Unlike chemotherapy, the maximum tolerated dose (MTD) of molecularly targeted agents and immunotherapy may not pose significant clinical benefit over the lower doses. By simultaneously considering both toxicity and efficacy endpoints, phase I/II trials can identify a more clinically meaningful dose for subsequent phase II trials than traditional toxicity-based phase I trials in terms of risk-benefit tradeoff. To strengthen and simplify the current practice of phase I/II trials, we propose a utility-based toxicity probability interval (uTPI) design for finding the optimal biological dose, based on a numerical utility that provides a clinically meaningful, one-dimensional summary representation of the patient's bivariate toxicity and efficacy outcome. The uTPI design does not rely on any parametric specification of the dose-response relationship, and it directly models the dose desirability through a quasi binomial likelihood. Toxicity probability intervals are used to screen out overly toxic dose levels, and then the dose escalation/de-escalation decisions are made adaptively by comparing the posterior desirability distributions of the adjacent levels of the current dose. The uTPI design is flexible in accommodating various dose desirability formulations, while only requiring minimum design parameters. It has a clear decision structure such that a dose-assignment decision table can be calculated before the trial starts and can be used throughout the trial, which simplifies the practical implementation of the design. Extensive simulation studies demonstrate that the proposed uTPI design yields desirable as well as robust performance under various scenarios.