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We propose a mixed-integer linear model that solves the multiple heterogeneous knapsack problem, minimising the wasted space of the bins, taking into account their priority and considering the following constraints: non-overlapping, boundaries and positioning (both constrained and free), rotations (around the vertical axis), orthogonal displacement, weight limit, static stability, weight distribution in a pyramidal region and load bearing considering items' arbitrary centre of mass (CoM). In the experiments, the priority parameter is set to prioritise smaller bins, but the model is generic to cover other cases. We study the trade-off of adding more constraints to make the problem more realistic and the complexity of finding a solution. We introduce new metrics that facilitate the comparison of datasets used in experiments. These metrics allow the export of theoretical results in the industry. We also propose a constructive heuristic named weight first best fit to handle large-scale instances in a reasonable time.

Predicting the market’s behavior to profit from trading stocks is far from trivial. Such a task becomes even harder when investors do not have large amounts of money available, and thus cannot influence this complex system in any way. Machine learning paradigms have been already applied to financial forecasting, but usually with no restrictions on the size of the investor’s budget. In this paper, we analyze an evolutionary portfolio optimizer for the management of limited budgets, dissecting each part of the framework, discussing in detail the issues and the motivations that led to the final choices. Expected returns are modeled resorting to artificial neural networks trained on past market data, and the portfolio composition is chosen by approximating the solution to a multi-objective constrained problem. An investment simulator is eventually used to measure the portfolio performance. The proposed approach is tested on real-world data from New York’s, Milan’s and Paris’ stock exchanges, exploiting data from June 2011 to May 2014 to train the framework, and data from June 2014 to July 2015 to validate it. Experimental results demonstrate that the presented tool is able to obtain a more than satisfying profit for the considered time fram

In this paper we present the Group Seat Reservation Knapsack Problem with Profit on Seat. This is an extension of the the Offline Group Seat Reservation Knapsack Problem. In this extension we introduce a profit evaluation dependant on not only the space occupied, but also on the individual profit brought by each reserved seat. An application of the new features introduced in the proposed extension is to influence the distribution of passengers, such as assigning seats near the carriage centre for long journeys, and close to the door for short journeys. Such distribution helps to reduce the excess of dwelling time on platform. We introduce a new GRASP based algorithm that solves the original problem and the newly proposed one. In the experimental section we show that such algorithm can be useful to provide a good feasible solution very rapidly, a desirable condition in many real world systems. Another application could be to use the algorithm solution as a startup for a successive branch and bound procedure when optimality is desired. We also add a new class of problem with five test instances that represent some challenging real-world scenarios that have not been considered before. Finally, we evaluate both the existing model, the newly proposed model, and analyse the pros and cons of the proposed algorithm.

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