Traveling Salesman Problems (TSPs) have been a long-lasting interesting challenge to researchers in different areas. The difficulty of such problems scales up further when multiple objectives are considered concurrently. Plenty of work in evolutionary algorithms has been introduced to solve multi-objective TSPs with promising results, and the work in deep learning and reinforcement learning has been surging. This paper introduces a multi-objective deep graph pointer network-based reinforcement learning (MODGRL) algorithm for multi-objective TSPs. The MODGRL improves an earlier multi-objective deep reinforcement learning algorithm, called DRL-MOA, by utilizing a graph pointer network to learn the graphical structures of TSPs. Such improvements allow MODGRL to be trained on a small-scale TSP, but can find optimal solutions for large scale TSPs. NSGA-II, MOEA/D and SPEA2 are selected to compare with MODGRL and DRL-MOA. Hypervolume, spread and coverage over Pareto front (CPF) quality indicators were selected to assess the algorithms’ performance. In terms of the hypervolume indicator that represents the convergence and diversity of Pareto-frontiers, MODGRL outperformed all the competitors on the three well-known benchmark problems. Such findings proved that MODGRL, with the improved graph pointer network, indeed performed better, measured by the hypervolume indicator, than DRL-MOA and the three other evolutionary algorithms. MODGRL and DRL-MOA were comparable in the leading group, measured by the spread indicator. Although MODGRL performed better than DRL-MOA, both of them were just average regarding the evenness and diversity measured by the CPF indicator. Such findings remind that different performance indicators measure Pareto-frontiers from different perspectives. Choosing a well-accepted and suitable performance indicator to one’s experimental design is very critical, and may affect the conclusions. Three evolutionary algorithms were also experimented on with extra iterations, to validate whether extra iterations affected the performance. The results show that NSGA-II and SPEA2 were greatly improved measured by the Spread and CPF indicators. Such findings raise fairness concerns on algorithm comparisons using different fixed stopping criteria for different algorithms, which appeared in the DRL-MOA work and many others. Through these lessons, we concluded that MODGRL indeed performed better than DRL-MOA in terms of hypervolumne, and we also urge researchers on fair experimental designs and comparisons, in order to derive scientifically sound conclusions.

Short term memory that records the current population has been an inherent component of Evolutionary Algorithms (EAs). As hardware technologies advance currently, inexpensive memory with massive capacities could become a performance boost to EAs. This paper introduces a Long Term Memory Assistance (LTMA) that records the entire search history of an evolutionary process. With LTMA, individuals already visited (i.e., duplicate solutions) do not need to be re-evaluated, and thus, resources originally designated to fitness evaluations could be reallocated to continue search space exploration or exploitation. Three sets of experiments were conducted to prove the superiority of LTMA. In the first experiment, it was shown that LTMA recorded at least $50\%$ more duplicate individuals than a short term memory. In the second experiment, ABC and jDElscop were applied to the CEC-2015 benchmark functions. By avoiding fitness re-evaluation, LTMA improved execution time of the most time consuming problems $F03$ and $F05$ between 7% and 28% and 7% and 16%, respectively. In the third experiment, a hard real-world problem for determining soil models’ parameters, LTMA improved execution time between 26% and 69%. Finally, LTMA was implemented under a generalized and extendable open source system, called EARS. Any EA researcher could apply LTMA to a variety of optimization problems and evolutionary algorithms, either existing or new ones, in a uniform way.

Rehabilitation aids help people with temporal or permanent disabilities during the rehabilitation process. However, these solutions are usually expensive and, consequently, inaccessible outside of professional medical institutions. Rapid advances in software development, Internet of Things (IoT), robotics, and additive manufacturing open up a way to affordable rehabilitation solutions, even to the general population. Imagine a rehabilitation aid constructed from accessible software and hardware with local production. Many obstacles exist to using such technology, starting with the development of unified software for custom-made devices. In this paper, we address open issues in designing rehabilitation aids by proposing an extensive rehabilitation platform. To demonstrate our concept, we developed a unique platform, RehabHand. The main idea is to use domain-specific language and code generation techniques to enable loosely coupled software and hardware solutions. The main advantage of such separation is support for modular and a higher abstraction level by enabling therapists to write rehabilitation exercises in natural, domain-specific terminology and share them with patients. The same platform provides a hardware-independent part that facilitates the integration of new rehabilitation devices. Experience in implementing RehabHand with three different rehabilitation devices confirms that such rehabilitation technology can be developed, and shows that implementing a hardware-independent rehabilitation platform might not be as challenging as expected.

Reporting the empirical results of swarm and evolutionary computation algorithms is a challenging task with many possible difficulties. These difficulties stem from the stochastic nature of such algorithms, as well as their inability to guarantee an optimal solution in polynomial time. This research deals with measuring the performance of stochastic optimization algorithms, as well as the confidence intervals of the empirically obtained statistics. Traditionally, the arithmetic mean is used for measuring average performance, but we propose quantiles for measuring average, peak and bad-case performance, and give their interpretations in a relevant context for measuring the performance of the metaheuristics. In order to investigate the differences between arithmetic mean and quantiles, and to confirm possible benefits, we conducted experiments with 7 stochastic algorithms and 20 unconstrained continuous variable optimization problems. The experiments showed that median was a better measure of average performance than arithmetic mean, based on the observed solution quality. Out of 20 problem instances, a discrepancy between the arithmetic mean and median happened in 6 instances, out of which 5 were resolved in favor of median and 1 instance remained unresolved as a near tie. The arithmetic mean was completely inadequate for measuring average performance based on the observed number of function evaluations, while the 0.5 quantile (median) was suitable for that task. The quantiles also showed to be adequate for assessing peak performance and bad-case performance. In this paper, we also proposed a bootstrap method to calculate the confidence intervals of the probability of the empirically obtained quantiles. Considering the many advantages of using quantiles, including the ability to calculate probabilities of success in the case of multiple executions of the algorithm and the practically useful method of calculating confidence intervals, we recommend quantiles as the standard measure of peak, average and bad-case performance of stochastic optimization algorithms.