed a general methodology for multiobjective optimization that allows representing the outcome of a Pareto optimal solution by a hyperrectangle. The sides of the hyperrectangle are defined by lower and upper bounds on the outcome components, i.e., intervals of possible objective function values. Such a representation makes sense if the Pareto optimal solution cannot be derived with the available computation resources. Beyond the research interest, to be of practical value, methodologies of that kind have to be computationally effective and scalable. In this work, we show that our methodology can be effectively coupled with any MIP optimization solver. With that, as long as an analyst is willing to accept a (sufficiently tight) interval representation of the Pareto optimal solution outcome instead of its exact outcome, our methodology scales multiobjective-based analyses well beyond the reach of the MIP solver itself. We operationalize our methodology in the form of a workflow (we nicknamed it Crescent Workflow ). We illustrate the workflow working on several large-scale instances of the multiobjective multidimensional 0–1 knapsack problem with three objectives.

Practical decision-making very often results in complex multiobjective optimization problems that can be solved only by advanced software. At present, it is available for singleobjective optimization and much less for multiobjective optimization. Therefore, the most common approach to multiobjective optimization is to reduce (scalarize) to its singleobjective optimization equivalent. To this aim, the objectives are aggregated into a weighted (parametrized) sum of objectives. However, this form of scalarization does not guarantee that each Pareto optimal solution can be derived. We present a free web-based application to automate scalarizing multiobjective mixed integer optimization problems by a specific form of scalarization, the process which can be tedious for large-scale instances. This form of scalarization guarantees that every Pareto optimal solution is derivable.

Due to recent globalization of financial markets, investors have access to large numbers of assets. It may be beneficial for them to focus on a limited number of assets filtered out by some meaningful procedure. This, however, can result in selecting portfolios which, in terms of reward and risk, are not efficient in the original set of assets. A challenge is to have ways for determining subsets of assets in which the effect of lost efficiency would be minimal. To meet this challenge, we propose a method for asset reduction, based on the notion of layers of maxima and the concept of nondominated sorting. We conduct experiments on large problems derived from the USA stock market data. Our approach resulted in a much smaller loss of efficiency compared to two representative asset reduction methods known from the literature. We test the approach viability via computational experiments on the mean–variance problem of portfolio selection, with and without the cardinality constraints, and real-life data consisting of up to 1000 assets.

In radiotherapy planning, which involves optimization, efforts to produce better (more effective and at the same time with lesser adverse effects) patient radiation plans must trade-off with higher computing times needed to achieve this goal. Computing times is the key (but not only) factor in radiotherapy planning, which is always performed in clinical workflows regimes. ‘Win–win’ is when better plans can be produced within a non-increasing time budget. This work reports on the authors’ attempt to put radiotherapy planning in a ‘win–win’ situation. We looked into unexploited till now reserves, which lie in the performance of optimization methods and algorithms, namely the reserves in performing linear algebra computations when such methods are applied to radiotherapy. A specific feature of such applications is the necessity of numerous sparse matrix $$\times$$ vector computations, with matrices and vectors of large sizes. Our first step was to propose ways to include sparse matrix procedures from existing libraries into an optimization algorithm for testing experiments. Our second step in our quest for reserves was to resort to High Performance Computing. We chose graphical processing units because of their versatility, low cost, accessibility, and the existence of linear algebra libraries dedicated to these platforms. We report on the reserves identified in this way, i.e., on speedups of optimization computations achievable by such an optimization algorithm hybridization. We tested our hybrid algorithm numerically on a clinical case.

Searching over the Pareto front for the most preferred decision requires providing multiple Pareto optimal solutions to an instance of the general multiobjective optimization problem. This process, especially for large-scale problems can be time consuming and even can go over the resource (time, memory required) budget. In that case, lower and upper bounds are necessary to judge if the solutions derived thus far are acceptable approximations of the Pareto optimal ones. To this aim we provide lower and upper bounds for the general multiobjective optimization problem. This work generalizes our similar development valid for a special case.

CS 5301 (EEGR 5301) Professional and Technical Communication (3 semester credit hours) This course utilizes an integrated approach to writing and speaking for the technical professions. The advanced writing components of the course focus on writing professional quality technical documents such as proposals, memos, abstracts, reports, letters, emails, etc. The advanced oral communication components of the course focus on planning, developing, and delivering dynamic, informative and persuasive presentations. Advanced skills in effective teamwork, leadership, listening, multimedia and computer generated visual aids are also emphasized. Graduate students will have a successful communication experience working in a functional team environment using a real time, online learning environment. (3-0) Y CS 5302 Topics in Computer Science (3 semester credit hours) May be repeated for credit as topics vary (6 semester credit hours maximum). Prerequisite: CS 5343. (3-0) Y CS 5303 Computer Science I (3 semester credit hours) Computer science problem solving. The structure and nature of algorithms and their corresponding computer program implementation. Programming in a high level block-structured language (e.g., PASCAL, Ada, C++, or JAVA). Elementary data structures: arrays, records, linked lists, trees, stacks and queues. Prerequisite: ENCS majors only. (3-0) R CS 5330 Computer Science II (3 semester credit hours) Basic concepts of computer organization: Numbering systems, two's complement notation, multi-level machine concepts, machine language, assembly programming and optimization, subroutine calls, addressing modes, code generation process, CPU datapath, pipelining, RISC, CISC, and performance calculation. Prerequisite or Corequisite: CS 5303. (3-0) R CS 5333 Discrete Structures (3 semester credit hours) Mathematical foundations of computer science. Logic, sets, relations, graphs and algebraic structures. Combinatorics and metrics for performance evaluation of algorithms. Prerequisite: ENCS majors only. (3-0) S CS 5336 Programming Projects in Java (3 semester credit hours) Overview of the objectoriented philosophy. Implementation of object-oriented designs using the Java programming environment. Emphasis on using the browser to access and extend the Java class library. Prerequisite: CS 5303 or equivalent experience. (3-0) R CS 5343 Algorithm Analysis and Data Structures (3 semester credit hours) Formal specifications and representation of lists, arrays, trees, graphs, multilinked structures, strings, and recursive pattern structures. Analysis of associated algorithms. Sorting and searching, file structures. Relational data models. Prerequisite: CS 5303. Prerequisite or Corequisite: CS 5333. (3-0) S CS 5348 Operating Systems Concepts (3 semester credit hours) Processes and threads. Concurrency issues including semaphores, monitors and deadlocks. Simple memory management. Virtual memory management. CPU scheduling algorithms. I/O management. File management. Introduction to distributed systems. Must have a working knowledge of C and Unix. Prerequisite: CS 5330. Prerequisite or Corequisite: CS 5343. (3-0) S CS 5349 Automata Theory (3 semester credit hours) Deterministic and nondeterministic finite automata; regular expressions, regular sets, context-free grammars, pushdown automata, context free languages. Selected topics from Turing Machines and undecidability. Prerequisite: CS 5333. (3-0) S CS 5375 Principles of UNIX (3 semester credit hours) Design and history of the UNIX operating system. Detailed study of process and file system data structures. Shell programming in UNIX. Use of process-forking functionality of UNIX to simplify complex problems. Interprocess communication and coordination. Device drivers and streams as interfaces to hardware

In one of our earlier works, we proposed to approximate Pareto fronts to multiobjective optimization problems by two-sided approximations, one from inside and another from outside of the feasible objective set, called, respectively, lower shell and upper shell. We worked there under the assumption that for a given problem an upper shell exists. As it is not always the case, in this paper we give some sufficient conditions for the existence of upper shells. We also investigate how to constructively search infeasible sets to derive upper shells. We approach this issue by means of problem relaxations. We formally show that under certain conditions some subsets of lower shells to relaxed multiobjective optimization problems are upper shells in the respective unrelaxed problems. Results are illustrated by a numerical example representing a small but real mechanical problem. Practical implications of the results are discussed.

We argue that rankings, as they are commonly used, can be, and perhaps are, misleading and potentially harmful. With little extra effort, however, one can gain much more insight into relations among the objects ranked and, in the consequence, gain a better understanding of the ranking. The fundamental notion used to compare and evaluate rankings in our analysis is that of Pareto optymality. General claims are illustrated with the ranking of Polish universities published by Perspektywy monthly in 2016. This note is based on results that are well known in the areas of multiobjective optimization and multiple-criteria decision analysis. The objective of the note is to point to the shortcomings and potential pitfalls behind the common use and understanding of rankings

When solving large-scale multiobjective optimization problems, solvers can get stuck with the memory or time limit. In such cases, one is left with no information how far is the best feasible solution, found before the optimization process has stopped, to the true Pareto optimal solution. In this work, we show how to provide such information when solving multiobjective multidimensional knapsack problems by a commercial mixed-integer linear solver. We illustrate the proposed approach on biobjective multidimensional knapsack problems derived from singleobjective multidimensional knapsack problems from the Beasley OR Library.

We present an integral approach to solving multiple criteria decision problems in sequences of intelligence, modeling, choice and review phases, often iterated, to identify the most preferred decision variant. The approach taken is human-centric, with the user taking the final decision being a sole and sovereign actor in the decision making process. To ensure generality, no assumption about the Decision Maker preferences or behavior is made. Likewise, no specific assumption about the underlying formal model is made. The intended goal of the approach is to lower the cognitive barrier related to unsupported use of multicriteria methodologies in day-to-day practice. We present successful application of this approach to a number of practical problems.

In this paper, we approach the Airport Gate Assignment Problem by Multi-objective Optimization as well as Evolutionary Multi-objective Optimization. We solve a bi-criteria formulation of this problem by the commercial mixed-integer programming solver CPLEX and a dedicated Evolutionary Multi-objective Optimization algorithm. To deal with multiple objectives, we apply a methodology that we developed earlier to capture decision-maker preferences in multi-objective environments. We present the results of numerical tests for these two approaches.