Conference Agenda

Solving stochastic multi-objective programming, especially when integrated with integer optimization, presents significant challenges, particularly in harnessing parallelism and effectively utilizing CPU-GPU systems to address this issue. Therefore, a critical need arises for a method that can leverage parallel computing capabilities and efficiently utilize CPU-GPU systems to generate all efficient solutions for this complex problem. In this context, we introduce a novel exact approach that integrates two techniques: the l-shaped stochastic two-stage method and the exact method. This combined methodology aims to generate all efficient solutions, particularly in the deterministic case. We assess the performance implications of parallel computing through a specialized numerical demonstration, illustrating the various stages of our computational results. This process involves randomly solving numerous examples to construct a database, ultimately serving as validation for both proposed methods, particularly the parallel one.

In portfolio optimization, balancing risk and return is crucial. Traditional models like the Markowitz often fail to capture the complex nature of uncertainties, leading to inadequate decision-making. Our research advances this by evolving the Markowitz model into a multi-objective framework that simultaneously optimizes multiple aspects such as return, volatility, solvency ratio, and transaction volume. This approach significantly improves asset allocation by addressing challenges from incomplete knowledge and fluctuating parameters in real-world scenarios.

We explore multi-objective robust optimization to bolster decision support and enhance risk management, focusing on uncertainties that impact only volatility parameters amid varying economic conditions. Our methodology, diverging from the typical single objective focus, involves adapting robust optimization to multi-objective scenarios. This innovation offers robust solutions across diverse economic scenarios without relying on probabilistic predictions, focusing instead on minimizing regret relative to a benchmark solution. Our findings indicate that this strategy effectively identifies portfolios that perform well across various scenarios, confirming the value of focusing on areas near the benchmark solution for portfolio managers. This approach not only supports practical application but also opens avenues for further research into optimizing portfolio strategies under uncertainty.

Future work will aim to quantify these strategies further and compare their effectiveness using real asset data, enhancing our understanding of robust multi-objective optimization under partial uncertainty.

In chemical plant design, the engineer’s aim is to determine the most preferable design parameters for a plant layout - such as reactor volume or distillation column diameter, and number of stages - by optimization of a process flowsheet model. The preferability of a plant design is defined by multiple objectives, for example product purities, energy consumption, CO2 emissions or investment and operational costs.

In many instances, external factors (e.g. feed stream conditions, prices or reaction model parameters) are uncertain. These factors influence the objectives at the design stage but their impact will be known when the plant is operated. This allows the operator to react and adjust operational settings such as pressures or reflux ratios during operation. Accounting for this specific type of uncertainty within the general multi-objective nature of the plant design problem results in a multi-objective adjustable robust optimization (MARO) problem.

We present two approaches to solve the MARO problem of chemical plant design. In the sequential approach, the uncertain problem is first treated as an objective-wise worst-case robust problem, and candidate designs with optimal worst-case outcomes are selected. Subsequentially, the adjustability of operational parameters is accounted for, and the (overly pessimistic) outcome prediction of the first phase is refined for the candidate designs. In the decision rule approach, we approximate the dependency of the optimal operational settings on the uncertain factors by affine linear mappings and solve the reformulated problem. We discuss advantages and disadvantages of both approaches and illustrate their usefulness in different planning situations.

The Entscheidungsnavi is an open-source decision support system based on multi-attribute utility theory, that offers various methods for dealing with uncertainties. To model decisions with uncertainties, decision-makers can use two categories: Forecast and Parameter Uncertainties. Forecast Uncertainty is modeled with (combined) influence factors using discrete, user-defined probability distributions or predefined ‘worst-median-best’ distributions. Parameter Uncertainty allows imprecision for utilities, objective weights, and probability distributions. To analyze these uncertainties, the Entscheidungsnavi offers several methods and tools, like a robustness check, based on (Monte Carlo) simulations and a sensitivity analysis. The objective weight analysis provides insights into the effects of different objective weight combinations. Indicator impacts, tornado diagrams, and risk profiles visualize the impact of uncertainties in a decision under risk. Risk profiles also enable a check for stochastic and simulation dominance. This contribution presents the complete range of methods for dealing with uncertainties in the Entscheidungsnavi using a hypothetical case study.